Conference Agenda

Phase field modeling has been widely applied to model the evolution of domain patterns in various phase transformation problems. Existing phase-field models for the evolution of domain structures in ferroelectrics are based on an Allen-Cahn-type evolution law. This evolution law successfully captures equilibrium domain structures. However, it fails to capture rate effects due to its assumption of a linear kinetic relation between the thermodynamic driving force acting on a domain wall and the domain wall velocity. To overcome this limitation, we propose a new phase field model for ferroelectrics (Guin and Kochmann, 2022), one that incorporates nonlinearities in the kinetics of domain walls and fully accounts for electro-mechanical coupling. As a multi-phase-field generalization of the model of Alber and Zhu (2013), it is based on the domain volume fraction of each variant as the primary phase field and incorporates the anisotropic dielectric, elastic, and piezoelectric properties of the different variants. This multi-phase field generalization further allows imposing different kinetic relations in different types of domain walls. This new phase field model is validated through a comparison with the target sharp-interface model embedding nonlinear kinetics. With the ability to easily modify these different material properties, we investigate multiphysical effects to the growth of the ferroelectric embryo, and show the open challenge (in common with all ferroelectric phase field models) of the magnitude of the interfacial energy of the regularized domain wall.

Ferroelectrics exhibit many interesting effects, both linear and nonlinear, which is why these materials are widely used in science and industry. Recently, the nonlinear effects have also been employed in the field of energy harvesting [1, 2, 3], while for a long time only linear effects were exploited. Moreover, nonlinear effects are irreversible and are accompanied by energy dissipation, which generally leads to a temperature rise of the material. For modeling the characteristic nonlinear effects of ferroelectric materials, there are various possibilities, in particular microphysical and, phenomenological models.

For describing mutually coupled dissipative processes in ferroelectrics, in particular ferroelectric domain switching and viscoelasticity, a hybrid micromechanical - rheological constitutive model is developed and embedded in the framework of a multiscale modeling approach. The mathematical theory is consistent against the background of rational thermodynamics and deals with two types of internal variables. The advanced modeling approach is applied to identify novel energy harvesting cycles exploiting dissipative effects, resulting in a major electric work output.

REFERENCES

[1] W. Kang, L. Chang and J. E. Huber, Nano Energy 93 (2022), p. 106862.

[2] L. Behlen, A. Warkentin and A. Ricoeur, Smart Mater. Struct. 30 035031 (2021).

[3] A. Warkentin, L. Behlen and A. Ricoeur, Smart Mater. Struct. 10.1088/1361-665X/acafba (2023).

Magneto-active elastomers (MAE) are one of many emerging functional materials. Research applications span mechanical, civil, and biomedical engineering as actuators, sensors, vibration absorbers and vibration isolators. MAE consist of a soft elastomeric matrix filled with small, relatively rigid magnetizable inclusions. Set in a magnetic field, the inclusions deform the microstructure and, at the macro-scale, either stiffen by up to three orders of magnitude or bend to large strains.

Most MAE models focus on magneto-mechanical constitutive relations. This contribution showcases other physical phenomena and their coupled interactions. These phenomena include thermo-mechanical coupling and viscous dissipation leading to heat generation within the material. The model is capable of capturing dynamic effects, particularly when MAE are used as vibration absorbers. Formulated for three-dimensional finite deformations, this model handles incompressible material behavior through a Q1P0 finite element framework.

This study explores the relationship between magnetic fields and deformation in Ferromagnetic Shape Memory Alloys (FSMA), which are materials capable of sensing and actuation. These alloys can exhibit high strains of up to 6% when subjected to a magnetic field. To achieve this goal, a finite deformation formulation approach is proposed based on the multiplicative decomposition of the deformation gradient. In addition, a magneto-thermo-mechanical constitutive model for FSMA is discussed, which is based on a specific Helmholtz free energy function. The evolution equations of the internal magnetic and mechanical state variables are determined using a transformation function, and the model parameters are calibrated under different loading conditions. Finally, the model predictions for FSMA are compared against experimental results.

The renewable energy supply, the independence of fossil resources, as well as the change in mobility act as a driving force on technological innovation. To meet these challenges of our time, new and particularly powerful highperformance magnets are necessary [1], relying on new earth abundant materials and resource efficient processes. It has been shown that composite materials consisting of ferromagnetic grains separated by paramagnetic interphases can contribute to significant improvements in coercivity, when these interphases decouple the magnetic exchange between the individual grains, compare [2]. Novel processing routes based on severe plastic deformations (SPD) or additive manufacturing (AM) can be an option to tailor such magnetic composites. Here, the micromagnetic theory can be applied to numerically predict the magnetization distributions on fine scales. Due to their flexibility, finite elements are well suited to discretize and analyze strongly heterogeneous microstructures [3]. The evolution of the magnetization vectors is described by the Landau-Lifshitz-Gilbert equation, which requires the numerically challenging preservation of the Euclidean norm of the magnetization vectors, see [4,5]. With the aim to correctly reproduce the behavior of magnetic materials, competing energy contributions are considered within the energy functional, which are also responsible for the formation of magnetic domains. Also, grain boundaries, defect layers and misoriented grains can have a huge impact on the macroscopic hysteresis behavior of magnetic materials. Especially magnets formed by SPD are exposed to the potential stress-induced defects that might outweigh their

production benefits. Hence, micromagnetics analyses are performed to estimate the risks and challenges of these novelties.

[1] O. Gutfleisch, et al.: Magnetic Materials and Devices for the 21st Century: Stronger, Lighter, and More Energy Efficient. Advanced Materials, 23, 821–842, (2011).

[2] M. Soderznick, et al.: Magnetization reversal of exchange-coupled and exchange-decoupled Nd-Fe-B magnets observed by magneto-optical Kerr effect microscopy. Acta Materialia, 135, 68–76, (2017).

[3] A. Vansteenkiste, et al.: The design and verification of MuMax3. AIP Advances, 4, 107133, (2014).

[4] A. Prohl: Computational Micromagnetism. Springer, (2001).

[5] M. Reichel, B.-X. Xu and J. Schröder: A comparative study of finite element schemes for micromagnetic mechanically coupled simulation. Journal of Applied Physics, 132, 183903, (2022).

We present an efficient, robust, objective, singularity-free, and path independent formulation for director fields based on optimization on manifolds. This approach allows for accurate and efficient computations of director fields that arise in geometrically non-linear structural models such as the Reissner-Mindlin shell model, in material models of Cosserat-type and in micromagnetic simulations. In this contribution, we investigate the influence of interpolation on manifolds on locking as well as the application of element technologies, such as enhanced assumed strains and the discontinuous Galerkin method.

The numerical methods are implemented into the open source code Ikarus (https://ikarus-project.github.io/), which enables rapid algorithm prototyping, even for optimization on manifolds, thus highlighting the user-friendly interface of this software.

The pertinent constraint for director fields requires to retain unit length of the director during deformation, which can be satisfied by interpreting the constraint as a restriction on the design space. By transforming the problem from “constrained optimization on an unconstrained space” to “unconstrained optimization on a constrained space”, the structure of the problem is retained, and the design space is reduced. The transformation to an unconstrained optimization problem on a manifold requires generalization of concepts, such as the incremental update of design variables, to account for living on a manifold instead of living in a linear vector space.

For the interpolation on nonlinear manifolds, we utilize the ideas on geometric finite elements presented by Sander (2012) and Grohs (2011). The combination of element technologies such as enhanced assumed strains with the optimization on manifolds approach promises an efficient and accurate solution method for director fields. Numerical examples are presented in the context of micromagnetics, Reissner-Mindlin shells and three-dimensional beams to demonstrate the efficiency and accuracy of the approach.

Sander, O., Geodesic finite elements on simplicial grids. Int. J. Num. Meth. Engng. (2012) 92:999–1025. https://doi.org/10.1002/nme.4366

Grohs, P., Finite elements of arbitrary order and quasiinterpolation for data in Riemannian manifolds. Seminar for Applied Mathematics, ETH Zürich, (2011). https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-56.pdf

Müller, A., Bischoff, M. A Consistent Finite Element Formulation of the Geometrically Non-linear Reissner-Mindlin Shell Model. Arch Computat Methods Eng (2022). https://doi.org/10.1007/s11831-021-09702-7

Recently, the concept of hierarchic structural element formulations has been developed in the group of the authors with a focus on shear deformable Reissner-Mindlin shell formulations [1], [2]. Via reparametrization of the kinematic variables, these formulations possess distinct degrees of freedom for transverse shear. One effect of this hierarchic parametrization is that the resulting elements are intrinsically free from transverse shear locking.

However, the hierarchic structure can also be exploited for an intrinsically selective mass scaling, i.e., a scaling down of the high shear frequencies, which limit the critical time step although being of minor importance for the structural response, while keeping the low bending dominated branch of the frequency spectrum unaffected. This stands in contrast to conventional mass scaling for shear deformable elements, where total rotational inertia is scaled and, therefore, also bending frequencies are manipulated.

In linear kinematics, the hierarchic parametrization leads to an additive structure throughout the kinematic equations, i.e., a clear separation between a Kirchhoff-Love type bending part and an additional shear part. For nonlinear shell kinematics, the assumption of only small shear rotations was made to preserve this additive structure [3].

In this contribution, we present recent investigations on intrinsically selective mass scaling with hierarchic isogeometric structural element formulations and discuss the effects of transverse shear parametrization in transient problems. Additionally, we critically discuss the necessity of a fully nonlinear treatment of shear deformation parts as described in [4].

References:

[1] R. Echter, B. Oesterle and M. Bischoff, A hierarchic family of isogeometric shell finite elements. Comput. Methods Appl. Mech. Engrg., Vol. 254. pp. 170-180, 2013.

[2] B. Oesterle, E. Ramm and M. Bischoff, A shear deformable, rotation-free isogeometric shell formulation. Comput. Methods Appl. Mech. Engrg., Vol. 307, pp. 235-255, 2016.

[3] B. Oesterle, R. Sachse and E. Ramm and M. Bischoff, Hierarchic isogeometric large rotation shell elements including linearized transverse shear parametrization. Comput. Methods Appl. Mech. Engrg., Vol. 321. pp. 383-405, 2017.

[4] Q. Long, P. B. Bornemann and F. Cirak, Shear-flexible subdivision shells. Int. J. Numer. Meth. Engng., Vol. 90, pp. 1549-1577, 2012.

The critical time step in explicit transient analyses depends on the highest frequency of the discretized system. In case of thin-walled structures discretized by solid or solid-shell elements, the critical time step, which is a key factor for computational efficiency, is limited by the highest frequencies related to thickness stretch of the elements [1].

Selective mass scaling (SMS) concepts aim at scaling down the highest frequencies, while keeping the low frequencies as unaffected as possible. Most established SMS concepts are designed for discretizations composed of solid or solid-shell elements, as can be seen for instance in [1,2]. They are designed such that at least translational inertia is preserved. Accuracy of these SMS concepts can be increased by extending the construction of scaled mass matrices in such a way that, additionally, rotational inertia is preserved. But this increases computational costs in case non-linear analyses including large rotations, since scaled mass matrices are anisotropic and need to be reassembled during simulation. These additional costs do not pay off in most applications.

