  The paper is devoted to the study of a mathematical model for the
thermomechanical evolution of metallic shape memory alloys. The main novelty of
our approach consists in the fact that we include the possibility for these
materials to exhibit voids during the phase change process. Indeed, in the
engineering paper has been recently proved that voids may appear when the
mixture is produced by the aggregations of powder. Hence, the composition of
the mixture varies (under either thermal or mechanical actions) in this way:
the martensites and the austenite transform into one another whereas the voids
volume fraction evolves. The first goal of this contribution is hence to state
a PDE system capturing all these modelling aspects in order then to establish
the well-posedness of the associated initial-boundary value problem.
