On wave propagation in porous media with strain gradient effects

A porous material with large irregular holes is here studied as a hyperelastic continuum with latent microstructure, and the mechanical balance equations are derived from the general ones for a medium with ellipsoidal microstructure. This is done by imposing the kinematical constraint of microstretch bounded to the macrodeformation: in this case, the microstructure disappears, apparently, and the response of the material involves higher gradients of the displacement without incurring known constitutive inconsistencies. An application to the propagation of asymptotic waves compatible with such a model is also considered. Physical situations corresponding to an axisymmetric motion either in spherical or cylindrical symmetry are considered, and it is shown that the time evolution of the wave amplitude factor is governed by the spherical and cylindrical Korteweg–deVries equations, respectively.