Nonnodal Extended Finite-Element Method for Crack Modeling with Four-Node Quadrilateral Elements

A nonnodal extended finite-element method (NXFEM) was developed to predict two-dimensional dynamic failure with four-node quadrilateral elements. A new nonnodal enrichment scheme is presented such that the enriched quadrilateral finite elements satisfy the linear completeness and represent a strong discontinuity, i.e., crack. The enrichment bases for both solutions and the gradient fields are included in the finite-element approximation through the nonnodal enrichment scheme. The partition of unity is also naturally satisfied without adopting additional neighbor blending elements. To facilitate an implementation of the NXFEM into pre-existing finite-element analysis software, a generalized notation is proposed which is universally applicable to both quadrilateral and triangular finite elements. The developed method was initially verified with a convergence study on benchmark near-crack-tip field problems. The effectiveness of the method was further demonstrated with mixed-mode dynamic failure problems.