One‐Dimensional Wave Propagation in Transversely Isotropic Viscoelastic Materials

The propagation of transverse waves in an anisotropic elastic solid is investigated both in the presence and absence of viscous effects. After discussing in detail the appropriate mathematical models for transversely isotropic viscoelastic materials, we have studied the propagation of bulk shear waves. In particular, we have investigated the break of simple waves and the admissibility of shocks when dissipative effects are negligible, and have provided conditions on the existence of kinks waves (also known as viscous shocks) when dissipation has to be taken into account. Particular attention has been paid also to the propagation of small but finite amplitude waves within the fourth-order weakly nonlinear theory of viscoelasticity.