Title: An effective design method for mechanical metamaterials with negative Poisson's ratios

Authors: Jie Xu; Mi Xiao; Hao Li; Liang Gao

Addresses: State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China ' State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China ' State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China ' State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China

Abstract: This paper proposes an effective method for the design of mechanical metamaterials by combining the parametric level set method (PLSM) with the energy-based homogenisation method (EBHM), where the topologies and shapes of microstructures periodically distributed in the material with negative Poisson's ratios are optimised simultaneously. Firstly, the effective properties of the materials are calculated by the EBHM under the topologies of microstructures, where the stress and strain theorems work as the basic theoretical framework rather than the asymptotic theory. Secondly, under the definition of the objective function to seek for the negative Poisson's ratio, the PLSM is used to evolve the topological configurations of microstructures until the bulk material is to be featured with a negative Poisson's ratio. Thirdly, the discrete wavelet transform (DWT) is utilised to deal with the full matrix of the globally supported radial basis function (GSRBF) interpolation. The proposed method can efficiently design the microstructure with the negative Poisson's ratio on the premise of ensuring the calculation accuracy. Several numerical examples are provided to illustrate the effectiveness of the proposed method for design of microstructures considering the orthotropy and isotropy. [Submitted 31 August 2019; Accepted 26 November 2019]

Keywords: metamaterials; topology optimisation; parametric level set method; PLSM; energy-based homogenisation method; EBHM; discrete wavelet transform; DWT.

DOI: 10.1504/IJMR.2021.117902

International Journal of Manufacturing Research, 2021 Vol.16 No.3, pp.309 - 324

Received: 31 Aug 2019
Accepted: 26 Nov 2019
Published online: 04 Oct 2021 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article