Quasi-static rate-independent evolutions: characterization, existence, approximation and application to fracture mechanics∗. (4th August 2014) - Negri, Matteo
Abstract : We characterize quasi-static rate-independent evolutions, by means of their graph parametrization, in terms of a couple of equations: the first gives stationarity while the second provides the energy balance. An abstract existence result is given for functionals ℱ of class C 1 in reflexive separable Banach spaces. We provide a couple of constructive proofs of existence which share common features with the theory of minimizing movements for gradient flows. Moreover, considering a sequence of functionals ℱ n and its Γ -limit ℱ we provide, under suitable assumptions, a convergence result for the associated quasi-static evolutions. Finally, we apply this approach to a phase field model in brittle fracture.