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B. Werner, M. Todt, H. E. Pettermann:
"Nonlinear finite element study of beams with elasto-plastic damage behavior in the post-buckling regime";
Vortrag: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Vienna; 18.02.2019 - 22.02.2019.

Lattice materials can be described as arrangements of rigid-jointed beams. Loads on the macroscopic level of the lattice material can cause a loss of structural stability on the microscopic level and therefore, the buckling of beams. In this study the post-buckling behavior of beams with elasto-plastic material properties and ductile damage is investigated with the finite element method to reveal the effect of progressing damage and localization on the post-buckling deformation. The aim is to find a proper discretization to predict damage and localization sufficiently accurate for varying buckling modes. At the same time it has to be computational inexpensive enough to investigate the macroscopic response. The macroscopic response is usually determined by analysing large sections of the lattice material and by modeling the microstructure explicitly. The present study also includes the investigation of the mesh dependency. To determine a proper discretization the beam element type, the number of elements, the number of section points, as well as the boundary conditions are varied in the numerical analyses. The results are compared to a reference solution from a simulation with a much finer discretization. The applied elasto-plastic material with ductile damage is characterized by perfect plasticity and a very early onset of damage. The damage leads to localization and a rapid decline of the reaction forces. The predicted deformations deviate from the initial eigenmode shapes with progressing damage and localization. Based on the presented results the macroscopic behavior of damaged lattice materials can be investigated in future studies.