In view of future applications in brain mechanics, I also became interested in finite-strain models of soft poroelastic solids (Biot-Coussy mixture theory). In this context, I studied the propagation of plane waves in incompressible fluid saturated porous media. The analysis highlights the existence of a nonlinear poroelastic compression wave, and the evolution of corresponding nonlinear acceleration waves is described. The main result is that the speed of poroelastic P-waves is similar to that of skeleton-supported S-waves (Figure). However, the poroelastic wave follows a nonlinear evolution, while shear waves evolve in a quasi linearly degenerate fashion, see the article in the Proceedings of the Royal Society A (2021) link. Ongoing works are of computational nature.