Topology optimization is an important basis for the design of components. Here, the optimal structure is found within a design space subject to boundary conditions. Thereby, the specific material law has a strong impact on the final design. An important kind of material behavior is hardening: then a, for instance, linear-elastic structure is not optimal if plastic deformation will be induced by the loads. Since hardening behavior has a remarkable impact on the resultant stress field, it needs to be accounted for during topology optimization. In this contribution, we present an extension of the thermodynamic topology optimization that accounts for this non-linear material behavior due to the evolution of plastic strains. For this purpose, we develop a novel surrogate model that allows to compute the plastic strain tensor corresponding to the current structure design for arbitrary hardening behavior. We show the agreement of the model with the classic plasticity model for monotonic loading. Furthermore, we demonstrate the interaction of the topology optimization for hardening material behavior results in structural changes.

翻译：拓扑优化是构件设计的重要基础。在满足边界条件的设计空间内，可找到最优结构。其中，特定的材料本构关系对最终设计具有显著影响。硬化是一种重要的材料行为：当载荷会引发塑性变形时，例如线性弹性结构便不再是最优设计。由于硬化行为对应力场具有显著影响，拓扑优化过程中必须予以考虑。本文提出了一种热力学拓扑优化的扩展方法，该方法能够处理因塑性应变演化导致的非线性材料行为。为此，我们开发了一种新型替代模型，可在任意硬化行为下计算与当前结构设计相对应的塑性应变张量。我们验证了该模型与单调加载条件下经典塑性模型的一致性。此外，我们展示了针对硬化材料行为的拓扑优化与结构变化之间的相互作用。