Elastic‐Wave Propagation in Chiral Metamaterials: A Couple‐Stress Theory Perspective
Shahin Eskandari, Wu Xu, Slight Chen, Bilen Emek Abali, Valérie Orsat, Abdolhamid Akbarzadeh
Abstract
Chiral metamaterials, lacking centrosymmetry at the unit cell level, exhibit acoustic activity and are promising candidates for elastic‐wave manipulation. For numerical analysis, their complex structures require substantial computational resources, making wave propagation simulations of chiral metamaterials challenging. Well‐known homogenization methods, based on the classical Cauchy continuum, fail to predict acoustic activity in chiral metamaterials. This failure is due to the use of even‐order material property tensors, which only account for centrosymmetric behavior, overlooking the intrinsic chirality and microrotations essential for tailored acoustic responses. In this study, augmented asymptotic homogenization based on couple‐stress theory (CST) is employed. The governing partial differential equations involve second‐ and fourth‐order spatial derivatives of displacements. Herein, their solution is demonstrated both analytically in a closed form for the low‐frequency range and numerically using COMSOL Multiphysics, employing the equation‐based module. The homogenized results are verified by comparing with band diagram and polarization rotation analysis results derived from conducting a computationally expensive detailed modelling. The analytical and numerical results are closely aligned with the predictions of the detailed modelling in the low‐frequency domain, indicating that asymptotic homogenization with CST offers an efficient and accurate method for predicting the acoustic activity of rationally designed chiral metamaterials.