A generalized finite element method for the simulation of three-dimensional dynamic crack propagation

Abstract

This paper is aimed at presenting a partition of unity method for the simulation of three-dimensional dynamic crack propagation. The method is a variation of the partition of unity finite element method and hp-cloud method. In the context of crack simulation, this method allows for modeling of arbitrary dynamic crack propagation without any remeshing of the domain. In the proposed method, the approximation spaces are constructed using a partition of unity (PU) and local enrichment functions. The PU is provided by a combination of Shepard and finite element partitions of unity. This combination of PUs allows the inclusion of arbitrary crack geometry in a model without any modification of the initial discretization. It also avoids the problems associated with the integration of moving least squares or conventional Shepard partitions of unity used in several meshless methods. The local enrichment functions can be polynomials or customized functions. These functions can efficiently approximate the singular fields around crack fronts. The crack propagation is modeled by modifying the partition of unity along the crack surface and does not require continuous remeshings or mappings of solutions between consecutive meshes as the crack propagates. In contrast with the boundary element method, the proposed method can be applied to any class of problems solvable by the classical finite element method. In addition, the proposed method can be implemented into most finite element data bases. Several numerical examples demonstrating the main features and computational efficiency of the proposed method for dynamic crack propagation are presented.