In this contribution, we present recent investigations on SMS techniques, which are based on a concept from finite element technology, that is the Discrete Strain Gap (DSG) method [3]. We show that these novel SMS concepts naturally preserve both translational and rotational inertia and possess high accuracy. In addition, having non-linear problem classes including large rotations in mind, we show how to develop efficient isotropic DSGSMS concepts which avoid the need for reassembly of scaled mass matrices.

REFERENCES

[1] G. Cocchetti, M. Pagani und U. Perego. Selective mass scaling and critical time-step estimate for explicit dynamics analyses with solid-shell elements. Computers & Structures, Vol. 127, pp. 39–52, 2013.

[2] L. Olovsson, K. Simonsson und M. Unosson. Selective mass scaling for explicit finite element analyses. Int. J. Numer. Meth. Engng., Vol. 63(10), pp. 1436–1445. 2005.

[3] K.-U. Bletzinger, M. Bischoff und E. Ramm, A unified approach for shear-locking-free triangular and rectangular shell finite elements. Computers & Structures, Vol. 75(3), pp. 321-334. 2000.

For the description of the load-bearing behavior of structures, the degree of statical indeterminacy is a fundamental property that formally describes the number of missing equilibrium equations necessary to calculate the internal forces. The formal definition of the degree of statical indeterminacy as one single number neglects the distribution of statical indeterminacy within the structure. This neglect can lead to situations where a structure, which is kinematic in one direction and statically indeterminate in another direction is denoted as statically determinate. Thus, mechanisms, which are relevant in the field of deployable structures, and possibilities for prestressing are overlooked. The redundancy matrix, first described by Bahndorf (1991), quantifies the distribution of statical indeterminacy in the structure.

The redundancy matrix is an idempotent matrix, meaning that its eigenvalues are either zero or one. Associated with the eigenvalue of one, which occurs exactly in the quantity that matches the degree of statical indeterminacy, the respective eigenvectors span a space of incompatible elongations (von Scheven et al. (2021)). This space matches the description of self-stress states, described by Pellegrino and Calladine (1986). The eigenvectors associated with the zero eigenvalues span a space that includes states where prescribed elongations match the total elongations. In this case, displacements are present without imposing normal forces, even in statically indeterminate structures. The information about states of stress-free displacements and displacement-free stresses can e.g. be used in the decision-making process of actuator placement in adaptive civil structures (Wagner et al. (2018)) and it might also be used in the adaption process of deployable structures (Veuve et al. (2017)) or for maintenance issues like monitoring stresses in certain parts of a structure.

This contribution presents examples of using the redundancy matrix in the design and assessment of civil engineering structures, especially of deployable structures.

References:

Bahndorf, J. (1991). Zur Systematisierung der Seilnetzberechnung und zur Optimierung von Seilnetzen. Ph. D. thesis, University of Stuttgart, Stuttgart.

Pellegrino, S. and C. Calladine (1986). Matrix analysis of statically and kinematically indeterminate frameworks. Int. Journal of Solids and Structures 22(4), 409–428.

Veuve, N., A. C. Sychterz, and I. F. Smith (2017, December). Adaptive control of a deployable tensegrity structure. Engineering Structures 152, 14–23.

von Scheven, M., E. Ramm, and M. Bischoff (2021). Quantification of the redundancy distribution in truss and beam structures. Int. Journal of Solids and Structures 213, 41–49.

Wagner, J. L., J. Gade, M. Heidingsfeld, F. Geiger, M. von Scheven, M. Böhm, M. Bischoff, and O. Sawodny (2018). On steady-state disturbance compensability for actuator placement in adaptive structures. at - Automatisierungstechnik 66(8), 591–603.

Nanoporous metals, built out of complex ligament networks, can be produced with an additional level of hierarchy [S. Shi et al., Science 371, 1026-1033, 2021]. The resulting complexity of the structure makes modeling of the mechanical behaviour computationally highly expensive and time consuming. In addition, multiaxial stresses occur in the higher hierarchy ligaments. Therefore, knowledge of the multiaxial material behaviour, including the 6D yield surface, is required. For finite element (FE) modeling, we separate the hierarchical nanoporous structure into the upper and lower level of hierarchy. This allows independent adjustment of structural parameters on both hierarchy levels and therefore an efficient analysis of structure-property-relationships. Furthermore, a promising approach to significantly reduce computational cost is to use surrogate models and FE-beam models to predict the mechanical behaviour of the lower level of hierarchy.

As a first step towards such a model, we studied the elastic behaviour and yield surfaces of idealized diamond and Kelvin beam models, representation of the lower level of hierarchy, using FE simulations. The yield surfaces exhibit pronounced anisotropy, which could not be described properly by models like the Deshpande-Fleck model for isotropic solid foams. For this reason, we used data-driven and hybrid artificial neural networks, as well as data-driven support vector machines and compared them regarding their potential for the prediction of these yield surfaces. All considered methods turned out to be well suited and resulted in relative errors < 4.5. Of the considered methods, support vector machines exhibit the highest generalization and accuracy in 6D stress space and outside the range of the used training data.

Implementation of the trained SVC into Abaqus [A. Hartmaier, Materials 13, 1060, 2022] results in a promising agreement with the mechanical material response of the original FE beam model, provided that a non-associated flow rule is used. Furthermore, the evolution of the yield surface for higher plastic strains during radial loading were included and as such allow an implementation of the hardening behaviour into the UMAT.

In recent years, the application of lattice structures in additive manufacturing (AM) has gained a lot of attention due to their unique properties, such as high surface-to-volume ratio and self-supporting capabilities. They enable the production of complex parts that are difficult or even impossible to manufacture using conventional methods such as casting or machining. However, despite the advantages of 3D printing over conventional manufacturing technologies, its potential is limited by various phenomena such as warpage due to residual stresses and strains or porosity, leading to a lack of knowledge about the mechanical properties of lattice structures and hindering their commercial application.

To address this shortcoming, this study employs Finite Element Analysis (FEA) to examine the influence of residual stress and porosity defects on the mechanical properties of lattice structures, including Young's modulus, yield strength, and Specific Energy Absorption (SEA). The simulation results are validated through experimental data on the compressive behavior of lattice structures produced through Laser Powder Bed Fusion (L-PBF) with varying parameters. The sequentially coupled thermomechanical finite element model utilized in the simulation evaluates the thermal histories and residual stress evolution throughout the entire AM process. The findings of this study provide valuable insights into the mechanical properties of lattice structures, paving the way for their practical applications in diverse fields.

Apart from experimentation, computational models are helpful to aid understanding and subsequently predict the damage processes of concrete under fire, considering physical effects such as chemical dehydration or aggregate-matrix mismatch. These temperature-driven multi-physical deterioration processes are mainly influenced by the macroscopic effective thermal conduction because it predominantly governs the macroscopic temperature distribution. To quantify all degradation factors according to the macroscopic effective thermal conductivity separately, a multiscale model for concrete is proposed.

Four scales of observation characterize the concrete, namely hydrates, cement paste, mortar, and concrete. Based on Eshelby-type homogenization techniques, such as Mori-Tanka and Self-Consistent schemes, the effective thermal conductivity of different blended concretes is calculated at elevated temperatures, considering thermally induced chemical porosity increase of hydrates, initial microcrack density, aggregate degradation, and aggregate-matrix bonding via interfacial transition zones (ITZ).

A stoichiometric model based on an Arrhenius equation is used to predict the volume fraction of chemical dehydration products and porosity at the level of hydrates. The porosity increase and initial crack density lowers the thermal conductivity on the cement paste level, which is calculated using the Mori-Tanaka homogenization framework by considering randomly distributed spherical pores and three orthogonal oriented penny-shaped inclusions, respectively embedded in the matrix material. The effective thermal conductivity of mortar and concrete is determined within the same framework using an analytical expression based on the Kapitza resistance, which characterizes the ITZ morphology.

Concretes with different water-to-cement ratios, aggregate types, and cement paste conductivities are analyzed after the validation process in a sensitivity study comparing the influence on the effective thermal conductivities of concrete at elevated temperatures. Furthermore, the influence of the ITZ morphology and initial crack density is studied in detail. Based on the discussed analyses, it is demonstrated that the model predicts the thermal conductivity deterioration of different concretes or cement compositions from 20°C to 850°C with adequate accuracy.

Current research aims at the targeted introduction of residual stresses into components during their manufacturing process instead of minimizing them, for example, by subsequent heat treatments. Hot bulk forming processes offer a good opportunity to modify residual stresses in a specific way, since the interactions of thermal, mechanical and metallurgical kind can be exploited. In general, such a hot bulk forming process of a steel component can be divided into three steps: First, the component is heated to over 1000°C, which leads to a full austenitization of the material and an assumed to be stress-free initial configuration. Subsequently, forming takes place at this high temperature before the component is cooled down to room temperature. This third step results in a diffusion controlled or diffusionless phase transformation on the microscale based on the cooling rate, see [1].

In this contribution, the focus is on the last process step, i.e., cooling. Different cooling media lead to different phase transformations, which in turn lead to different residual stress distributions in the component. Motivated by the definition of residual stresses, which are characterized by the scale they act on, multi-scale finite element simulations of this cooling process are performed. The comparison of two- and three-dimensional boundary value problems shows the importance of the third dimension to represent the temperature development in the component and to predict residual stress distributions well. For this reason, a three-dimensional FE^2 calculation is presented, see [2], in which the microscale is determined by a three-dimensional representative volume element. The resulting residual stresses on macro- and microscale are evaluated and discussed.

[1] B.-A. Behrens, J. Schröder, D. Brands, K. Brunotte, H. Wester, L. Scheunemann, S. Uebing, C. Kock. Numerische Prozessauslegung zur gezielten Eigenspannungseinstellung in warmmassivumgeformten Bauteilen unter Berücksichtigung von Makro- und Mikroskala, Forschung im Ingenieurwesen (Engineering Research), 10.1007/s10010-021-00482-x, 2021.

[2] J. Schröder. A numerical two-scale homogenization scheme: the FE2-method. In J. Schröder and K. Hackl (Eds.), Plasticity and Beyond - Microstructures, Crystal-Plasticity and Phase Transitions, Volume 550 of CISM Courses and Lectures, 1–64. Springer, (2014).

A recent thrust in structural alloys research is the development of advanced Austenitic steels strengthened by nano-scale precipitates. Of the candidate precipitate phases, nanoscale dispersions of the ordered BCC (B2) NiAl phase have been demonstrated to provide significant increases in yield strength, while allowing reasonable ductility despite the intermetallic nature of this phase. The chemical complexity of the alloy involving small sizes of the particles on the order of few nm severely complicates the physically based prediction of macroscale mechanical properties induced by the characteristics of the particles and their ensembles.

Therefore, we use an integrated computational materials engineering (ICME) approach towards materials design with the aim of predicting mechanical properties such as yield strength based on an input material microstructure. Given the small size and high density of precipitates in the current alloy, we develop a coarse-grained approach for predicting a representative critical resolved shear stress (CRSS) inside local volume elements following the percolation idea for flow-stress from Kocks and Mecking [1]. Using this approach, we model realistic nano-precipitate size distributions in large scale Discrete Dislocation Dynamics (DDD) simulations with the aim of predicting macroscale mechanical properties.

