Viscoelastodynamics of swelling porous solids at large strains by an Eulerian approach

A model of saturated hyperelastic porous solids at large strains is formulated and analyzed. The material response is assumed to be of a viscoelastic Kelvin--Voigt type, and inertial effects are considered, too. The flow of the diffusant is driven by the gradient of the chemical potential and is coupled to the mechanics via the occurrence of swelling and squeezing. Buoyancy effects due to the evolving mass density in a gravity field are covered. Higher-order viscosity is also included, allowing for physically relevant stored energies and local invertibility of the deformation. The whole system is formulated in a fully Eulerian form in terms of rates. The energetics of the model is discussed, and the existence and regularity of weak solutions is proved by a combined regularization-Galerkin approximation argument.