A framework for deformation, generalized diffusion, mass transfer and growth in multi-species multi-phase biological tissues

In previous works, the authors have addressed the chemo-mechanical couplings that control much of the behaviour of many geological materials and biological tissues. The analyses accounted for deformation, mass transfer and generalized diffusion. Simulations of initial and boundary value problems involving equilibrium and transient ionic replacements have been performed via the finite element method. The thermodynamic framework underlying these developments has not been published yet and it is described here. ux of the paper is to aggregate the phenomenon of growth to the previous models. For that purpose, the mixture system is considered thermodynamically open. The contributions, by the surroundings, to the balances of mass, momentum, energy and entropy of each species of the mixture, and of the mixture as a whole, are systematically accounted for. Previous studies in single phase solids have ensured satisfaction of the balance equations, but they developed growth laws separately from the thermodynamics, and failed to satisfy the Clausius–Duhem inequality. Using the continuum thermodynamics of irreversible processes in a mixture context, we show here, for the first time, how satisfaction of the Clausius–Duhem inequality motivates and structures the growth law.