Quasi-static rate-independent evolutions: characterization, existence, approximation and application to fracture mechanics∗. (4th August 2014)

• Record Type: Journal Article
• Authors: Negri, Matteo
• Is Part Of: ESAIM. Volume 20:Number 4(2014:Oct.)
• Page Start: 983
• Page End: 1008
• Publication Date: 2014-08-04
• Subjects: Quasi-static evolutions, -- phase-field; System analysis -- Periodicals; Calculus of variations -- Periodicals; Mathematical analysis -- Periodicals; Mathematical optimization -- Periodicals; Control theory -- Periodicals; 515.64
• DOI: 10.1051/cocv/2014004
• Languages: English
• ISSNs: 1292-8119

Abstract

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.