This work seeks to fill the gap in modeling plastic deformation phenomena in stainless steels incorporating chemical heterogeneities on the nanoscale and resulting mechanical properties. Informed by atomistic simulations (DFT/MD), discrete microstructural data extracted from atom probe tomography, and meso-scale modeling (DDD) we present a unique coarse-graining approach in predicting material yield strength for materials with nanoprecipitates.

[1] U.F. Kocks, H. Mecking, Progress in Materials Science 48 (2003) 171–273

This study presents a new interpretation of the turbulence-interface interactions during the interfacial fragmentation process based on the concept of enstrophy transport. We carried out fully-resolved volume of fluid simulations of the decaying homogeneous isotropic turbulence in the presence of interfacial structures and analyzed the spectral fluxes of enstrophy production/destruction due to different vorticity transport mechanisms. We highlight the scale-dependent nature of the surface tension mechanism in competition with the vortex stretching mechanism that eventually features two characteristic length scales: (i) the length scale where the spectral rate of surface tension changes sign from negative to positive and distinguishes between enstrophy-reducing fragmentation process and enstrophy-releasing coalescence events across the scales. (ii) The length scale where the rate of enstrophy production by the surface tension balances the disruptive mechanism of vortex stretching. This corresponds to a similar length scale where the energy cascade of two-phase turbulence starts to pile up energy at small scales compared to its single-phase similitude. We further connect the latter to the interfacial statistics and reveal that at this length scale, the size distribution of droplets distinctly changes to a sharper slope. The analysis further discloses that decreasing the surface tension coefficient or viscosity as well as increasing the density of the dispersed phase enhances the vortex stretching effect and dilates the spectral range at which the surface tension contribution is negative toward the smaller scales, and thus facilitates the fragmentation. Whereas the higher surface tension coefficient, higher viscosity, or lower density ratio expands the spectral range associated with a positive contribution of surface tension toward the larger scales and suppresses the fragmentation events. This analysis offers a new interpretation of the Hinze scale in turbulence that is essential for the DNS and LES of two-phase flows.

The flow generated by the breaking of free-surface waves in a periodic domain is simulated numerically by means of a gas-liquid multiphase Navier-Stokes solver. The solver relies on the Volume-of-Fluid (VOF) approach, and interface tracking is carried out by using a novel algebraic scheme based on a tailored TVD limiter (Pirozzoli et al., 2019). The solver is proved to be characterized by low numerical dissipation, thanks to the use of the MAC scheme, which guarantees discrete preservation of total kinetic energy in the case of a single

phase. The low artificial dissipation and the potentiality of the algebraic VOF used is analyzed and highlighted through the simulation of the benchmark proposed by Estivalezes et al., 2022, where the ability of algebraic VOF to work for both miscible and immiscible fluids is demonstrated, allowing lower dissipated energy. After, both two- and three-dimensional simulations of wave breaking have been carried out, and the analysis is presented in terms of energy dissipation, air entrainment, bubble fragmentation, statistics and distribution. Particular attention is paid to the analysis of the mechanisms of viscous dissipation. For this purpose, coherent vortical structures (Horiuti and Takagi, 2005), are identified and the different behaviour of vortex sheets and vortex tubes are highlighted, at different Re. The correlation between vortical structures and energy dissipation demonstrates clearly their close link both in the mixing zone and in the pure water domain, where the coherent structures propagate as a consequence of the downward transport. Notably, it is found that the dissipation is primarily connected with vortex sheets, whereas vortex tubes are mainly related to flow intermittency.

The tendency of initially distant droplets in gas flows to convene and form clusters - known as droplet grouping - is an important phenomenon which affects evaporation rates and combustion dynamics, for example. Despite its relevance to technical applications, this grouping behavior and its governing factors are not yet fully understood, in particular in turbulent, compressible flows. Therefore, related work often focuses on a laminar, monodisperse droplet stream, which consitutes the most fundamental configuration subject to grouping and has been studied analytically, numerically as well as experimentaly.

While those investigations consider incompressible gas flows, this talk examines the grouping behavior in the compressible regime through direct numerical simulation (DNS), using a high-order level-set ghost fluid framework. We address arising challenges such as the mass loss inherent to the level-set method and propose a simple approach to track the individual droplets through the computational domain. In order to gain insights into the grouping mechanics, the impact of the initial droplet alignment, the Reynolds number and other parameters is studied in detail. The results are also compared with reference data from experiments and incompressible DNS to unveil compressibility effects in droplet grouping.

Most industrial processes involve multiphase turbulent flows. Therefore, understanding the underlying physics is of primary importance for reducing pollutant emissions and also for improving the safety protocols in industry processes. In this regard, numerical simulations provide a valuable tool due to their lower cost compared to experiments. Furthermore, simulations allow us to overcome current instrumentation limits. In this context, the phase-field method is coming to the fore for its ease of implementation and good scalability. However, its most well-known implementations, based on the conservative Cahn-Hilliard equation, have limitations on the density and viscosity ratios preventing us from studying realistic cases. Recently, novel approaches proposed a conservative Allen-Cahn equation which guarantees the solution boundedness. We show the results of a 2D rising bubble in a quiescent fluid at Reτ = 10 where the motion is only due to the density ratio between the carrier and dispersed phase. In particular, two different density ratios are analysed: ρr = 0.1−0.01. We characterize the shrinkage phenomenon by comparing the instantaneous profiles of the phase field with the theoretical profiles, then we quantify the mass loss in each case.

We investigate the heat transfer process in a multiphase turbulent system composed by a swarm of large and deformable drops and a continuous carrier phase. For a fixed shear Reynolds number, 𝑅𝑒𝜏 = 300, a constant drops volume fraction, Φ ≃ 5.4%, and a fixed Weber number, 𝑊𝑒 = 3.0, we perform a campaign of direct numerical simulations (DNS) of turbulence coupled with a phase-field method and the energy equation; the Navier-Stokes equations are used to describe the flow field, while the phase-field method and the energy equation are used to describe the dispersed phase topology and the temperature field, respectively. Considering several Prandtl numbers, 𝑃𝑟 = 1, 2, 4 and 8, we study the heat transfer process from warm drops to a colder turbulent flow. Using detailed statistics, we first characterize the time evolution of the temperature field in both the dispersed and carrier phase. Then, we develop an analytic model able to accurately reproduce the behaviour of the dispersed and continuous phase temperature. We find that an increase of the Prandtl number, obtained via a decrease of the thermal diffusivity, leads to a slower heat transfer between the dispersed and carrier phase. Finally, we correlate the drop diameters and their average temperatures.

Isogeometric Analysis was proposed more than ten years ago by Tom Hughes et al. to bridge the gap between computer-aided design and the finite element method. The original method uses Non-Uniform Rational B-Splines (NURBS) for the description of geometry and solution in the context of mechanics. Later, Buffa and Vazquez showed how B-Splines can form a De Rham sequence and thus made the methods interesting for multiphysics simulations including electromagnetism. More recently, mortaring and boundary elements methods have been developed, such that there is a large zoo of isogeometric methods available. This presentation will discuss those methods with the aim to optimize electric machines in the context of e-mobility.

In the past two decades, the development of cutting-edge soft-computing technologies and their application to engineering problems has demonstrated huge potential to simulate complex non-linear problems. Machine learning and computer vision can play a significant role in supporting decision-making for infrastructure design, construction, and operation in several ways. They are often use for automated design and real-time optimization, virtual control of the construction process, to support real-time monitoring to make informed decisions regarding asset maintenance, repair, or replacement, estimation of the environmental impacts and optimisation of resources or processes to promote sustainability, and so on.

However, the development of robust prediction tools based on Machine Learning (ML) techniques requires the availability of complete, consistent, accurate, and large datasets. The application of ML in structural engineering has been limited because, although real-size experiments provide complete and accurate data, they are time-consuming and expensive. If we look at large infrastructure projects, the available data is often incomplete and associated with uncertainties or is difficult to interpret. Over the past decades, a vast amount of data has been collected about the condition of our structures and stored in asset management systems in reports, however, this data was collected in an unsystematic manner and often presented in a highly subjective way. The average data scientist spends more than 60% of their time on collecting, organizing, and cleaning data instead of the actual analysis. This is why there is an increasing trend of producing synthetic data. While synthetic data offers benefits compared to real-world data (e.g., increased data quality, scalability and interoperability), it is limited mostly due to bias, lack of realism and accuracy, and the inability to represent the response of complex systems.

In this talk, I will discuss the balance of real-word and synthetic data and how to best leverage the strengths of both to maximise the potential of ML to support decision making for design, construction and maintenance of structures and infrastructure. I will reflect on how ML algorithms and their application in structural engineering have evolved over the past decade, their potential and limitations, and the way forward. Finally, I will present several examples of how ML can be used to optimise structural design [1,2], to virtually control the construction process and minimise the impact on the existing environment [3], and to support visual inspection and maintenance of structures, providing a high level of consistency and automation [4].

References

[1] Cabrera, M., Ninic, J. and Tizani, W., 2023.. Eng with Comp, pp.1-19.

[2] Ninić, J., Gamra, A., Ghiassi, B., 2023. Underground Sp.

[3] Ninić, J., et al., 2017. Tun and Underground SpTech, 63, pp.12-28.

[4] Bush, J. et al., 2021. EG-ICE, Berlin, Germany (pp. 421-431).

The long-standing challenge of simultaneously satisfying all physical requirements for hyperelastic constitutive models, which have been widely debated over the last few decades, could be regarded as "the main open problem of the theory of material behavior"[3].

This is particularly true for neural network (NN)-based constitutive modeling of hyperelastic materials, especially for the compressible case.

Therefore, a hyperelastic constitutive model based on physics-augmented neural networks (PANNs) is presented which fulfills all common physical requirements by construction, and in particular, is applicable for compressible material behavior.

This model combines established hyperelasticity theory with the latest machine learning advancements, using an input-convex neural network (ICNN) to express the hyperelastic potential.

The presented model satisfies common physical requirements, including compatibility with the balance of angular momentum, objectivity, material symmetry, polyconvexity, and thermodynamic consistency [1,2].

To ensure that the model produces physically sensible results, analytical growth terms and normalization terms are used. These terms, which have been developed for both isotropic and transversely isotropic materials, guarantee that the undeformed state is exactly stress-free and has zero energy [1].

The non-negativity of the hyperelastic potential is numerically verified by sampling the space of admissible deformations states.

Finally, the applicability of the model is demonstrated through various examples, such as calibrating the model on data generated with analytical potentials and by applying it to finite element (FE) simulations.

Its extrapolation capability is compared to models with reduced physical background, showing excellent and physically meaningful predictions with the proposed PANN.

[1] Linden, L., Klein, D. K., Kalina, K. A., Brummund, J., Weeger, O. and Kästner, M., Neural networks meet hyperelasticity: A guide to enforcing physics, (submitted 2023).

[2] Kalina, K. A., Linden, L., Brummund, J. and Kästner, M., FEANN - An efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining, Comput. Mech. (2023).

[3] Truesdell, C. and Noll, W., The Non-Linear Field Theories of Mechanics. 3rd ed. Springer Berlin Heidelberg, 2004.

