Elastic nonlinearities and wave distortion in heterogeneous materials containing constrained negative stiffness inclusions

This paper demonstrates the enhancement of acoustic nonlinearities in a heterogeneous elastic material consisting of negative stiffness metamaterial structures embedded in an isotropic linear elastic matrix. Standard formulations of nonlinear elasticity are employed to determine the effective isotropic nonlinear bulk modulus of the composite. Acoustic parameters of nonlinearity, which characterize the distortion of a propagating acoustic wave through this heterogeneous material, are determined by relating the bulk modulus to the nonlinear equation of state. The effects of varying the values of the inclusion and matrix parameters are presented and discussed.