Thermodynamic topology optimization for hardening materials

TL;DR

The work extends thermodynamic topology optimization to hardening materials by coupling an extended Hamilton-functional formulation with a novel non-dissipative surrogate for plastic strains. A SIMP-based density interpolation and a parabolic density evolution equation enable simultaneous optimization of topology and microstructure under arbitrary hardening behavior, without path dependence for monotonic loading. validated against classic elasto-plastic models, the surrogate reproduces monotonic hardening behavior and reveals substantial differences in optimal structures compared with purely elastic designs, while achieving significant computational efficiency through a neighbored element method. The approach supports efficient, physics-informed design of components with realistic material hardening, facilitating rapid exploration of material choices and hardening profiles in engineering practice.

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.

Figures (15)

• Figure 1: Flowchart of the proposed numerical implementation of the thermodynamic topology optimization including hardening materials.
• Figure 2: Overview of investigated material behavior: elastic and different types of hardening including models.
• Figure 3: Overview of the decision criteria for microstructural update cases using the surrogate model with non-hardening. No hysteresis occurs due to the motivation of the model, i. e., vanishing dissipation function.
• Figure 4: Material point curve of the surrogate model and the classic elasto-plastic model for non-hardening materials and ideal plasticity, respectively. The new idea about the surrogate model is the "virtual" unloading with no hysteresis compared to the physical unloading.
• Figure 5: Comparing the classic and the surrogate model by a FEM simulation on a given structure which is loaded in 100.0 steps to the maximum load of $\boldsymbol{u}=-0.05mm$ accounting for different hardening characteristics shows very small differences in the plastic strains.