提出了一种有限元子划分结合子结构的方法来模拟裂纹扩展问题。提出的方法中，将单元分为三类：被裂纹贯穿的单元，包含裂尖的单元和常规单元。对前两类单元进行子划分，每个单元的归类随裂纹的扩展而动态变化。覆盖一条裂纹的前两类单元子划分后构成一个子结构，子结构也是动态的，跟随裂纹的扩展而逐步扩大。本文的方法可以使裂纹沿任意路径扩展而不受初始网格的限制，裂纹扩展后无需对结构整体的网格重划分，结构整体分析的总自由度也不变。用该方法计算无限大平面中心裂纹的应力强度因子，模拟三点弯梁跨中裂纹的扩展，验证了计算精度，并进一步用该方法模拟了非均质材料中裂纹的扩展，考核了对复杂裂纹扩展问题的适用性。%A novel numerical algorithm combining finite element sub-partition and substructure was devel- oped to simulate crack extension. In this strategy, all elements are grouped into three sorts：elements sep- arated by a crack,elements containing crack tip and normal elements. The first and second sorts of ele- ments will be sub-partitioned. Grouping of elements are dynamic varying with crack extension. The sub- partitioned elements covering one crack are viewed as a sub-structure. This sub-structure is thereby dy- namic also for its element member will increase when the crack expands. In this algorithm, a crack can expand along any path and free from the limit of original mesh, global re-mesh is not needed and the total freedom dimension keeps the same whether cracks extend or initiating new cracks. This method was a- dopted to calculate the stress intensity factors of central crack in infinite plane and to simulate the crack propagation in three-point bending beam to validate its accuracy. It was further used in inhomogenous material to demonstrate its adaptability for simulating of complex path cracking.
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