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

The crux 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.