. . . . . . . . . . . . . . . . . . . . . . . . . "The acoustoelastic effect is how the sound velocities (both longitudinal and shear wave velocities) of an elastic material change if subjected to an initial static stress field. This is a non-linear effect of the constitutive relation between mechanical stress and finite strain in a material of continuous mass. In classical linear elasticity theory small deformations of most elastic materials can be described by a linear relation between the applied stress and the resulting strain. This relationship is commonly known as the generalised Hooke's law. The linear elastic theory involves second order elastic constants (e.g. and ) and yields constant longitudinal and shear sound velocities in an elastic material, not affected by an applied stress. The acoustoelastic effect on the other hand inc"@en . . . . . . . . . . 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"Acoustoelastic effect"@en . . . . . . "38390513"^^ . . . . . . . . . "The acoustoelastic effect is how the sound velocities (both longitudinal and shear wave velocities) of an elastic material change if subjected to an initial static stress field. This is a non-linear effect of the constitutive relation between mechanical stress and finite strain in a material of continuous mass. In classical linear elasticity theory small deformations of most elastic materials can be described by a linear relation between the applied stress and the resulting strain. This relationship is commonly known as the generalised Hooke's law. The linear elastic theory involves second order elastic constants (e.g. and ) and yields constant longitudinal and shear sound velocities in an elastic material, not affected by an applied stress. The acoustoelastic effect on the other hand include higher order expansion of the constitutive relation (non-linear elasticity theory) between the applied stress and resulting strain, which yields longitudinal and shear sound velocities dependent of the stress state of the material. In the limit of an unstressed material the sound velocities of the linear elastic theory are reproduced. The acoustoelastic effect was investigated as early as 1925 by Brillouin. He found that the propagation velocity of acoustic waves would decrease proportional to an applied hydrostatic pressure. However, a consequence of his theory was that sound waves would stop propagating at a sufficiently large pressure. This paradoxical effect was later shown to be caused by the incorrect assumptions that the elastic parameters were not affected by the pressure. In 1937 Francis Dominic Murnaghan presented a mathematical theory extending the linear elastic theory to also include finite deformation in elastic isotropic materials. This theory included three third-order elastic constants , , and . In 1953 Huges and Kelly used the theory of Murnaghan in their experimental work to establish numerical values for higher order elastic constants for several elastic materials including Polystyrene, Armco iron, and Pyrex, subjected to hydrostatic pressure and uniaxial compression."@en . . . "42502"^^ . . . . . . . . . . . . . . . .