The prevailing paradigm to model the behavior of rubber-like materials is hyperelasticity. However, phenomenological constitutive modeling is prone to uncertainty and results in loss of information as data coming from experiments are not used directly in calculations. Aside, selecting an appropriate strain energy function for the problem under consideration is left to the engineer and is often based on experience.

Data-driven approaches are a promising alternative to constitutive modeling. We present a new data-adaptive approach to model hyperelastic rubber-like materials at finite strains. Our proposed modeling procedure combines the advantages of phenomenological hyperelasticity with the data-driven paradigm of directly including experimental data in calculations. Import constraints, such as thermodynamic consistency, material objectivity and frame indifference and material symmetry are satisfied a priori. In essence, we suggest formulating a finite-element-like approximation of the strain energy function as a sum of basis functions multiplied by parameters. The basis functions are expanded over the space of invariants which is, in the most generic form, formed by the principal invariants of the right Cauchy-Green tensor. Support points are distributed in the space of invariants, which are the points at which the parameters are defined. In other words, the parameters are the values of the discrete strain energy function at the support points. We consider linear Lagrangian polynomials as basis functions which boils down to (bi)linear interpolation of the parameters. The parameters are determined based on measured full-field displacements, e.g. obtained from Digital-Image-Correlation, and reaction forces by solving a non-linear optimization problem. Within this optimization problem, the 2-norm of the residual vector, which is the difference between measured and computed displacements and reaction forces, is minimized by altering the parameters. The proposed discrete approximation to the strain energy function is flexible enough to discover any admissible form of strain energy function and the fact that our approach does not rely on measured stresses is an advantage over many data-driven approaches presented to date.

We verify our approach and show that computation times are similar compared to those of phenomenological models. By numerical examples, we illustrate that only a moderate number of parameters is required to approximate well-known smooth strain energy functions sufficiently well and demonstrate the ability of our approach to re-identify an extended number of parameters. We also show the robustness of our approach against noisy experimental data.

Finite linear viscoelastic (FLV) or quasi-linear viscoelastic (QLV) models are commonly used to model the constitutive behavior of polymeric materials. However, these models are limited in their ability to accurately represent the nonlinear viscoelastic behavior of materials, particularly in capturing their strain-dependent viscous behavior. To address this issue, we have developed viscoelastic Constitutive Artificial Neural Networks (vCANNs), a novel physics-informed machine learning framework. vCANNs rely on the concept of generalized Maxwell models with nonlinear strain (rate)-dependent properties represented by neural networks. With their flexibility, vCANNs can automatically identify accurate and sparse constitutive models for a wide range of materials. To test the effectiveness of vCANNs, we trained them using stress-strain data from various synthetic and biological materials under different loading conditions, e.g., relaxation tests, cyclic tension-compression tests, and blast loads. The results show that vCANNs can learn to accurately and efficiently represent the behavior of these materials without human guidance.

Ensuring the safe and reliable operation of critical load-bearing components requires maintaining their mechanical integrity. Constitutive material models play a crucial role in analyzing mechanical integrity, and their accuracy is essential for assessing the structural integrity of load-bearing components. Notably, mechanical integrity assessments of high temperature components require constitutive models representing the highly nonlinear deformation response of alloys under various loading scenarios and across a wide temperature range. The Chaboche viscoplastic model is among the most well-known constitutive models for representing the isotropic-kinematic hardening behavior of materials. This model employs a set of differential equations to define the viscoplastic strain rate tensor as a function of the stress tensor and several scalar and tensorial internal variables. Calibrating this model for different temperature and loading conditions however requires using experimental data from various mechanical tests and determining a large number of model parameters, which is typically achieved by performing a computationally expensive inverse analysis. To address this computational challenge, we propose a new method that leverages scientific machine learning to accelerate solving the inverse problem. Specifically, we use the Physics Informed Neural Networks (PINNs) framework to incorporate the Chaboche model formulation into neural networks. In this contribution, we illustrate the framework in application to Hastelloy X, by calibrating and determining >30 model parameters based on observations from various cyclic tests at different strain rates in the temperature range of 22-1000°C.

Many materials exhibit history-dependency in their response. This is evident in the inelastic response of solid materials or in the hysteretic retention curve of multiphase porous materials. Within multiscale simulation of history-dependent materials, the underlying work focuses on testing and comparing different supervised machine learning (ML) approaches to generate suitable constitutive models. This includes the application of recurrent neural networks (RNN), the application of 1D convolutional neural network (1D CNN), and the application of the eXtreme Gradient Boosting (XGBoost) library.

The database used in the supervised learning relies on lower scale two-phase lattice Boltzmann simulations, applied to deformable and anisotropic representative volume elements (RVEs) of the porous materials as presented in [1,2]. In the training, the inputs will include the capillary pressure and its history in addition to the porosity, whereas the output will include the degree of saturation. The comparison among the different ML approaches will include the accuracy in predicting the correct saturation degree and the efficiency concerning the training.

REFERENCES

[1] Heider, Y; Suh H.S.; Sun W. (2021): An offline multi-scale unsaturated poromechanics model enabled by self-designed/self-improved neural networks. Int J Numer Anal Methods;1–26.

[2] Chaaban, M.; Heider, Y.; Markert, B. (2022): A multiscale LBM–TPM–PFM approach for modeling of multiphase fluid flow in fractured porous media. Int J Numer Anal Methods Geomech, 46, 2698-2724.

Studying the evolution of alloy polycrystalline microstructures under the action of thermomechanical loads such as those occurring during metal additive manufacturing (AM), quenching, welding, laser rescanning, etc., can help identify the impact of different process parameters on the origin of residual stresses, plastic deformations, the eventual mechanical response. This information can be used to guide the aforementioned processes to design microstructures with a desired response.

To that end, a polycrystal thermo-elasto-viscoplastic finite element (T-EVP-FE) model has been developed. It takes into account the strong coupling between evolving temperatures and stresses under thermomechanical boundary conditions. The constitutive laws of the model include the generalised 3D Hooke’s law, a viscoplastic power law that accounts for the shear rate from each slip system, a Voce-type hardening law, and the generalised Fourier law of heat conduction.

Recently, a series of laser scanning experiments have been performed using a novel laser-SEM (scanning electron microscope) experimental setup; this device is a coupling between a continuous wave fibre laser and an environmental SEM. In these experiments, electron backscattered diffraction was performed before and after laser scanning to study the role of laser scanning on an AM 316L stainless steel microstructure. The experiment revealed the formation of misorientation bands, and hence, geometrically necessary dislocations, that vary as a function of the laser scanning velocity. The T-EVP-FE model has been applied to simulate these laser scanning experiments.

In this talk, the model will be presented, the microstructure state will be compared with experimental observations and the role of laser scan velocity on the evolution of intergranular residual stresses, plastic deformation, stress concentrations, geometrically necessary dislocation formation, etc. will be discussed.

The solution of multi-field problems and the numerical implementation by means of the finite element method constitute a sophisticated part of the characterisation of complex material behaviour. Particularly the implementation into commercial finite element codes is of major importance for practical and industrial applications. Although the wide range of available finite element codes (e.g. Abaqus) provides the opportunity for multiphysical modelling, those implementations are rather restricted to the solution of two coupled field equations. In [1, 2] an Abaqus UMAT framework was introduced to use the balance of linear momentum and the heat equation for the solution of two arbitrary coupled field equations of Laplace-type. An extension of the framework to the solution of three coupled Laplace equations is presented in this contribution.

A comprehensive implementation framework for such a three-field problem into the finite element software Abaqus is provided. The procedure is derived for a micromorphic approach in thermomechanics. Although the provided framework contributes to a particular three-field problem, it is not limited to a particular application or a specific number of coupled field equations from a conceptual point of view. The solution of the considered system of equations is separated onto two coupled domains and is based on a two-instance formulation.

To assess the framework for a particular constitutive model, a gradient-enhanced damage model in a thermo-mechanical setting is adopted and representative simulation results are discussed on a local and a global level. Since the framework is not limited to the solution of three coupled field equations, the extension to arbitrary multi-field problems is discussed.

[1] Ostwald R., Kuhl E., Menzel A. (2019) On the implementation of finite deformation gradient-enhanced damage models. Computational Mechanics 64(847-877). https://doi.org/10.1007/s00466-019-01684-5.

[2] Seupel A., Hütter G., Kuna M. (2018) An efficient FE-implementation of implicit gradient-enhanced damage models to simulate ductile failure. Engineering Fracture Mechanics 199:41-60. https://doi.org/10.1016/j.engfracmech.2018.01.022.

High concentrations of vacancies in crystals may be the result of large plastic deformations or irradiation. Void formation and subsequent growth are well-known to be involved in swelling of irradiated materials and seem to play an important role for the nucleation and evolution of porosity in the early stages of ductile failure as recent experiments suggest [1]. Vacancy diffusion and void formation have been modelled using spatially resolved approaches like the phase-field method. Taking into account that vacancies induce an eigenstrain field, which emerges from the relaxation of the surrounding crystal lattice if a single atom is removed, indicates that the evolution of vacancy concentration needs to be properly coupled to the elastic stress field.

In our recent work [2], we proposed a model for coupling elastically driven vacancy diffusion with a phase-field model of void surfaces, which overcomes the short-comings of former models and closely reproduces the sharp interface solution for small-strain elasticity. This is achieved by making the vacancy eigenstrain a function of the non-conserved order parameter used to distinguish the void and crystal phase. With the recent findings and aiming at being able to numerically analyze the early stages of ductile failure as implied by the mentioned experiments, we present the extension of our model to finite strains. Using a multiplicative split for the deformation gradient, a proper coupling of kinematics and the kinetics of vacancy–void interactions is emphasized. A thermodynamically consistent definition of the energy contributions and the derivation of the resulting driving forces based on the underlying phase-field description are outlined. The model is verified with benchmark problems and the influence of the chemo-mechanical coupling is discussed. The implementation of the governing equations in the multi-physics software tool DAMASK [3] allows a coupling to different plasticity laws, like e.g. continuum dislocation dynamics theory for modelling creep or ductile failure.

[1] P. J. Noell et al. Nanoscale conditions for ductile void nucleation in copper: Vacancy condensation and the growth-limited microstructural state. Acta Materialia, 184:211–224

[2] K. A. Pendl and T. Hochrainer. Coupling stress fields and vacancy diffusion in phase-field models of voids as vacancy phase. [Accepted for publication in Computational Materials Science]

[3] F. Roters et al. DAMASK – The Düsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale. Computational Materials Science, 158:420–478

In the present work, a variational formulation for coupled chemo-mechanical problems in elastic and dissipative solids at infinitesimal strains is outlined. In doing so, it is seen that the gradient of the primary fields additionally enter the energetic and dissipative potential functions, resulting in additional balance equations. The governing balance equations of the coupled problem are derived as Euler equations of the incremental variational principles, formulated in a continuous-and discrete-time setting. Furthermore, the variables governing the inelastic process are locally condensed which yields a reduced global problem that is solved in a discrete-space-time setting. The symmetric structure of the proposed framework with respect to the primary and state variables is an advantage, and this is exploited in the numerical treatment within the finite element paradigm. The framework is applied to Cahn-Hilliard- type diffusion and Allen-Cahn-type phase transformation in elastic and dissipative solids. The applicability of the proposed framework is demonstrated by means of two- and three-dimensional representative numerical simulations.

