Mathematical Modelling of a Solid–Liquid Mixture with Mass Exchange Between Constituents

The mechanical behavior of a mixture composed by an elastic solid and a fluid that exchange mass is investigated. Both the liquid flow and the solid deformation depend on how the solid phase has increased (di-minished) its mass, i.e. on the mass conversion between constituents. The model is developed introducing a decomposition of the solid phase deformation gradient. In particular, exploiting the criterion of maximiza-tion of the rate of dissipation, we determine an explicit evolution equation for the so–called growth tensor which involves directly the solid stress ten-sor. An example of a possible choice of the constitutive functions is also presented