Wave propagation in compressible hyperelastic solids in the presence of powerless internal forces

Although nonlinear elastodynamics has been widely studied since the second half of the last century, still nowadays, some aspects of this theory need a more systematic analysis. Based on the classical theory of simple materials of differential type and the results on the analytical form of constitutive models consistent with the laws of thermodynamics, we here analyze the wave propagation in compressible hyperelastic materials in the case in which the effects due to powerless internal forces are not negligible. We show that powerless internal forces affect the wave propagation in compressible hyperelastic solids by contributing to nonlinear wave dispersion and allowing the propagation of traveling waves.