SOLUZIONI VISCO-ENERGETICHE PER PROBLEMI DI EVOLUZIONE RATE-INDEPENDENT

In the thesis we describe the new notion of Visco-Energetic solutions to rate-independent systems (X, E, d) driven by a time dependent energy E and a dissipation quasi-distance d in a general metric-topological space X. As for the classic Energetic approach, solutions can be obtained by solving a modified time Incremental Minimization Scheme, where at each step the dissipation (quasi-)distance d is incremented by a viscous correction (e.g. proportional to the square of the distance d), which penalizes far distance jumps by inducing a localized version of the stability condition. We prove a general convergence result and a typical characterization by Stability and Energy Balance in a setting comparable to the standard energetic one, thus capable to cover a wide range of applications. Some of these applications, such as the evolution of Allen-Cahn energies and of some elastic material driven by noncovex energies, are included in the thesis and are explained in full details.