A geometrical model for mechanical media described in the frame of extended irreversible thermodynamics with internal variables

In previous papers geometrical models were developed within the rational irreversible thermodynamics with internal variables. In this contribution we construct a general model for mechanical simple materials with internal variables in the framework of extended irreversible thermodynamics. In particular, we introduce in the thermodynamic state space the heat flux and internal variables of scalar, vectorial and tensorial type with their gradients. % Thus, we obtain a general formalism for this geometrical model and general results that can be applied in different types of mechanical media presenting internal defects, like dislocations, disclinations, porous channels, point defects and so on. For this purpose, we work out the dynamical system on the fibre bundle of the processes, and, introducing the transformations induced by the process, the entropy function and the entropy 1-form. The achievement of the entropy 1-form is the starting point to investigate an extended thermodynamical phase space. Finally, a geometrical model for porous media filled by a fluid flow is recalled as an example of the obtained general results