A better understanding of the stress-deformation behavior of concrete structures under different loading and environmental conditions is inevitable to maintain the structural integrity and to avoid catastrophic failures. In the framework of continuum damage mechanics, several material models have been developed in the past to investigate the constitutive response of concrete under different conditions. It has been observed from the experimental studies that the elastic response and stiffness degradation of concrete are dependent on the orientation of micro-cracks and direction of applied loading. This necessitates the incorporation of damage-induced anisotropy[1] in material models for concrete.

In this regard, an anisotropic damage model that describes the softening response of concrete under different loading conditions is developed applying finite element formulations. A two dimensional damage effect tensor is employed to describe the anisotropic evolution of damage. Damage models that take account of the softening responses are known for their spurious mesh dependencies. An implicit gradient enhancement technique introducing an internal length scale is implemented to overcome the numerical difficulties due to damage localization[2]. The model is verified, calibrated and validated considering various experimental results from the literature including monotonic and cyclic loading cases with different load patterns.

[1] R. Desmorat, F. Gatuingt, F. Ragueneau. Nonlocal anisotropic damage model and related computational aspects for quasi-brittle materials. Engineering Fracture Mechanics, 74(10), 1539-1560, (2006).

[2] R.H.J. Peerlings, R. De Borst, W.A.M. Brekelmans and J.H.P. De Vree. Gradient enhanced damage for quasi-brittle materials. International Journal for Numerical Methods in Engineering, 39, 3391-3403 (1996).

Accumulation of plastic deformation in the surface layer of rails and wheels during many rolling contact loading cycles can result in fatigue crack initiation. The behavior and strength of this highly deformed and anisotropic layer are thus key properties of a rail or wheel material. Establishing crack initiation criteria that account for the properties of the material and are experimentally validated is of great importance in railway engineering.

In this contribution, test results from previously conducted axial-torsion experiments on pearlitic R260 steel specimens have been used to assess the accuracy of available crack initiation criteria as well as to suggest modified criteria. In the experiments, solid test bars were predeformed by torsion under different nominal axial stresses to replicate the anisotropic material in the surface layer of rails. Some of the predeformed specimens were re-machined into a thin-walled tubular shape and then subjected to further cyclic multiaxial loading.

Various crack initiation criteria for rolling-contact situations have been proposed in the literature. However, anisotropy has not been considered in many of them, or they are limited to a specific loading condition, or they are not based on experimental data. In this contribution, we predict the cyclic plasticity and anisotropy evolution during the tests by using a finite strain plasticity model and FEM. Then, by using the obtained stress and strain histories, several crack initiation criteria are evaluated as a post-processing step and further improved by considering the effect of anisotropy.

The recording and evaluation of component life in electric drive systems is considerably complicated by the newly used materials and material compositions. Particularly critical are electrical subcomponents which have beam welded connections made of high-purity copper. Due to the strong coupling between stress and strength as well as the novel material properties, established methods of weld strength analysis cannot be applied without restriction. Therefore, an adapted procedure for the evaluation of the fatigue properties of these junctions is to be developed with the aim of a computational proof of service life under high-frequency vibration loads in the VHCF range.

The aim of the talk is to present the complex and thermally determined properties of the special welding spot and the inherent fatigue properties. On the one hand, the extensive and variable test program in relation to the investigated impact types as well as initial sheet configurations will be discussed. On the other hand, a self-contained methodology is to be presented, which guarantees the transferability of the simulatively determined strength between different welded joints. It is based on the NuMeSis method presented by KAFFENBERGER [1], which evaluates the specific, static notch stress situation based on real measured weld seam geometries of steel components. The transferability of the fatigue strength between different welded joints is then achieved by the combined consideration of the micro-support effect according to NEUBER [2] and the weakest link model according to WEIBULL [3]. The transfer of this method from statically loaded steel welds to high-frequency loaded copper welds requires both the embedding of the method in the methodologies of computational vibration fatigue as well as profound numerical changes of the method. This guarantees an efficient, automated evaluation and the consideration of the special properties of the high-purity copper material. Together with other influencing factors such as the presence of internal defects, this procedure leads to a self-contained evaluation concept for welded copper compounds.

[1] Kaffenberger, Vormwald: Considering size effects in the notch stress concept for fatigue assessment of welded joints, Computational Materials Science 64, 2012, S. 71-78

[2] Neuber: Über die Berücksichtigung der Spannungskonzentration bei Festigkeitsberechnungen, Konstruktion 20 Heft 7, 1968, S. 245-251

[3] Weibull: A statistical theory of the strength of materials, Royal Swedish Institute for Engineering Research, 1939

Computational multiscale methods are well-established tools to predict and analyse material behaviour across scales. They are applied so as to reveal the influence of the underlying microstructure on effective material properties and enable complex multi-physics interactions to be accounted for in simulations. Whereas multiscale approaches for thermo-mechanical problems and electro-active solids have been in the focus of intense research in the past decade, rather few works have so far focused on electrical conductors.

Based on the recent works [1,2] this material class and, in particular, the influence of mechanically-induced microscale defects on the effective conductivity is subject of the present contribution. At the outset of the developments, a quasi-stationary setting is assumed such that Maxwell’s equations reduce to the continuity equation for the electric charge and to Faraday’s law of induction. Scale-bridging relations for the kinematic- and flux-type quantities are established, their consistency with an extended Hill-Mandel condition is shown and a closed-form solution for the effective macroscale conductivity tensor based on the underlying microscale boundary value problem is provided.

In view of the experimental investigations [3,4] the effective conductivity tensor, as a fingerprint of the material microstructure, is of primary interest. To study the applicability of the proposed approach, focused ion beam milling is used in a first step to generate geometrically well-defined microstructures [4]. In a second step, focus is laid on mechanically-induced micro-cracks in metal thin films [3]. Both sets of microstructures are electrically characterised by means of four point probe resistance measurements and analysed by means of the proposed computational multiscale scheme. Good accordance between experiment and simulation is achieved which shows the applicability of the proposed multiscale formulation.

[1] T. Kaiser, A. Menzel, An electro-mechanically coupled computational multiscale formulation for electrical conductors, Archive of Applied Mechanics, 91, 1509–1526 (2021)

[2] T. Kaiser, A. Menzel, A finite deformation electro-mechanically coupled computational multiscale formulation for electrical conductors, Acta Mechanica, 232, 3939–3956 (2021)

[3] T. Kaiser, M.J. Cordill, C. Kirchlechner, A. Menzel, Electrical and mechanical behavior of metal thin films with deformation-induced cracks predicted by computational homogenisation, International Journal of Fracture 231, 233–242 (2021)

[4] T. Kaiser, G. Dehm, C. Kirchlechner, A. Menzel, H. Bishara, Probing porosity in metals by electrical conductivity: Nanoscale experiments and multiscale simulations, European Journal of Mechanics A/Solids, 97, 104777 (2023)

Internal traverse grinding (ITG) with electroplated cBN tools and under high speed conditions if a highly efficient process for the machining of hardened steel components. In ITG, the grinding wheel consists of a conical roughing zone and a cylindrical finishing zone. The tool is fed in axial direction into a revolving workpiece, performing roughing and finishing in a single axial stroke. Due to the process kinematics, the process forces during ITG are dependent on the current material removal rate, which varies during the process. The mechanical compliance of the entire system, consisting of both tool- and workpiece spindle, the workpiece clamping device, and all other components in the flow of force, result in shape deviations of the workpieces after machining.

We recently proposed a multi-scale simulation framework to model ITG with electroplated CBN wheels numerically [1]. A digital grinding wheel, based on real grain geometries obtained from optical measurements, was implemented in a geometric physically-based simulation (GPS) to simulate the engagement of each individual grain during the process. The normal force contributions of each individual grain were modelled by a single-grain force model, which was calibrated against two-dimensional Finite Element Simulations of single grain cuts. By taking into account both the system compliance and the total normal force, the deflection between tool and workpiece was modelled in the GPS.

Based on the simulation results, different compensation strategies for the NC tool path were implemented and compared, and a significant reduction of the shape deviations was achieved.

[1] Tsagkir Dereli T, Schmidt N, Furlan T, Holtermann R, Biermann D, Menzel A. Simulation Based Prediction of Compliance Induced Shape Deviations in Internal Traverse Grinding. Journal of Manufacturing and Materials Processing. 2021; 5(2):60. https://doi.org/10.3390/jmmp5020060

The present study concerns the laminar mixed convection flow over a heated or cooled horizontal plate of finite length at a zero angle of attack and a small Richardson number. The plate is located either in a channel or in a semi-infinite space behind a flow straightener. In the limit of a small Prandtl number, these conditions correspond to the boundary-layer solutions of Müllner and Schneider (2010), and Schneider (2000), respectively.

The hydrostatic pressure difference between the plate's lower and upper sides and the Kutta condition at the trailing edge induce a circulation with a global effect on the flow around the plate. In contrast to the classical aerodynamics problem of an isothermal flow around an inclined plate, the thermal wake also contributes to the circulation in the outer flow. This circulation can lead to flow separation at the bottom side of a heated plate (or an upper side of a cooled plate) when the Richardson number exceeds a certain threshold, depending on the Reynolds and Prandtl numbers.

The steady two-dimensional solution of the governing equations under the Boussinesq approximation is computed with the Finite Element solver FEniCS. Goal-oriented adaptive mesh refinement is employed in order to resolve both the viscous and the thermal boundary layers.

In the talk, the numerical solution will be compared to the boundary-layer solutions. The effect of the governing parameters on the flow will be investigated, also beyond the range of validity of the boundary-layer solutions. For a plate inside a channel, the flow separates close to the leading edge even for relatively low values of the Richardson number. The threshold Richardson number for separation decreases with increasing Reynolds number. For certain parameters, multiple steady two-dimensional solutions come into existence, differing by the size of the separation bubble. We show that the separation can be suppressed by bending a short leading section of the plate. Finally, we consider the effect of a heat source at the leading edge of a cooled plate.

References

M. Müllner and W. Schneider, Heat Mass Transf. 46, 1097-1110 (2010)

W. Schneider, Proc. 3rd Eur. Therm. Sci. Conf., 195-198 (2000)

The virtual element method (VEM) has been demonstrated to be effective in a variety of engineering problems. In recent years, it has gained high interest in both mathematics and engineering communities. In this work, a low order virtual element method for the treatment of three-dimensional contact problems with non-conforming interface meshes is presented. The contact conditions can be employed on different enforcing strategies. For non-conforming meshes, a node-to-surface enforcement leads to wrong force distributions at the contact interface. Here, we utilise a mesh adaptivity strategy, which leads to conforming meshes at the contact interface, without introducing new elements or changing the ansatz. In fact, we take advantage of the useful feature of the virtual element method, which allows to introduce new topological nodes during the simulation. It allows to employ a very simple node-to-node contact formulation for the treatment of contact. Thus, this work presents a simple geometrical approach to cut element faces and introduce new nodes into the existing mesh. Beside a node-to-node contact formulation, this also allows to treat the contact pairs as polygonal pairs and thus to use a surface-to-surface contact formulation. To validate the presented methodology, numerical examples in 3D are performed, including the contact patch test and Hertzian contact problem.

