Unit Cell Synthesis for Design of Materials With Targeted Nonlinear Deformation Response

Abstract

A systematic unit cell synthesis approach is presented for designing metamaterials from a unit cell level, which are made out of linearly elastic constitutive materials to achieve tunable nonlinear deformation characteristics. This method is expected to serve as an alternative to classical Topology Optimization methods (solid isotropic material with penalization or homogenization) in specific cases by carrying out unit cell synthesis and subsequent size optimization (SO). The unit cells are developed by synthesizing elemental components with simple geometries that display geometric nonlinearity under deformation. The idea is to replace the physical nonlinear behavior of the target material by adding geometric nonlinearities associated with the deforming entities and thus, achieve large overall deformations with small linear strains in each deformed entity. A case study is presented, which uses the proposed method to design a metamaterial that mimics the nonlinear deformation behavior of a military tank track rubber pad under compression. Two unit cell concepts that successfully match the nonlinear target rubber compression curve are evaluated. Conclusions and scope for future work to develop the method are discussed.