On the influence of internal degrees of freedom on dispersion in microstructured solids

In the present paper a model describing wave propagation in the nonlinear dispersive media with microstructure is investigated. The model is based on the continuum approach following Mindlin's and Eringer's earlier theories which model a microstructure as a deformable cells in a macrostructure assuming that the deformation gradient is small. A generalized version of the Mindlin model called the Mindlin–Engelbrecht–Pastrone model (MEP) is used. The MEP model is solved numerically using the pseudospectral method and localized initial conditions together with periodic boundary conditions. The main focus of the study is on clarifying the influence of internal degrees of freedom of a microstructure on solutions.