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.