Wave velocity formulas to evaluate elastic constants of soft biological tissues

We use the equations governing infinitesimal motions superimposed on a finite deformation in order to establish formulas for the velocity of (plane homogeneous) shear bulk waves and surface Rayleigh waves propagating in soft biological tissues subject to uniaxial tension or compression. Soft biological tissues are characterized as transversely isotropic incompressible nonlinearly elastic solids. The constitutive model is given as an strain-energy density expanded up to fourth order in terms of the Green strain tensor. The velocity formulas are written as  ρv2=a0+a1e+a2e2 where ρ is the mass density, v is the wave velocity, ak are functions in terms of the elastic constants and ee is the elongation in the loading direction. These formulas can be used to evaluate the elastic constants since they determine the exact behavior of the elastic constants of second, third, and fourth orders in the incompressible limit.