A Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results

摘要: We give a precise mathematical formulation of variational model for the irreversible quasi-static evolution brittle fractures proposed by G. A. Francfort and J.-J. Marigo, based on Griffith's theory crack growth. In two-dimensional case we prove an existence result show that total energy is absolutely continuous function time, although cannot exclude possibility bulk surface may present some jump discontinuities. This proved time-discretization process, where at each step global minimization performed, with constraint new contains all cracks formed previous time steps. procedure provides effective way to approximate evolution.