A continuum chemoporomechanical formulation for swelling and phase transitions in highly hydrated biological tissues

We develop a continuum chemo–poro–mechanical formulation for the description of swelling and phase-transition phenomena in highly hydrated fiber-reinforced biological tissues, exemplified by the vitreous body of the eye. Unlike many finite-strain swelling theories, where swelling is introduced through a prescribed multiplicative decomposition of the deformation gradient, the present formulation regards solvent concentration as an independent thermodynamic field variable coupled to the volumetric deformation through a hydration constraint. Within the framework of hybrid mixture theory, the governing equations are derived systematically from the Principle of Virtual Power in the presence of constraints and completed by thermodynamically consistent constitutive prescriptions obtained from the dissipation inequality. The proposed framework combines in a unified continuum formulation anisotropic elasticity associated with collagen fibrils, solid-solvent mixing, dissipative solvent transport, and gradient-enhanced interfacial energetics. The gradient contribution allows the description of localized hydration heterogeneities and diffuse transitions between gel-rich and fluid-rich regions, providing a continuum representation of liquefaction phenomena. The resulting governing equations naturally include an extended Darcy’s law in which fluid transport is driven by the difference between hydrostatic pressure and chemical potential. The formulation is specialized to the case of free swelling in simple geometries, where analytical asymptotic solutions are derived and compared with numerical simulations. The proposed framework provides a continuum-mechanical basis for investigating swelling, hydration heterogeneities, and localized liquefaction in the vitreous body and, more generally, in highly hydrated biological tissues.