Dynamic equations of acoustic wave propagation in pre-deformed materials

Two approaches to obtaining dynamic equations for the propagation of displacement small disturbances are considered. These approaches are based on the use of models of hyperelastic and hypoelastic materials. We showed that these equations are interrelated. For the case of a plane monochromatic wave, expressions of acoustic tensors are obtained. A comparative analysis of the effect of preliminary deformations on the propagation velocity of acoustic waves in isotropic and anisotropic materials is carried out. In the model of a hypoelastic material, the acoustic tensor depends on a nonholonomic measure of finite deformations. A nonholonomic measure of deformations is defined in such a way that its first invariant does not change during shape change, and the deviator does not depend on volumetric deformations. In this regard, the use of a hypoelastic material model allows us to obtain more reliable results when calculating phase velocities in an isotropic material with preliminary deformation.