Intra-extrafibrillar mixture formulation of soft charged hydrated tissues

The volume of the intrafibrillar water space – i.e. the water contained inside the collagen fibers – is a key parameter that is relevant to concepts of connective tissue structure and function. Because existing theories of finite deformation of cartilaginous tissues do not distinguish between intra- and extrafibrillar water, we derive a chemo-electro-mechanical formulation of quasi-static finite deformation including such distinctions. The model features a porous solid saturated with two fluid compartments, in which an arbitrary number of solutes are dissolved. Each fluid compartment has its own fixed charge density. Incompressible deformation is assumed. Each fluid compartment is assumed to be locally electroneutral. Balance laws are derived for each constituent and for the mixture as a whole. A Lagrangian form of the second law of thermodynamics for incompressible porous media is used to derive the constitutive restrictions of the medium. The material properties are shown to be contained in one strain energy function and a matrix of friction tensors. The formulation is consistent with the experimental finding (Maroudas et al., 1991) that the intrafibrillar water content is regulated by the osmotic pressure gradient between the extra- and intrafibrillar compartments.