Conference Agenda

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.