期刊
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
卷 38, 期 -, 页码 271-305出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2017.05.002
关键词
BV-evolution; Cohesive fracture; Karush-Kuhn-Tucker conditions
资金
- ERC Advanced Grant QuaDynEvoPro [290888]
- ERC FP7-IDEAS-ERC-StG [256872]
- grant Analisi multiscala di sistemi complessi con metodi variazionali of GNAMPA (Gruppo Nazionale per l'Analisi Matematica, la Probabilita, e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica)
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 lambda-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 BV-evolution, in parametrized form, characterized by Karush-Kuhn-Tucker conditions, for the internal variable, equilibrium and energy identity. (C) 2017 Elsevier Ltd. All rights reserved.
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