Modeling of nonlinear shear waves in soft solids

Abstract

An evolution equation for nonlinear shear waves in soft isotropic solids is derived using an expansion of the strain energy density that permits separation of compressibility and shear deformation. The advantage of this approach is that the coefficient of nonlinearity for shear waves depends on only three elastic constants, one each at second, third, and fourth order, and these coefficients have comparable numerical values. In contrast, previous formulations yield coefficients of nonlinearity that depend on elastic constants whose values may differ by many orders of magnitude because they account for effects of compressibility as well as shear. It is proposed that the present formulation is a more natural description of nonlinear shear waves in soft solids, and therefore it is especially applicable to biomaterials like soft tissues. Calculations are presented for harmonic generation and shock formation in both linearly and elliptically polarized shear waves.