Second-order effects on the wave propagation in finite elasticity

In this paper, for arbitrary sufficiently small deformations, the propagation of the acceleration waves in isotropic and homogeneous materials is discussed in the contest of second–order elasticity by using a perturbation method. This method allows us to determine the first-order terms of the speeds as well as the amplitudes both of the principal waves and the waves in any arbitrary direction of propagation, when the undisturbed region is subjected to an arbitrary deformation. Finally, some numerical results are presented in some conventional Mooney-Rivlin materials.