Regularized X-FEM Modeling of Arbitrary 3D Interacting Crack Networks

Abstract

An extension to the Regularized eXtended Finite Element Method (RX-FEM) is proposed that allows arbitrary 3D cracks through a novel hierarchical enrichment algorithm. The technique avoids geometric consideration of how a crack cuts elements or intersects other cracks. Each crack is described separately in terms of its sign distance function and regularized step function, which are only recorded for nodes in the region where the gradient of the regularized step function is non-zero. The algorithm creates a set of superimposed nodes, referred to as node twins, and elements, referred to as twinned elements, for each crack and determines the connectivity of the element twins using the involved crack indices. The displacement jump is calculated between each pair of element twins corresponding to the same crack, and a cohesive zone model (CZM) is formulated for each pair of twins to model crack opening. Following the theory for the novel method, several examples are presented that illustrate capabilities of the new method that the traditional RX-FEM formulation lacked. A quasi-2D example of offset crack propagation is considered and successfully compared with published results. Additionally, two 3D examples involving perpendicularly intersecting cracks are considered, illustrating the intersection of two crack fronts and correct partitioning of the domain into eight fragments due to three crossing cracks, respectively.