|
The acoustoelastic effect describes 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.〔Brillouin, L., "Les tensions de radiation; leur interprétation en mécanique classique et en relativité", J. Phys. Radium, (1925)〕 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 paradoxial effect was later shown to be caused by the incorrect assumptions that the elastic parameters where not affected by the pressure.〔Tang, S., "Wave propagation in initially-stressed elastic solids", Acta Mechanica, (1967)〕 In 1937 Murnaghan 〔Murnaghan, F., "Finite Deformations of an Elastic Solid", American Journal of Mathematics, (1937)〕 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 〔Huges, D. S., Kelly, J. L., "Second-Order Elastic Deformation of Solids", Physical Review, (1953)〕 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. == Non-linear elastic theory for hyperelastic materials == The acoustoelastic effect is an effect of finite deformation of non-linear elastic materials. A modern comprehensive account of this can be found in.〔Ogden, R. W., "Non-linear elastic deformations", Dover publications Inc., Mineola, New York, (1984)〕 This book treats the application of the non-linear elasticity theory and the analysis of the mechanical properties of solid materials capable of large elastic deformations. The special case of the acoustoelastic theory for a compressible isotropic hyperelastic material, like polycrystalline steel, is reproduced and shown in this text from the non-linear elasticity theory as presented by Ogden.〔 :Note that the setting in this text as well as in 〔 is isothermal, and no reference is made to thermodynamics. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「acoustoelastic effect」の詳細全文を読む スポンサード リンク
|