Topology optimization methods based on nonlinear and dynamic crash simulations

Topology optimization for crashworthiness has been investigated during the last years, starting from methods based on linear elastic and static simulations or so-called equivalent static loads (ESL) obtained by a single nonlinear crash simulation with a subsequent optimization loop based on the linear stiffness matrix and the corresponding sensitivities. Both methods do not consider material nonlinearities in their optimization process, which are essential for structural components designed for energy absorption, although it is well-known that plasticity and failure play an important role. As alternative, optimization methods have been proposed, which use fully nonlinear and dynamic crash simulations. The first method, presented for example in Patel’s PhD thesis, is based on a hybrid cellular automata approach (HCA) and derives optimal structures using a homogenized energy density approach where each finite element (cell) is modified until the highest degree of homogeneity is achieved. Because this is not fully appropriate for thin-walled structures, Hunkeler modified the approach (HCA-TWS – Hybrid Cellular Automata for Thin-walled Structures) such that deformation energy is only homogenized between larger structural entities (i.e. thin ribs / walls). The most recent method, the EA-LSM, a combined level set method (LSM) and evolutionary approach, was then proposed by Bujny et al. where more appropriate objectives and constraints can be used with the drawback of higher computational costs. In this paper, the latest results for HCA-TWS and EA-LSM will be presented. Special focus is here the investigation of the influence of different material models for plasticity. Examples are inspired by recent material model developments for magnesium alloys with a characteristic anisotropy in the plasticity model. As a result, it is shown that the optimal topologies depend on the material model and that it is necessary to use nonlinear and dynamic finite elements for crash topology optimization.