A computational framework of three dimensional configurational‐force‐driven crack propagation

Abstract

AbstractA variational formulation of quasi‐static brittle fracture is considered and a new finite‐element‐based computational framework is developed for propagation of cracks in three‐dimensional bodies. We outline a consistent thermodynamical framework for crack propagation in elastic solids and show that the crack propagation direction associated with the classical Griffith criterion is identified by the material configurational force which maximizes the local dissipation at the crack front. The evolving crack discontinuity is realized by the doubling of critical nodes and triangular interface facets of the tetrahedral mesh. The crucial step for the success of the procedure is its embedding into an r‐adaptive crack‐facet reorientation procedure based on configurational‐force‐based indicators in conjunction with crack front constraints. We further propose a staggered algorithm which minimizes the stored energy at frozen crack state followed by the successive crack releases at frozen deformation. This constitutes a sequence of positive definite subproblems with successively decreasing overall stiffness, providing a very robust algorithmic setting in the postcritical range. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)