Third- and fourth-order constants of incompressible soft solids and the acousto-elastic effect

• Published in: The Journal of the Acoustical Society of America Vol. 127; no. 5; pp. 2759 - 2763
• Main Authors: Destrade, Michel, Gilchrist, Michael D., Saccomandi, Giuseppe
• Format: Journal Article
• Language: English
• Published: Melville, NY Acoustical Society of America 01.05.2010; American Institute of Physics
• Subjects: Acoustics; Blocking; Constants; Density; Elastic Modulus; Elasticity; Elastodynamics; Elongation; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Linear Models; Models, Theoretical; Motion; Nonlinear acoustics, macrosonics; Nonlinear Dynamics; Physics; Sound; Sound waves; Wave propagation; Soft tissue; Incompressible material; Non linear elasticity; Non linear acoustics
• ISSN: 0001-4966; 1520-8524; 1520-9024; 1520-8524
• DOI: 10.1121/1.3372624

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.