#### Vol. 8, No. 1, 2013

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Wave velocity formulas to evaluate elastic constants of soft biological tissues

### Pham Chi Vinh and Jose Merodio

Vol. 8 (2013), No. 1, 51–64
##### Abstract

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 $\rho {v}^{2}={a}_{0}+{a}_{1}e+{a}_{2}{e}^{2}$ where $\rho$ is the mass density, $v$ is the wave velocity, ${a}_{k}$ are functions in terms of the elastic constants and $e$ 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.

##### Keywords
incompressible transversely isotropic elastic solids, soft biological tissues, shear bulk waves, Rayleigh waves, wave velocity, elastic constants