An effective design method for mechanical metamaterials with negative Poisson’s ratios

EasyChair Preprint 407

Abstract

In this paper, we propose a new method for the design of mechanical metamaterials by integrating the parametric level set method (PLSM) with the energy-based homogenization method (EBHM), where the topologies and shapes of material microstructures periodically distributed in the bulk material are optimized simultaneously. Firstly, material effective properties are evaluated by the EBHM under the topologies of material microstructures, where the average stress and strain theorems work as the basic theoretical framework rather than the asymptotic theory. Secondly, under the definition of the objective to seek for the negative Poisson’s ratios, the PLSM is employed to evolve the topologies of microstructures until the bulk material is to be featured with negative Poisson’s ratios. Several numerical examples for microstructures considering the orthotropy and isotropy are performed. A series of new and interesting material cells with negative Poisson’s ratio are obtained.

Keyphrases: Metamaterials, Parametric level set method, homogenization method, topology optimization

@booklet{EasyChair:407,
  author    = {Jie Xu and Hao Li and Mi Xiao and Liang Gao},
  title     = {An effective design method for mechanical metamaterials with negative Poisson’s ratios},
  doi       = {10.29007/3rjw},
  howpublished = {EasyChair Preprint 407},
  year      = {EasyChair, 2018}}