An Explicit Updated Lagrangian Fragile Points Method for Dynamic Fracture Simulations

Abstract

Dynamic fracture is a prevalent phenomenon in engineering structures subjected to dynamic loads, and reliable and simple numerical simulations of such phenomenon has been an ongoing research topic of computational mechanics. Although the finite element method (FEM) has been widely used for fracture simulations, there are still challenges such as the crack introduction and the mesh distortion. In recent years, meshless methods have emerged as potential alternatives to overcome these issues. In this paper, an explicit updated Lagrangian Fragile Points Method (FPM) is proposed for dynamic fracture simulations. The FPM is a point-based discontinuous meshless method, thus it on one hand circumvents the mesh distortion, and on the other hand allows for a simple, explicit introduction of cracks. In this paper, the formulations of the explicit updated Lagrangian FPM are introduced. Then the method is applied to various dynamic fracture problems including the spalling fracture and the crack branching, and for each cases the FPM provides convincing results. This paper shows that the explicit updated Lagrangian FPM is an effective yet simple numerical tool for predicting dynamic fracture. Note that though only small deformation dynamic fracture examples are used in this paper, the proposed method is able to handle finite strain problems, verified by some simple examples, since it is developed in the updated-Lagrangian form.