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.

摘要

有限元类方法中, 对于真实表现三维裂缝扩展的数值模拟较为少见, 而且往往是通过商业程序 实现。造成这一情况的原因, 除了几何上的复杂性以外, 开裂方向的判断是一个难点。多数情况下, 判断裂缝是否开裂以及扩展的方向依据的是局部应力状态, 这种方法在应用于三维情况时, 较难处理 裂缝在网格之间的协调关系。本文以扩展有限元(XFEM)为基础, 在计算域内引入与应力相关的函数 场, 进而求解函数的边值问题, 可一次求出所有扩展方向的包络面, 然后从中选出可能的扩展面作为 裂缝的开展方向。这种方法概念清晰, 较大程度地降低了描述裂缝扩展部分的编程难度, 适用于张拉 破坏问题, 可以同时模拟多条裂纹。