Acceleration waves in media with microstructure

Within the unified approach to modelling of media with microstructure we discuss the propagation of acceleration waves. We describe a medium with microstructure as an elastic continuum with strain energy density which depends on deformations and additional internal variable and their first gradients. We use a Nth-order tensor as a kinematical descriptor of the microstructure. By acceleration wave we mean an isolated surface propagating in medium across which second derivatives of some fields undergo discontinuity jump. Here we formulate the conditions of existence of acceleration waves as algebraic inequality expressed using acoustic tensor.