模拟三维裂纹问题的多尺度扩展有限元法

扩展有限元法模拟裂纹时独立于网格，因此该方法是目前求解裂纹问题最有效的数值方法。为了在计算代价不大的情况，实现大型结构分析中考虑小裂纹或提高裂纹附近精度，在裂纹附近一般采用小尺度单元，其他区域采用大尺度单元。提出了分析三维裂纹问题的多尺度扩展有限元法，在需要的地方采用小尺度单元。基于点插值构造了六面体任意节点单元。所有尺度单元都采用8节点六面体单元，这样六面体任意节点单元可方便有效地连接不同尺度单元。采用互作用积分法计算三维应力强度因子。边裂纹和中心圆裂纹算例分析结果表明，该方法是正确和有效的。

A multiscale extended finite element method for modeling three-dimensional crack problems

Owing to the mesh-independent crack modeling, the extended finite element method (XFEM) is up to now most effective approach for modeling crack problem. In order to consider small cracks in the analysis of large structure or improve the accuracy around the cracks at a low cost, the fine-scale mesh is generally required around the cracks, whereas the coarse-scale mesh is used outside the cracks. A multiscale XFEM for three-dimensional crack modeling is proposed, which enables one to use a refined mesh only where it is required. The arbitrary-node hexahedron element is developed based on the point interpolation method. The eight-node hexahedron element is used for any scale element; thus the arbitrary-node hexahedron element can conveniently and effectively connect elements with different scales. The three-dimensional stress intensity factors are evaluated with the interaction integral method. Examples including an edge-crack problem and a central circle crack problem are given to illustrate the correctness and efficiency of the proposed method.