Topology Optimization of Metamaterial Microstructures for Negative Poisson’s Ratio under Large Deformation Using a Gradient-Free Method

• DOI: 10.32604/cmes.2023.046670
• Publication Date: 2024-01-16T06:13:39Z
• Authors: Weida Wu; Yiqiang Wang; Zhonghao Gao; Pai Liu
• Keywords: Topology optimization; Homogenization; Poisson's ratio; Asymptotic homogenization

Negative Poisson's ratio (NPR) metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control energy absorption.However, when subjected to significant stretching, NPR designed under small strain assumption may experience a rapid degradation performance.To address this issue, study aims design maintaining targeted large by taking advantage of the geometry nonlinearity mechanism.A representative periodic unit cell is modeled considering nonlinearity, its topology using gradient-free method.The microstructural topologies described with material-field series-expansion (MFSE) MFSE method assumes spatial correlation material distribution, which greatly reduces number required variables.To conveniently desired deformation, we propose two-stage metamaterial optimization method, fully takes dimension reduction benefits Kriging surrogate model technique.Initially, use homogenization find preliminary assumption.In second stage, begin minimize deviations from value deformation.Using strategy solution technique, successfully obtain group that can sustain different NPRs range [-0.8, -0.1] uniaxial stretching up 20% strain.Furthermore, typical microstructure designs fabricated tested through experiments.The experimental results show good consistency our numerical results, demonstrating effectiveness present gradientfree strategy.