To precisely model crack growth, accurate calculations of crack front loading and crack deflection angles are essential. These calculations require solutions of the underlying boundary value problems (BVPs), which are typically obtained by applying numerical methods, e.g., the finite element method (FEM). However, since accuracy and computational cost of the analyses are in general competing aspects, compromises often must be made to generate satisfactory results in acceptable times. In contrast, the use of more efficient methods, both for the solution of the BVP as well as for the subsequent crack tip loading analyses, can substantially lower the computational effort while maintaining desired accuracies. The virtual element method (VEM) is a fairly new discretization scheme for the numerical solution of BVPs, and can be interpreted as a generalization of the FEM. Since the VEM can handle arbitrary polytopal meshes in a straightforward manner, it provides a higher degree of flexibility in the discretization process than the FEM, which turns out to be profitable in terms of both computing times and accuracy.

In the context of numerical applications of fracture mechanics, the probably most attractive feature of the VEM results from the possibility to employ elements of complex shapes, which may be convex as well as concave. Consequently, crack growth simulations benefit from the fact that incremental changes in the geometry of a crack do not require any remeshing of the structure, but rather crack paths can run through already existing elements. Although the method has already proved to provide an efficient tool for crack growth simulations in plane problems, there is still further research required regarding the efficient and precise evaluation of crack front loading quantities and the extension towards spatial crack problems.

This work aims to discuss aspects of the virtual element method for crack tip loading analyses and crack growth simulations. Classical as well as advanced concepts of numerical fracture mechanics are adopted and implemented in connection with the VEM, carefully investigating and exploiting the advantages and opportunities the discretization method offers in this regard. Crack growth simulations based on the VEM are performed and results are compared to reference solutions as well as solutions obtained by the FEM.

The finite element method can become susceptible to mesh distortion and numerical instabilities at huge deformations. As an alternative numerical method, the Material Point Method (MPM) can be used for this purpose, combining the advantages of the Lagrangian description of the bodies while solving the equations of interest on the Eulerian grid, see [1]. In the MPM, bodies are discretized as material points while their mechanical properties are mapped to the background grid on which the equations are solved. In this contribution, numerical examples are presented that are subject to large deformations in the context of dynamic processes. These examples exhibit a kind of mesh-dependence in different quantities. Therefore, the focus of this contribution is on the improvement and increase in stability of the numerical results, which is achieved by translations of the grid. Within this method, the origin of the background grid is shifted randomly at the beginning of each time step in a small manner in each direction. This shifting procedure can be interpreted as smearing the grid over time, eliminating the mesh-dependence shown in the resulting quantities.

References:

[1] D. Sulsky, Z. Chen und H. Schreyer. “A particle method for history-dependent materials”. In: Comput. Method Appl. M. 118.1-2 (1994), S. 179-196. doi: 10.1016/0045-7825(94)90112-0.

Many data-driven approaches in computational material engineering and mechanics rely on realistic volume elements for conducting numerical simulations. Examples include multiscale simulations based on neural networks or reduced-order models as well as the exploration and optimization of structure-property linkages. This motivates microstructure characterization and reconstruction (MCR). In previous contributions, MCRpy [1] has been introduced as a modular open-source tool for descriptor-based MCR, where any descriptors can be used for characterization and any loss function combining any descriptors can be minimized using any optimizer for reconstruction. A key feature of MCRpy is that differentiable descriptors are available and can be used in conjunction with gradient-based optimizers. This allows the underlying optimization problem to converge several orders of magnitude faster than with the previously used stochastic optimizers [2, 3]. While MCRpy and the gradient-based reconstruction have been presented in previous contributions for microstructures with multiple phases, the present contribution extends these concepts towards orientation maps.

After a brief introduction to MCRpy, the main difficulties of extending gradient- and descriptor-based microstructure reconstruction to orientation maps are discussed. Besides the symmetry of orientation itself after 360°, additional crystal symmetries need to be incorporated and singularities need to be avoided. For this reason, differentiable statistical descriptors are defined in terms of symmetrized harmonic basis functions defined on the 4D unit quaternion hypersphere [4]. Based on a generic combination of descriptors comprising two-point statistics of orientation information and the orientation variation, the optimization problem is defined in the fundamental region of a neo-Eulerian orientation space. These and other measures are motivated and discussed in detail. The capabilities of the method are demonstrated by exemplarily applying it to various microstructures. In this context, it is mentioned that all algorithms are made publicly available in MCRpy and it is demonstrated how to use them. Furthermore, it is shown how to extend MCRpy by defining a new microstructure descriptor in terms of any desired orientation representation or basis function and readily using it for reconstruction without additional implementation effort.

[1] Seibert, Raßloff, Kalina, Ambati, Kästner, Microstructure Characterization and Reconstruction in Python: MCRpy, IMMJ, 2022

[2] Seibert, Ambati, Raßloff, Kästner, Reconstructing random heterogeneous media through differentiable optimization, COMMAT, 2021

[3] Seibert, Raßloff, Ambati, Kästner, Descriptor-based reconstruction of three-dimensional microstructures through gradient-based optimization, Acta Materialia, 2022

[4] Mason, Analysis of Crystallographic Texture Information by the Hyperspherical Harmonic Expansion, PhD Thesis, 2009

In the context of homogenization approaches, data-driven methods entail advantages due to the ability to capture complex behaviour without the assumption of a specific material model. Constitutive model based data-driven methods approximating the constitutive relations by training artificial neural networks and the method of constitutive model free data-driven computational mechanics, directly incorporating stress-strain data in the analysis, are distinguished. Neural network based constitutive descriptions are one of the most widely used data-driven approaches in computational mechanics. In contrast to this, the method of distance minimizing data-driven computational mechanics enables to bypass the material modelling step entirely by iteratively obtaining a physically consistent solution, which is close to the material behaviour represented by the data. A generalization of this method providing increased robustness with respect to outliers in the underlying data set is the maximum entropy data-driven solver. Additionally, a tensor voting enhancement based on incorporating locally linear tangent spaces enables to interpolate in regions of sparse sampling.

In this contribution, a comparison of artificial neural networks and data-driven computational mechanics is carried out based on nonlinear elasticity. General differences between machine learning, distance minimizing as well as entropy maximizing based data-driven methods concerning pre-processing, required computational effort and solution procedure are pointed out. In order to demonstrate the capabilities of the proposed methods, numerical examples with synthetically created datasets obtained by numerical material tests are executed.

The accurate bending of sheet metal structures is critical in a variety of industrial and scientific contexts, whether it is to modify existing components or achieve specific shapes. Laser peen forming (LPF) is an advanced process for sheet metal applications that involves using mechanical shock waves to deform a specific area to a desired radius of curvature. The degree of deformation achieved through LPF is affected by various experimental factors such as laser energy, the number of peening sequences, and specimen thickness. Therefore, it is important to understand the complex dependencies and select the appropriate LPF process parameters for forming or correction purposes. This study aims to develop a data-driven approach to predict the deformation obtained from LPF for different process parameters. The experimental data is used to train, validate, and test an artificial neural network (ANN). The trained ANN successfully predicted the deformation obtained from LPF. An innovative process planning approach is developed to demonstrate the usability of ANN predictions in achieving the desired deformation in a treated area. The effectiveness of this approach is demonstrated on three benchmark cases involving thin Ti-6Al-4V sheets: deformation in one direction, bi-directional deformation, and modification of an existing deformation in pre-bent specimens via LPF.

Crystal plasticity is the result of the motion of line like crystal defects, the dislocations. While many traits of crystal plasticity may be described by phenomenological models, the description of the well-known patterning of dislocations as well as the phenomenon of single crystal work-hardening caused by dislocation multiplication during plastic deformation, ask for continuum models rooted more directly in the collective behavior of dislocations. A promising homogenization approach in this realm is the so-called Continuum Dislocation Dynamics (CDD) framework, which is based on conservation laws for tensorial dislocation density measures. In other words, the CDD theory can be considered as a continuum representation of dislocation networks through a hierarchy of tensorial dislocation variables. [1]

In this work, we derive nonlinear expressions for source terms as required in CDD for modeling work-hardening, which is arguably the most salient feature of metal-plasticity. [2] For that purpose we use modern data-driven discovery methods, like the Sparse Identification of Nonlinear Dynamics (SINDy), to describe the highly nonlinear dynamics of dislocation multiplication. The SINDy algorithm is capable of identifying the few predominant terms in the corresponding governing equations based on a model library of predefined, possibly high-dimensional spaces of nonlinear functions using sparse regression techniques. [3]

The SINDy algorithm is applied on a large database of Discrete Dislocation Dynamics (DDD) simulations of the plastic deformation of FCC single crystalline copper under constant strain rate in 120 different loading directions with neglected cross-slip. The extraction of the underlying data of dynamic CDD tensor variables, consisting of density, curvature and velocity tensors of n-th order, from the DDD data is performed by a recently developed algorithm.

References

[1] Thomas Hochrainer, S. Sandfeld, M. Zaiser, and P. Gumbsch. Continuum dislocation dynamics: towards a physically theory of plasticity. Journal of the Mechanics and Physics of Solids, 63(1):167–178, 2014.

[2] Markus Sudmanns, Markus Stricker, Daniel Weygand, Thomas Hochrainer and Katrin Schulz. Dislocation multiplication by cross-slip and glissile reaction in a dislocation based continuum formulation of crystal plasticity. Journal of the Mechanics and Physics of Solids, 132:103695, 2019.

[3] Steven L Brunton, Joshua L Proctor, and J Nathan Kutz. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the national academy of sciences, 113(15):3932–3937, 2016.

The crude Monte Carlo method delivers an unbiased estimate of the probability of failure. However, the accuracy of the approach, i.e., the variance of the estimate, depends on the number of evaluated samples. This number must be very large for estimations of a low probability of failure. If the evaluation of each sample is computationally expensive, the crude Monte Carlo simulation strategy is impracticable. To this end, subset simulations are used to reduce the required number of evaluations. Subset simulations require a Markov Chain Monte Carlo sampler, e.g., the random walk Metropolis-Hastings algorithm [1]. The algorithm, however, struggles with sampling in low-probability regions, especially if they are narrow. Therefore, advanced Markov Chain Monte Carlo simulations are preferred. In particular, the Hamiltonian Monte Carlo method explores the target distribution space rapidly. Driven by Hamiltonian dynamics, this sampler provides a non-random walk through the target distribution [2]. The incorporation of subset simulation and Hamiltonian Monte Carlo methods has shown promising results for reliability analysis [3]. However, gradient evaluations in the Hamiltonian Monte Carlo method are computationally expensive, especially when dealing with high-dimensional problems and evaluating long trajectories. Integrating Hamiltonian Neural Networks in Hamiltonian Monte Carlo simulations significantly speeds up the sampling [4]. The extension to latent Hamiltonian neural networks improves the expressivity by adding neurons to the last layer. Furthermore, the enhancement of the No U-Turns Sampler to the Hamiltonian Monte Carlo results in the efficient proposal of the following states [5]. During the exploration of low-probability regions, an online error monitoring calls the standard NUTS sampler if the latent Hamiltonian Neural Network estimates are inaccurate. Based on this recent enhancement, we provide an efficient sampling strategy for subset simulations using latent Hamiltonian neural networks to replace the gradient calculation and speed up the Hamiltonian Monte Carlo simulation.

