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
where
is the mass
density,
is the
wave velocity,
are functions in terms of the elastic constants and
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.