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

Abstract

A model of saturated hyperelastic porous solids at large strains is formulated and analysed. 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.

A Cahn–Hilliard phase field model coupled to an Allen–Cahn model of viscoelasticity at large strains

“…Hence, the main state variable for elasticity is the velocity field, and the deformation gradient, entering in the elasticity constitutive assumptions, is determined solving a transport equation in terms of the velocity and the velocity gradient. A similar modelling approach for evolutionary models with finite viscoelasticity was implemented also in [3], which studies the Oldroyd-B model for a dilute polymeric fluid, in [8], which studies the motion of a class of incompressible heat-conducting viscoelastic rate-type fluids with stress-diffusion, in [4,12], which study problems in magnetoelasticity, in [20], which studies an evolutionary non-isothermal viscoelastic problem, and in [22], which studies the diffusion of a solvent in a saturated hyperelastic porous solid of viscoelastic Kelvin-Voigt type at large strains.…”