The prediction of crack propagation is an important engineering problem. In this work, combined with triangular plane stress finite elements, a new remeshing algorithm for crack opening problems was developed. The proposed algorithm extends the crack iteratively until a threshold maximum crack length is achieved. The crack propagation direction is calculated using the maximum tangential stress criterion. In this calculation, in order to smoothen the stress field in the vicinity of the crack tip, a weighted average of the stresses of the integration points around the crack tip is considered. The algorithm also ensures that there are always at least eight elements and nine nodes surrounding the crack tip, unless the crack tip is close to a domain boundary, in which case there can be fewer elements and nodes around the crack tip.

Four benchmark tests were performed showing that this algorithm leads to accurate crack paths when compared to findings from previous research works, as long as the initial mesh is not too coarse. This algorithm also leads to regular meshes during the propagation process, with very few distorted elements, which is generally one of the main problems when calculating crack propagation with the finite element method.

裂纹扩展的预测是一个重要的工程问题。在这项工作中，结合三角形平面应力有限元，开发了一种新的重新网格化算法来解决裂纹开口问题。所提出的算法迭代地扩展裂纹，直到达到阈值最大裂纹长度为止。使用最大切向应力准则计算裂纹扩展方向。在该计算中，为了使裂纹尖端附近的应力场平滑，考虑了裂纹尖端周围的积分点的应力的加权平均值。该算法还确保裂纹尖端周围始终至少有八个元素和九个节点，除非裂纹尖端靠近域边界，在这种情况下，裂纹尖端周围的元素和节点会更少。

进行了四个基准测试，表明与以前的研究成果相比，只要初始网格不太粗糙，该算法即可产生准确的裂纹路径。该算法还可以在传播过程中生成规则的网格，使元素变形很少，这通常是使用有限元方法计算裂纹扩展时的主要问题之一。