Analysis of a rapidly propagating crack using finite elements

An application of the finite element method to the rapidly propagating crack problem in two-dimensional domain is presented on the basis of the energy balance concept and the consistent mass formulation. The creation of the new crack surface is simulated by splitting the nodal points along the crack line successively. By introducing the Lagrange multiplier approach into the conventional finite element method of crack propagation analysis, the inconsistency in the method is avoided in that the crack grows by one element length at a time. Several numerical examples are given for rectangular plates made of polymethylmethacrylate (PMMA) with and without initial crack to show the applicability of the proposed method.