Evolution of a fibre-reinforced growing mixture

We consider a biological tissue that can be macroscopically modelled as a biphasic mixture composed of a fluid and a solid phase. The former is a multi-constituent fluid, and the latter consists of a deformable porous medium comprising matrix and fibre-like inclusions. Both phases are assumed to be composed of several constituents, and are allowed to experience exchange interactions. In response to these interactions, the solid phase may either grow or be absorbed. We assume that each of these behaviours leads to the development of material inhomogeneities. Material inhomogeneities are treated by enforcing Kroner's multiplicative decomposition of the solid-phase deformation gradient tensor, and introducing an inhomogeneity velocity "gradient". Through Onsager's principle, it is proven that inhomogeneity velocity "gradient" is related to the Mandel stress tensor of the solid phase, and chemical potentials of fluid constituents. This relation is used in order to show that, in response to growth (or adsorption), development of material inhomogeneities may trigger fibre reorientation in the solid phase by inducing the evolution in time of its texture tensor.