01237nas a2200121   4500008004300000245009800043210006900141260001300210520081600223100002101039700001901060856003601079       2002                        en_Ud  00aA Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results0 aModel for the QuasiStatic Growth of Brittle Fractures Existence   bSpringer3 aWe give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith\\\'s theory of crack growth. In the two-dimensional case we prove an existence result for the quasi-static evolution and show that the total energy is an absolutely continuous function of time, although we can not exclude that the bulk energy and the surface energy may present some jump discontinuities. This existence result is proved by a time discretization process, where at each step a global energy minimization is performed, with the constraint that the new crack contains all cracks formed at the previous time steps. This procedure provides an effective way to approximate the continuous time evolution.1 aDal Maso, Gianni1 aToader, Rodica  uhttp://hdl.handle.net/1963/3056