[1] W.K. Hastings. Biometrika 57 (1970) 97-109.

[2] M. Betancourt. arXiv preprint, arXiv:1701.02434 (2017).

[3] Z. Wang, M. Broccardo, J. Song. Struct. Saf. 76 (2019) 51-67.

[4] D. Thaler, S.L.N. Dhulipala, F. Bamer, B. Markert, M.D. Shields. Proc. Appl. Math. Mech. (2023);22:e202200188.

[5] S.L.N. Dhulipapla, Y. Che, M.D. Shields. arXiv preprint, arXiv:2208.06120v1 (2022).

Artificial intelligence (AI) applications have recently gained widespread attention due to their capabilities in the domains of speech and image recognition as well as natural language processing. This has drawn research attention towards AI and artificial neural networks (ANNs) in particular within numerous branches of applied mathematics and computational mechanics. The challenge of generating extensive training data for supervised learning of ANNs can be addressed by incorporating laws of physics into ANNs. Most of so-called physics informed neural network (PINN) [1] frameworks for structural mechanics applications incorporate the partial differential equations (PDEs) governing a specific problem within the loss function in the form of energy methods [2] or collocation methods [3].

Many structural mechanics problems are governed by stiff PDEs resulting in locking effects which have already been recognized in the early days of finite element analysis. Locking effects are present for all known discretization schemes, not only for finite elements, independent of the polynomial order or smoothness of the shape functions. This applies to both Galerkin-type solution methods and also collocation methods based on the Euler-Lagrange equations of the specific boundary value problem [4].

In this contribution, we examine the impact of stiff PDEs or locking effects on the accuracy and efficiency of PINN-based numerical solutions of problems in structural mechanics. First investigations on the use of PINNs for solving shear deformable beam and plate problems are presented. Different types of beam and plate formulations, as well as different types of collocation-based loss functions are evaluated and compared with respect to accuracy and efficiency.

REFERENCES

[1] M. Raissi, P. Perdikaris, G.E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, Vol. 378, pp. 686-707. 2019

[2] E. Samaniego, C. Anitescu, S. Goswami, V.M. Nguyen-Thanh, H. Guo, K. Hamdia, X. Zhuang, T. Rabczuk. An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications. Computer Methods in Applied Mechanics and Engineering, Vol. 362, 112790. 2020

[3] H. Guo, X. Zhuang, T. Rabczuk. A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate. Computers Materials & Continua. Vol. 59(2), pp. 433-456. 2019

[4] B. Oesterle, S. Bieber, R. Sachse, E. Ramm, M. Bischoff. Intrinsically locking-free formulations for isogeometric beam, plate and shell analysis. Proc. Appl. Math. Mech. 2018, 18:e20180039. 2018

In this contribution, we give an overview of methods and techniques

that we apply in our group to elucidate the specific behaviour

of functional nano-structures in the condensed phase on a molecular basis.

A special focus will be on materials that can be reversibly photoswitched by external light stimulus.

When molecular photo-switches, such as azobenzene or norbornadiene, are embedded into a sufficiently soft polymer matrix the resulting compound can undergo a mechanical deformation induced by light of a specific wavelength. These photo-sensitive compounds have the potential to be applied as soft actuators without the need for hard wired electronics or a separate energy source. Such characteristics are especially attractive in the design of micro-scale robots but also other applications such as high-speed data transfer or the conversion of photonic energy into a mechanical response holds great promise.

Despite these almost futuristic possibilities, photo-sensitive polymers have not yet experienced a sufficient attention in industrial applications. One important factor to increase the acceptance of this group of soft smart materials is the formulation of a rigorous constitutive modeling approach in combination with numerical simulation methods. Thus, in this contribution we present a photo-mechanical modeling approach solved with the help of a finite element implementation.

We develop a theoretical and computational framework to perform topology optimization of the representative volume element (RVE) of flexoelectric metamaterials [2].

The flexoelectric effect is an electromechanical coupling between polarization and strain gradient as well as strain and electric field gradients, present in small (micro-to-nano) scales [1]. It is universal to dielectrics, but, as compared to piezoelectricity, it is more difficult to harness as it requires small scales and field gradients. These drawbacks can be overcome by suitably designing geometrically polarized metamaterials made of a nonpiezoelectric base material but exhibiting apparent piezoelectricity [3].

We solve the governing equations of flexoelectricity on a high-order generalized-periodic Cartesian B-spline approximation space. The geometry is unfitted to the mesh, and described by a periodic level set function. Genetic algorithms are considered for the multi-objective optimization of the RVE topology, where area fraction competes with four fundamental piezoelectric functionalities (stress/strain sensor/actuator). During the optimization process, the RVE topologies are restricted to be fully-connected in a single group of material.

We obtain Pareto fronts and discuss the different material topologies depending on the area fraction and the apparent piezoelectric coefficient being optimized. Overall, we find RVE topologies exhibiting a competitive apparent piezoelectric behavior as compared to reference piezoelectric materials such as quartz and PZT ceramics. This opens the possibility to design a new generation of devices for sensing, actuation and energy harvesting application using a broad class of base materials.

References

[1] D. Codony, A. Mocci, J. Barceló-Mercader, and I. Arias: Mathematical and computational modeling of flexoelectricity. Journal of Applied Physics 130(23) (2021), 231102.

[2] F. Greco, D. Codony, H. Mohammadi, S. Fernández-Méndez, and I. Arias: Topology optimization of flexoelectric metamaterials with apparent piezoelectricity. arXiv preprint arXiv:2303.09448 (2023).

[3] A. Mocci, J. Barceló-Mercader, D. Codony, and I. Arias: Geometrically polarized architected dielectrics with apparent piezoelectricity. Journal of the Mechanics and Physics of Solids 157 (2021), 104643.

Although isotropic hardening plasticity is the most basic hardening type in material modeling, many existing models rely on an overly simplistic hypothesis: a direct relationship between yield stress and accumulated plasticity. Our recent publication [1] falsifies this hypothesis for one medium carbon steel. Furthermore, we investigated the yield surface evolution and its relation to the accumulated plasticity. Several distortional hardening models in the literature assume a direct relationship between the complete yield surface evolution and accumulated plasticity for uniaxial cyclic loading.

These identified modeling deficiencies underscore the necessity for new constitutive models. To tackle this need, we propose a novel plasticity formulation incorporating neural networks in a thermodynamically consistent framework. We extract and analyze the trained neural networks to identify new constitutive equations with sparse regression techniques, cf. [2]. The complete process results in the discovery of new evolution equations based on the experimental data. A notable finding is new interactions between the hidden state variables in the evolution laws. Based on these equations, we can design new specialized experiments to further understand the interplay between loading type and hardening behavior.

[1] K. A. Meyer and J. Ahlström, “The role of accumulated plasticity on yield surface evolution in pearlitic steel,” Mech. Mater., vol. 179, p. 104582, 2023, doi: 10.1016/j.mechmat.2023.104582.

[2] M. Flaschel, S. Kumar, and L. De Lorenzis, “Unsupervised discovery of interpretable hyperelastic constitutive laws,” Comput. Methods Appl. Mech. Eng., vol. 381, p. 113852, 2021, doi: 10.1016/j.cma.2021.113852.

The field of application of thin glass products is vast including various engineering branches such as e.g. electronics, medical equipment and automobiles. In order to realize a cost-efficient production of surface shapes with high accuracy and complexity, a novel replicative glass processing technique called non-isothermal glass molding has been developed (see [1]). However, the production of thin glass components using this technology still raises the issue of shape distortions, cracks and surface defects of molded parts. Therefore, the experimental investigation and mechanical modeling of glass above the glass transition temperature at finite strains are combined in order to simulate these glass forming processes.

Previous experimental studies have shown that the material behavior can be predicted adequately by the Maxwell model (see e.g. [2]). Based on this viscoelastic formulation (see [3]), the material law used is thermo-mechanically consistent and allows the prediction of rheological effects observed during the experiments. In particular, a stress-dependent relaxation time is used to describe the relaxation behavior and the dissipation generated is also taken into account. Regarding the experimental investigation, isothermal uniaxial compression tests above the glass transition temperature are performed for different strain rates and temperatures. By combining the experimental data with the simulation, a multi-curve-fitting is introduced. This nonlinear optimization lead to suitable material parameters with respect to distinct temperatures.

[1] A.-T. Vu, H. Kreilkamp, O. Dambon, and F. Klocke, Optical Engineering 55(7), 071207 (2016).

[2] T. Zhou, J. Yan, J. Masuda, and T. Kuriyagawa, Journal of Materials Processing Technology 209(9), 4484-4489 (2009)

[3] S. Reese and S. Govindjee, International Journal of Solids and Structures 35(26-27), 3455-3482 (1998)

It is still challenging in the field of topology optimization to optimize structures including the complex real-world material behavior. Nevertheless, the specific material behavior has significant influence on the optimal results. Therefore, we proposed a numerical efficient surrogate model for plasticity including hardening extending the established thermodynamic topology optimization (TTO). Even if the simulation results seem reasonable, experimental validation is still mandatory to ensure feasibility for real-world application.

Thus, we present the validation of the thermodynamic topology optimization including plasticity with hardening by comparison of experiments with optimization results. To this end, topology optimized structures are manufactured by additive manufacturing. The real material behavior needs to be determined from additively manufactured tensile specimens so that the material parameters for the specific hardening are considered during the optimization process. Subsequently, structures with respect to hardening as well as elastically reference are optimized and manufactured. Optimization results with pure elastic and plastic model are compared by experiments to show the importance of including hardening behavior within optimization for real-world application.

Finite element (FE) models are widely used to capture the mechanical behavior of structures. Uncertainties in the underlying physics and unknown parameters of such models can heavily impact their performance. Thus, to satisfy high precision and reliability requirements, the performance of such models is often validated using experimental data. In such model updating processes, uncertainties in the incoming measurements should be accounted for, as well. In this context, Bayesian methods have been recognized as a powerful tool for addressing different types of uncertainties.

Quasi-brittle materials subjected to damage pose a further challenge due to the increased uncertainty and complexity involved in modeling crack propagation effects. In this respect, techniques such as Digital Image Correlation (DIC) can provide full-field displacement measurements that are able to reflect the crack path up to a certain accuracy. In this study, DIC-based full field measurements are incorporated into a finite element model updating approach, to calibrate unknown/uncertain parameters of an ansatz constitutive model. In contrast to the standard FEMU, where measured displacements are compared to the displacements from the FE model response, in the force-version of the standard FEMU, termed FEMU-F, displacements are applied as Dirichlet constraints. This enables the evaluation of the internal forces, which are then compared to measured external forces, thus quantifying the fulfillment of the momentum balance equation as a metric for the model discrepancy. In the present work, the FEMU-F approach is further equipped with a Bayesian technique that accounts for uncertainties in the measured displacements, as well. Via this modification, displacements are treated as unknown variables to be subsequently identified, while they are allowed to deviate from the measured values up to a certain measurement accuracy. To be able to identify many unknown variables; including constitutive parameters and the aforementioned displacements, an approximative variational Bayesian technique is utilized.

