Stress-constrained Topology Optimization for Metamaterial Microstructure Design

2026-02-23

AI Summary

This study addresses the issue of stress concentration in metamaterial microstructure topology optimization, which commonly arises from the neglect of local stress constraints. To resolve this, the work systematically incorporates local stress constraints for the first time and extends the augmented Lagrangian method to simultaneously handle multiple local and global constraints under both static and cyclic loading conditions. The proposed approach effectively balances mechanical performance with structural safety, successfully generating two- and three-dimensional metamaterial microstructures that exhibit superior performance without stress concentrations. This advancement significantly enhances the applicability and reliability of topology optimization under realistic engineering loading scenarios.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Local Search
• Machine Learning: Optimization

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• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

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.

Problem

• stress-constrained
• topology optimization
• metamaterial
• microstructure design
• stress concentration

Innovation

• stress-constrained topology optimization
• metamaterial microstructure
• Augmented Lagrangian method
• local stress constraints
• cyclic loading