Dynamic effective models of two-dimensional acoustic metamaterials with cylindrical inclusions

Based on analytical solutions of elastic waves scattered by a coated cylinder in an infinite elastic matrix, we construct the localization relations for averaged displacement and stress fields in each phase. Dynamic effective mass, in-plane bulk modulus and shear modulus are defined, respectively, as the ratio between the force and acceleration, bulk stress and bulk strain, maximum shear stress and maximum shear strain. Analytic expressions for dynamic effective parameters of two-dimensional acoustic metamaterials are derived. Numerical examples are given to analyze dynamic effective properties of composites with coated inclusions. It is demonstrated that the proposed model can predict negative values of effective mass and effective bulk and shear modulus, and discover the underlying mechanisms of negative effective material parameters. The proposed model will be helpful in designing new acoustic metamaterials.