Simulation of three-dimensional tension-induced cracks based on cracking potential function-incorporated extended finite element method

Abstract

In the finite element method, the numerical simulation of three-dimensional crack propagation is relatively rare, and it is often realized by commercial programs. In addition to the geometric complexity, the determination of the cracking direction constitutes a great challenge. In most cases, the local stress state provides the fundamental criterion to judge the presence of cracks and the direction of crack propagation. However, in the case of three-dimensional analysis, the coordination relationship between grid elements due to occurrence of cracks becomes a difficult problem for this method. In this paper, based on the extended finite element method, the stress-related function field is introduced into the calculation domain, and then the boundary value problem of the function is solved. Subsequently, the envelope surface of all propagation directions can be obtained at one time. At last, the possible surface can be selected as the direction of crack development. Based on the aforementioned procedure, such method greatly reduces the programming complexity of tracking the crack propagation. As a suitable method for simulating tension-induced failure, it can simulate multiple cracks simultaneously.