A numerical example of a three-point bending case study is presented first to demonstrate the effectiveness of the proposed approach. The parameters of a gradient-enhanced damage material model are identified using noisy synthetic data, and the effect of measurement noise is studied. The ability of the suggested approach on identifying constitutive parameters is then validated using real experimental data from a three-point bending test. The full field displacements required as input to the inference setup are extracted through a digital image correlation (DIC) analysis of the provided raw images.

Metal additive manufacturing technologies, such as wire arc additive manufacturing (WAAM), allow the manufacturing of components with maximum freedom in the geometric design and specifically adjusted functional properties. However, WAAM-produced components possess a very wavy surface that exacerbates the numerical simulation of such components. As a result, common finite element approaches with low order shape functions are not suitable for these simulations.

Instead, the finite cell method is chosen for the simulation of tube-like WAAM-produced specimens under a combined tension-torsion load. First, the contour of the specimens is determined with a portable 3D scanning technique. Then, the mechanical response of the specimens is computed using the finite cell method, where a beforehand calibrated J2-plasticity model is applied. The polynomial order of the integrated polynomials is increased for convergence studies and the mechanical response of the specimens is compared to the experimental results. During the experiments, digital image correlation measurements are performed to compare even the full-field deformation to the simulation results. Here, we choose so-called radial basis functions as a global interpolation technique to obtain the in-plane strains and stretches in the curved surfaces for both experiment as well as simulation. Since the material parameters are determined from experimental tensile testing data, uncertainties in these parameters propagate to the numerical simulations of the tube-like specimens under tension-torsion load. To consider these uncertainties when comparing the experimental with the numerical results, the Gaussian error propagation is applied for estimating the uncertainty in the mechanical response.

Nonlinear multi-point constraints are used to model a wide range of features in engineering structures like incompressibility, inextensibility, rigidity or coupling of elements. The applied combination of such constraints can be either be non-redundant or redundant. There are three strategies to include nonlinear multi-point constraints in the finite element analysis: Lagrange multipliers, penalty method and master-slave elimination. Redundant nonlinear constraints are particularly challenging for all three methods. For Lagrange multipliers they can lead to a singular effective stiffness matrix and thus to divergence. For the penalty method redundancy worsens the convergence. For master-slave elimination redundant constraints lead to the selection of too many slave dofs or the wrong selection of master and slave dofs. This results in the failure of the method.

As the number of constraints in a given region of the system under study increases, the probability of the occurrence of redundant constraints also increases. For such problems it is not possible to detect the redundancy by hand because the coupling of constraints becomes very complex. An additional challenge is that the redundancy of constraints may change during the iterative solution process. Thus, redundant nonlinear constraints cannot be detected a priori in contrast to redundant linear constraints. Therefore, there is the need for an automatic detection and elimination of redundant nonlinear constraints during the simulation. However, in the literature redundancy has only been analyzed for certain combinations of constraints yet.

In this presentation we propose a direct, stable numerical method for the detection and elimination of arbitrary redundant nonlinear multi-point constraints that can be used for all three strategies. The corresponding treatment of the constraints has to be applied in each iteration. Thus, the presented method ensures the consistent linearization of the constraint forces and quadratic convergence is retained. We explain the algorithmic consequences on the three strategies due to the proposed method. In particular, we discuss the benefits of the method for the master-slave elimination as it gives also an automatic selection of master and slave dofs. We verify the method by selected examples and illustrate its influence on the numerical performance.

Isogeometric analysis (IGA) employs higher order polynomial shape functions, which are directly extracted from the CAD model. Unlike the standard Finite Element Method (FEM), which commonly uses Lagrange basis functions, IGA typically uses Non-Uniform Rational B-Splines (NURBS) or other types of splines. The use of spline-based FEM results in efficient computations with a relatively small number of elements, as increasing the order of NURBS basis functions enhances the convergence rate.

In the field of IGA, using high polynomial orders results in precise computations for structures that are exposed to static and dynamic loads. However, this also leads to highly accurate mass matrices with large bandwidths, resulting in increased computational effort, particularly for explicit dynamic analysis with a large number of time steps. To address computational efficiency, mass lumping techniques are commonly applied to achieve diagonal mass matrices, reducing the inversion of the mass matrix to a simple reciprocal operation. Many mass lumping schemes have been developed over time, but commonly the row-sum technique is attracted. These techniques were primarily invented fitting the requirements of standard FEM. Unfortunately, they deteriorate the convincing convergence rates of IGA when high polynomial orders are employed. Therefore, a lumping scheme tailored to IGA formulations using higher-order basis functions is necessary for efficient dynamic computations.

This study proposes the usage of dual basis functions as test functions in IGA element formulations with NURBS shape functions. By incorporating dual test functions, the Bubnov-Galerkin formulation is transferred to a Petrov-Galerkin formulation, resulting in non-symmetric stiffness matrices and - as effect of the duality - consistent diagonal mass matrices. For the presented formulation only dual basis functions are considered, which can be constructed by a combination of the initial NURBS shape functions. Hence, the changes by the dual formulation on element level can be shifted to an afterwards modification of the global matrices obtained from common IGA formulations. Thus, implementing this technique in existing codes is straightforward. Numerical examples demonstrate the efficiency of the dual approach compared to existing methods.

In modern applications of computer-aided design (CAD) for the analysis of shell structures, isogeometric analysis (IGA) is a powerful tool to incorporate both design and analysis. However, when it comes to multi-patch structures, C1-continuity across patches is not naturally fulfilled and computation of Kirchhoff-Love shells is not straightforward since well-defined second-order derivatives are necessary for the analysis. Furthermore, trimming is a major problem as the mathematical underlying of the CAD surface is not inherently suitable for standard IGA.

The approach presented in this talk deals with a Kirchhoff-Love shell formulation in the framework of scaled boundary isogeometric analysis [1,2] with C1-coupling. In scaled boundary (SB), the domain is described by its boundary and scaled to a scaling center, which we denote as an SB block. Thereby, each SB block consists of several IGA patches. This has the advantage of being applicable to multi-patch structures with various numbers of edges or boundaries. Besides, a possible trimming curve is easily incorporated into the boundary representation. The domain can be subdivided into several SB blocks to obtain star convexity. However, even for a single SB block, C1-continuity is not fulfilled across the IGA patches within the SB block. To show the feasibility of the coupling approach involving SB parametrizations, it heeds the concept of analysis-suitable G1 parametrizations [3] combined with special consideration of the basis functions in the scaling center. The method is especially powerful when it comes to complex geometries that cannot be described by a single IGA patch which is outlined in several examples.

[1] C. Arioli, A. Shamanskiy, S. Klinkel, and B. Simeon, “Scaled boundary parametrizations in isogeometric analysis”, Comput. Methods Appl. Mech. Eng., vol. 349, pp. 576–594, 2019.

[2] M. Chasapi and S. Klinkel, “A scaled boundary isogeometric formulation for the elasto-plastic analysis of solids in boundary representation”, Comput. Methods Appl. Mech. Eng., vol. 333, pp. 475–496, 2018.

[3] A. Collin, G. Sangalli, and T. Takacs, “Analysis-suitable G1 multi-patch parametrizations for C1 isogeometric spaces”, Comput. Aided Geom. Des., vol. 47, pp. 93–113, 2016.

Additive manufacturing enables the fabrication of geometrically complex structures, giving rise to a research focus on tailoring structures and material properties using numerical simulation. In lightweight engineering, continuous fiber composites are in great demand due to their superior strength-to-weight ratio. However, their anisotropic material properties pose difficulties for additive manufacturing processes: Planar 3D printing restricts fiber placement to a 2D plane, limiting the complexity of fabricated parts; current design methods for non-planar 3D printing (e.g., robotic arm) lack automated design methods with a performant integration of numerical simulation.

Another well-known problem of 3D-printed fiber composites is uncertainties in material parameters. Improvements in the micro-structure have been shown through consolidation or post-treatment (heat/pressure), reducing material variability. However, these methods are challenging to apply in non-planar 3D printing. Another approach is the experimental quantification of uncertainties in the material to incorporate them into the numerical simulation.

With the aim to contribute to design optimization for non-planar 3D printing of fiber composites, we develop a robust optimization methodology that considers firstly, the anisotropic nature of fiber composites and secondly, material uncertainties. The method is based on a ground structure discretization of the design space with 1D elements. It uses a heuristic approach for design optimization based on an optimality criteria for robustness aiming for equal strain energy distribution in the structure. The optimization methodology further utilizes the Certain Generalized Stresses Method (CGSM) for stochastic modeling to study the influence of the material uncertainties on the structural design.

Redundancy, and thus the degree of static indeterminacy, plays an important role in the design of structural systems. According to Linkwitz and Ströbel, the distribution of static indeterminacy in the system can be described by the redundancy matrix. The redundancy contribution of an element quantifies the internal constraint of the surrounding structure on this element. The sum of the redundancy contributions of all elements is equal to the degree of statical indeterminacy of the entire structure. The extension of Ströbel's notion for discrete truss systems to frames and continua can provide valuable insight into the load-bearing properties of a structure and has the potential to become an exciting new branch in the classical field of structural analysis.

Obviously, statical indeterminacy and its distribution in a structure have a decisive influence on the structural behavior. Therefore, the redundancy matrix can be a good measure to understand and evaluate structural behavior. It can also be used for robust design optimization and assessment of imperfection sensitivity during the assembly process.

The computation of the redundancy matrix generally requires a high effort due to the necessity of expensive matrix operations. A closed-form expression for the redundancy matrix can be derived via a factorization that is based on singular value decomposition. For moderately redundant systems it proves to be computationally very efficient. For small modifications of the structure, such as adding, removing, and swapping elements, generic algebraic formulations can be derived for efficiently updating the redundancy matrix.

While the redundancy matrix concept has only been applied to linear analysis, it can be extended to the nonlinear regime. In this case, the contribution of the nonlinear load transfer can be analyzed separately. Furthermore, the redundancy matrix allows for a simple extension of the notion of static indeterminacy to nonlinear analysis.

Simulations for predicting critical process variables in machining applications have been carried out for years. One important simulation-based analysis class in this context is the Finite Element Method (FEM). It is challenging to model the process with FEM as the metal is subjected to extensive deformation at high strain rates and temperatures. This large deformation is primarily irreversible and requires a plastic material model. The so-called orthogonal cutting process is a good abstraction of machining applications, where only a 2D representation is considered. It involves a tool cutting through a workpiece, forming chips. The shape of these chips is a crucial validation criterion for the accuracy of the simulation. One way to improve the representation of geometries in FEM simulations is to utilize Isogeometric Analysis (IGA), where the classical Lagrangian basis functions are replaced by the basis of Non-Uniform Rational B-Splines (NURBS). As these splines are commonly used for the representation of geometries in CAD models, IGA bridges the analysis with the initial design geometry.

The workpiece is modeled with a plastic material model, the Johnson-Cook hardening model, which includes a strain-rate dependency. Another crucial detail to model is the contact between the tool and the workpiece. In this work, we model the tool as a rigid B-Spline and employ a penalty contact formulation. Our focus is to investigate the influence of employing Isogeometric Analysis for the chip-forming process and the resulting chips. Furthermore, we compare the results to a classical FEM approach.