Large strain viscoelastic swelling of charged hydrated porous media

Abstract

Currently, most models that describe the swelling behaviour of soft biological tissues or artificial hydrogels are restricted either to small strains or to finite but purely elastic skeleton deformations. In fact, these types of charged hydrated materials undergo large viscoelastic deformations, where the porous meshwork formed by protein or polymer compounds exhibits so-called intrinsic viscoelastic properties (Hayes & Bodine 1978; Mak 1986). These flow-independent viscoelastic effects are strongly coupled with the dissipative phenomena resulting from the interstitial fluid flow (Ehlers & Markert 2001) and the electrochemical (osmotic and electrostatic) swelling mechanisms (Lai et al. 1991; Huyghe & Janssen 1997). Following this, it is the goal of this contribution to merge the advances of finite viscoelasticity laws and the state-of-the-art in electrochemical swelling theories within a well founded multiphasic concept. In particular, we proceed from the macroscopic Theory of Porous Media (TPM), where an extended Ogden-type viscoelasticity formulation is embedded accounting for the large strain behaviour of the charged molecular meshwork. As usual, this materially incompressible solid meshwork is assumed to be saturated by an incompressible interstitial fluid which itself is an ideal mixture composed of a liquid solvent (water) and dissolved electrolytes (mobile anions and cations). Excluding chemical reactions and restricting the presentation to the quasi-static case and monovalent electrolytes (here: Na+ Cl−), the model equations are expressed in terms of three primary variables, namely the solid displacements u S , the effective pore-fluid pressure (hydraulic and osmotic) p and the salt concentration cm of the interstitial fluid. Thus, allowing for an efficient numerical treatment within the finite element method (FEM), even large 3-dimensional problems can be solved at suitable computational costs.