The Role of Substrate Elastic Modulus in the Strain-Dependent Behavior of Electromagnetic Metamaterials: Analytic Description, Multiphysics Modeling, and Test Results

Metamaterial strain-dependent electromagnetic (EM) behavior is strongly influenced by its constituent materials. Metamaterials, like all composites, may exhibit complicated strain profiles when subjected to mechanical loading. At the unit cell level, the degree of non-uniformity in the strain profile is a function of loading, unit cell geometry, and the relative stiffness contributions of the composite’s constituent materials (in this case, copper conductive traces and a polymer dielectric substrate). Analytic expressions and multi-physics modeling are utilized to describe the relationship between substrate modulus, strain, and EM behavior. Testing was conducted to corroborate and validate the multi-physics models. An interesting result of this research is that depending upon the Elastic Modulus of the substrate, a consistent strain profile applied at the unit cell level can result in either a positive or negative shift in the metamaterial’s resonant frequency.