A quasi-static evolution generated by local energy minimizers for an elastic material with a cohesive interface. (December 2017)

• Record Type: Journal Article
• Authors: Negri, M.; Scala, R.
• Is Part Of: Nonlinear analysis. Volume 38(2017)
• Page Start: 271
• Page End: 305
• Publication Date: 2017-12
• Subjects: BV-evolution -- Cohesive fracture -- Karush–Kuhn–Tucker conditions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.05.002
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We deal with a model for an elastic material with a cohesive crack along a prescribed fracture set. We consider two n -dimensional elastic bodies and a cohesive law, on their common interface, with incompenetrability constraint and general loading–unloading regimes. We first provide a time-discrete evolution by means of local minimizers of the energy with respect to the L 2 -norm of the crack opening displacement. The choice of this norm is due to technical reasons (the λ -convexity of the energy) and is in analogy with the classical approach in quasi-static brittle fracture, where the evolution of the system is condensed into the evolution of the crack. In the "time-continuous" limit we obtain a B V -evolution, in parametrized form, characterized by Karush–Kuhn–Tucker conditions, for the internal variable, equilibrium and energy identity.