Wave propagation in solids with vectorial microstructures

The goal of this article is to provide different frameworks to the study of the wave propagation in complex elastic solids, namely, the singular surfaces method, the asymptotic analysis and the hierarchy of waves. A new point of view for the model of vectorial microstructures is given, and one-dimensional models (widely studied in the literature) are briefly presented. In the last part a two-dimensional non-dissipative model is analyzed in detail using the “slaving principle” and the Jacobi elliptic functions.