Acoustoelasticity and the elastic constants of the soft biological tissues

We analyze the acoustoelastic study of material moduli that appear in the constitutive relations that characterize the response of anisotropic nonlinearly elastic bodies, in particular, materials reinforced with one set of fibers along one direction. Studies dealing with acoustoelastic coefficients in incompressible solids modeled by means of strain-energy density functions expanded up to different orders in terms of the Green strain tensor can be found in the literature. In this paper, we connect that analysis and the parallel one developed from the general theory of nonlinear elasticity which is based on strain energies that depend on the right Cauchy–Green deformation tensor. Establishing this relation explicitly will improve understanding of the mechanical properties of soft biological tissues among other materials.