Direct stress minimization in electro‐mechanical metamaterials

Abstract

AbstractMetamaterials are artificially created multiscale materials with many different applications [1]. We assume periodic microstructure. No specific length scale is demanded for the differentiation between the scales. Instead, we consider the microscale as consisting of repeating unit cells, whereas the macroscale is the scale, where desired and sometimes unusual physical effects occur. The precise arrangement and geometry at the microscale level is responsible for the macroscopic material behavior, which can substantially differ from the original components it is made from. This way, unique material properties otherwise not found in nature (e.g. negative refractive materials [2]) are possible. Most previous research regarding metamaterials concentrated only on a single physical branch in each case, e.g. electromagnetic or acoustic metamaterials [3,4].In this contribution we present a class of theoretical electro‐mechanical metamaterials by combining insulating and conducting materials. Our aim is to directly control and reduce the resulting total stress of insulating materials by counteracting the mechanical stress through the application of an electric field, which is created by a conducting material. The solution of the resulting minimization problem is related to the eigenvalues of the mechanical stress tensor. Additionally, we discuss the constrained cases of tension and compression and cover the plane stress case. We show numerical results for all cases and discuss the limits of such a material.