Abstract
Some results concerning numerical experiments based on a variational model for quasi-static Griffith-type brittle fracture are presented. The analysis is essentially based on a formulation of variational fracture given by Francfort and Marigo, the main difference being the fact that we rely on local rather than on global minimization. Propagation of fracture is obtained by minimizing, in a step by step process, a form of energy that is the sum of bulk and interface terms. To solve the problem numerically we adopt discontinuous finite elements based on variable meshes and search for the minima of the energy through descent methods. In order to get out of small energy wells, a mesh dependent relaxation of the interface energy, tending to the Griffith limit as the mesh size tends to zero, is adopted. The relaxation consists in a carefully tailored cohesive type approximation of the interface energy tuned by few parameters. The role of such parameters is investigated.
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Angelillo, M., Babilio, E. & Fortunato, A. Numerical solutions for crack growth based on the variational theory of fracture. Comput Mech 50, 285–301 (2012). https://doi.org/10.1007/s00466-012-0755-1
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DOI: https://doi.org/10.1007/s00466-012-0755-1