Robust Algorithm for Brittle Fracture based on Energy Minimization

The paper outlines a variational formulation of brittle fracture in solids and considers its numerical implementation by a distinct finite element method. The starting point is a variational setting of fracture mechanics that recasts a monotonic quasistatic fracture process into a sequence of incremental minimization problems. The proposed implementation introduces discretized crack patterns with material-force-driven incremental crack-segment releases. These releases of crack segments constitute a sequence of positive definite subproblems with successively decreasing overall stiffness, providing an extremely robust algorithmic setting in the postcritical range. The formulation is embedded into accompanying r-adaptive crack-pattern reorientation procedures with material-force-based indicators, providing reorientations of elements at the crack-tip. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)