Acceleration waves in the nonlinear micromorphic continuum

Within the framework of the nonlinear elastic theory of micromorphic continua we derive the conditions for propagation of acceleration waves. An acceleration wave, also called a wave of weak discontinuity of order two, can be treated as a propagating nonmaterial surface across which the second derivatives of the placement vector and micro-distortion tensor may undergo jump discontinuities. Here we obtain the acoustic tensor for the micromorphic medium and formulate the conditions for existence of acceleration waves. As examples we consider these conditions for the linear micromorphic medium and for the relaxed micromorphic model.