Thermodynamic topology optimization for hardening materials

TL;DR

This paper extends thermodynamic topology optimization to include hardening materials by developing a surrogate model for plastic strains, enabling better design of structures with non-linear material behavior.

Contribution

It introduces a novel surrogate model for plastic strains in topology optimization, accounting for hardening behavior in non-linear materials.

Findings

Model agrees with classic plasticity models under monotonic loading

Topology optimization results show significant structural changes due to hardening behavior

Demonstrates the importance of including hardening in structural design

Abstract

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.