Third- and fourth-order constants of incompressible soft solids and the acousto-elastic effect - Destrade, Michel; Gilchrist, Michael D.; Saccomandi, Giuseppe (The Journal of the Acoustical Society of America, 2010)
Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination of third- and fourth-order elastic constants, especially in the case of incompressible isotropic soft solids, where the expressions are particularly simple. Specifically, it is simply a matter of expanding the expression for ρ v 2 , where ρ is the mass density and v the wave speed, in terms of the elongation e of a block subject to a uniaxial tension. The analysis shows that in the resulting expression: ρ v 2 = a + b e + c e 2 , say, a depends linearly on μ ; b on μ and A ; and c on μ , A , and D , the respective second-, third, and fourth-order constants of incompressible elasticity, for bulk shear waves and for surface waves.