On the thermodynamic consistency of the equivalence principle in continuum damage mechanics

We consider theories of continuum damage mechanics involving damage effect variables of different tensorial ranks. It turns out that orthotropic damage together with the use of Lemaitreʹs equivalence principle for the elastic part does not allow thermodynamic potentials such as the free enthalpy to exist. As the existence of these potentials is, however, a strict thermodynamic requirement, a theory employing orthotropic damage in this way is inconsistent. We show that the use of a rank-4 damage effect variable allows a consistent use of the equivalence principle.