The influence of the choice of a constitutive relation in the modelling of the wave propagation in pre-stressed medium

Abstract eng:
The most common constitutive relation in acoustoelasticity is the second-order constitutive relation expressed in terms of the Green-Lagrange strain tensor. The wave velocities in isotropic elastic media for the case of homogeneous pre-stress were derived by Hughes and Kelly (1953). This material model is characterized by the high sensitivity of material parameters to the small measurement errors. This rather bad property leads to the proposal of another material model with the second-order constitutive relation expressed in terms of the logarithmic strain tensor. For this material model the acoustic wave velocities were derived for three different types of homogeneous pre-stress.

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