Stress-constrained Topology Optimization for Metamaterial Microstructure Design

TL;DR

This paper develops a topology optimization framework incorporating local stress constraints for designing metamaterial microstructures, including under cyclic loading, to improve mechanical performance and avoid stress concentrations.

Contribution

It introduces an augmented Lagrangian method for multi-constraint topology optimization of metamaterials, extending to cyclic loading conditions.

Findings

Effective stress-constrained microstructure designs demonstrated in 2D and 3D benchmarks.

The framework successfully avoids stress concentrations in optimized metamaterials.

Designs under cyclic loading show improved durability and performance.

Abstract

Although stress-constrained topology optimization has been extensively studied in structural design, the development of optimization frameworks to enable the creation of metamaterials with optimal mechanical performance is still an open problem. This study incorporates local stress constraints into the topology optimization framework for metamaterial microstructure design, aiming to avoid the stress concentration in the optimized microstructure. For the efficient solution of multi-constraint topology optimization problems, the Augmented Lagrangian formulation is extended to address local minimization problems subjected to the combined action of local and global constraints. Additionally, as an extension of static load conditions, this study further investigates the design of metamaterial microstructures under cyclic loading. Finally, the effectiveness of the proposed approach is demonstrated through a series of two-dimensional and three-dimensional benchmark problems.