Open Access

ARTICLE

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

Weida Wu, Yiqiang Wang, Zhonghao Gao, Pai Liu^*

State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

* Corresponding Author: Pai Liu. Email:

(This article belongs to the Special Issue: Structural Design and Optimization)

Computer Modeling in Engineering & Sciences 2024, 139(2), 2001-2026. https://doi.org/10.32604/cmes.2023.046670

Received 10 October 2023; Accepted 10 November 2023; Issue published 29 January 2024

Abstract

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

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Keywords

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