Efficient computation of multiple solutions in quasibrittle fracture analysis Original Research Article

We propose a novel and efficient computational scheme for capturing the multiplicity of solutions that may exist at any loading step of a quasibrittle fracture analysis formulated as a linear complementarity problem (LCP). The algorithm proposed is based on successively augmenting the current LCP by complementarity constraints that effectively remove previously found solutions from the solution set. We focus on the single-step or so-called holonomic analysis for mode I behavior. The performance of the proposed approach is illustrated by means of physically meaningful benchmark problems.