Unified gradient flow structure of phase field systems via a generalized principle of virtual powers

In this paper we introduce a general abstract formulation of a variational thermomechanical model by means of a unied derivation via a generalization of the principle of virtual powers for all the variables of the system, possibly including the thermal one. In particular, through a suitable choice of the driv- ing functional, we formally get a gradient ow structure (in a suitable abstract setting) for the whole nonlinear PDE system. In this framework, the equations may be interpreted as internal balance equations of forces (e.g., thermal or me- chanical ones). We prove a global in time existence of (a suitably dened weak) solutions for the Cauchy problem associated to the abstract PDE system as well as uniqueness in case of suitable smoothness assumptions on the functionals.