|The thermo-mechanical behaviour of (visco)elastic and special
materials is determined by the coexistence of different configurations
at the micro-scale, changing due to thermo-mechanical loads (as in the
case of degrading mechanical properties in quasi-brittle materials).
The continuum damage theory, introduced in the framework of
solid-solid phase transitions, turns out to perform a good description
of the evolving damage phenomenon in materials losing their stiffness.
In particular, an order parameter delineates the state of the cohesion
in the body. The resulting PDE system we investigate couples
thermo-mechanical actions and phase dynamics and it is strongly
nonlinear and possibly degenerating in the elliptic equations for deformations.
We discuss existence of a solution in the case of complete damage.
This problem is still open in its original formulation, but some
answer has been given for suitable weak notion of solutions.
We introduce a new notion of solution, accounting for a new "interior" stress which implicitly
accounts for the state of damage of the material and write an
appropriate free energy. We recover a new PDE system describing
complete damage and we show the existence of a weak solution.