Third- and fourth-order constants of incompressible soft solids and the acousto-elastic effect.
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 ρv(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: ρv(2) = a+be+ce(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.
School of Electrical, Electronic, and Mechanical Engineering, University College Dublin, Belfield, Dublin 4, Ireland.
Michel
M
Destrade
Michael D
MD
Gilchrist
Giuseppe
G
Saccomandi
D000162:Acoustics; D055119:Elastic Modulus; D016014:Linear Models; D008962:Models, Theoretical; D009038:Motion; D017711:Nonlinear Dynamics; D013016:Sound