For structures, designed to withstand loading beyond their critical buckling load, the consideration of material damage that may occur within the post-critical response is necessary. Characteristic examples are composite and advanced structures, where either pre-existing damages or post-critical deformation represent the source of material damaging processes initiated within the post-critical response. Despite some work on path-following for nonlinear elastic systems being available within the research community, an extension to include material damage remains missing. The current work aims at closing this gap by developing a path-following solution algorithm that is capable of studying conventional elastic instability phenomena, such as tracing post-critical and critical subset paths for distinct and compound bifurcation phenomena, as well as determining and tracing damage initiation points and tracing post-critical paths associated with material damaging. The path-following solution algorithm is developed to facilitate semi-analytical model descriptions, with the governing functional, equilibrium equations and all damage growth conditions being determined symbolically. Characteristic elastic instability phenomena and interactions between structural instability with material damaging will be presented.

Lattice structures are increasingly favoured for their excellent strength-to-weight ratios, but they face the challenge of elastic buckling failure at low density. A novel type of lightweight and high-performance, collinear polymer lattice with the concept of stayed slender columns will be presented, which is fabricated through material extrusion additive manufacturing [1]. The buckling and post-buckling behaviour of perfect and imperfect stayed cells (UCs) and two-dimensional lattices are investigated analytically and experimentally.

The analytical study is performed reminiscent of [2] with a three degree of freedom system based on the general theory of elastic stability [3]. The Rayleigh-Ritz method is utilized to describe the deformation of the structure. The equilibrium states are calculated in a Python-based module "Pyfurc" [4]. Several deformation modes were analytically simulated to analyse their buckling behaviour. Parametric studies of perfect and imperfect systems are performed.

Uniaxial compression tests are conducted on the corresponding UCs and lattices to observe the buckling behaviour using digital image correlation.

The experimental and simulation results demonstrate that the ultimate loads of the UCs and lattices with stays are significantly increased compared to those without stays and that the load carrying capacity can be tuned with buckling-driven imperfections.

[1] Y. Ou, A. Köllner, A. Dönitz, T. Richter, and C. Völlmecke. "Material extrusion additive manufacturing of novel lightweight collinear stayed polymer lattices". In: International Journal of Mechanics Materials in Design (2024)

[2] Zschernack, C., Wadee, M. A., & Völlmecke, C. (2016). Nonlinear buckling of fibre-reinforced unit cells of lattice materials. Composite Structures, 136, 217-228.

[3] Thompson JMT, Hunt GW. A general theory of elastic stability. London: Wiley; 1973.

[4] pyfurc Documentation — pyfurc 0.2.3 documentation. 2023-01-12. url: https://pyfurc.readthedocs.io/en/latest/ (visited on 07/26/2023).

The crack propagation in layered materials is seen to grow in different ways. The kinking of the crack at the start of propagation or the deviation of the crack from its path are some cases identified as unstable crack propagation. The crack path stability primarily depends on the stress state near the crack tip. Based on the nature of stress, the crack path deviation is seen in the layered materials. The stress parallel to the crack surface, identified as T-stress, is responsible for different crack path trajectories (Cotterell, 1966). The effect of the nature of T-stress and the stress intensity factor on the crack path in layered materials is studied and shown in the literature. The crack path in the layered material can also travel in a wavy trajectory within the layer based on the competition between these two factors (Fleck, 1991). The crack path trajectory can also travel from one interface to another through a layer of adhesive. Symmetry plays an important role in the instability of crack propagation.

The study aims to portray the point of instability in the crack path in layered materials using the phase field approach. The effect of stress near the crack tip can be captured with the help of stress-based failure criteria (Miehe, 2015). This criterion will give a condition satisfying which the crack propagation will be seen.

Cotterell, B. (1966). NOTES ON THE PATHS AND STABILITY OF CRACKS. Int J Fract, 526–533.

Fleck, N. A. (1991). Crack path selection in a brittle adhesive layer. International Journal of Solids and Structures, 1683-1703.

Miehe, C. (2015). Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids. Computer Methods in Applied Mechanics and Engineering, 449-485.

The utilization of cold-formed steel (CFS) beams in moment-resisting frames (MRFs) has recently gained significant attention among researchers. It offers advantages such as lighter weight, cost-effectiveness, and faster construction. However, the CFS section is slender, making the members susceptible to buckling. Nevertheless, due to the low bending stiffness of the CFS sheet, it can be bent into any desired cross-section. Consequently, this capability allows for optimizing CFS cross-sections to improve structural performance. This study aims to improve the seismic performance of CFS flexural members by developing a methodology to obtain improved structural performance with enhanced non-linear post-peak behaviour. A detailed finite element (FE) model was developed using ABAQUS, considering material and geometric non-linearity. This model was subsequently validated with results available in the literature. A multi-objective genetic algorithm is linked to FE analysis to optimize the CFS cross-section to maximize moment capacity and ductility. Four cross-section prototypes were optimized, and the results were compared based on the Pareto front. Furthermore, based on simulation results, limit states of failure that cause the degradation of the stiffness and strength of the beam are identified. Additionally, seismic performance criteria such as energy dissipation and the effect of cyclic loading have been investigated.

Unlike current design approaches to local buckling of plates, which are based on empirical equations (e.g. the Winter equation or the Direct Strength equations), this research presents a novel analytical approach, focusing on outstand steel plates. The derivation of the method is rooted in the Föppl-von Karman equations, which are further simplified by making a number of basic mechanical assumptions about the post-buckling stress field reminiscent of the Vlasov assumptions. An approximate solution to the emerging differential equation is obtained, which assumes a polynomial displacement profile in the transverse direction of the plate. This solution agrees eminently well with the results of finite element simulations, both for the case of a geometrically perfect plate and a plate containing an initial imperfection. By combining the obtained post-buckling stress profile with a failure criterion based on von Karman’s effective width concept, a closed-form strength equation for compressed outstand plates is derived, which is seen to be a sole function of the plate slenderness and a dimensionless imperfection factor. This equation agrees closely with the available experimental data.