On the dynamics of non-linear viscoelastic solids with material moduli that depend upon pressure

We investigate the dynamic response, of a generalization of an incompressible Kelvin–Voigt viscoelastic solid, whose viscosity depends on the pressure. Bodies with pressure-dependent material moduli have relevance to numerous technologically significant problems in geomechanics, the mechanics of granular media and powder compaction. We obtain analytical results for creep and recovery phenomena as well as solutions to the propagation of waves in such bodies. We are able to obtain explicit exact solutions that clearly illustrate the marked difference in the response of bodies with pressure-dependent material moduli as opposed to their counterparts whose moduli do not depend on the pressure. We also show that the governing equations for such materials can change type, and that their solutions exhibit singularities and localization.