用于嵌入界面网格连接的稳定化MorteX方法
Stabilized MorteX method for mesh tying along embedded interfaces
摘要：
我们提出了一个统一的框架，以配合重叠网格在固体力学的应用。该框架是X-FEM方法和砂浆方法的结合，使用拉格朗日乘子来实现捆绑约束。如已知的，混合制剂易于发生网格锁定，这通过在系结界面附近出现虚假振荡来表现。为了克服这个固有的困难，我们提出了一个新的粗粒度插值的拉格朗日乘子。该技术包括在选择性分配的拉格朗日乘子的节点上的迫击炮侧，并在非局部插值的相关的牵引场。粗粒化间距的最佳选择仅由砂浆侧的网格与主网格的混合元素的数量之间的网格密度对比来指导。该方法是测试两个补丁测试（压缩和弯曲）不同的插值和元素类型，以及不同的材料和网格对比。最佳的网格收敛和去除寄生振荡也证明了Eshelby夹杂物问题的高对比度的夹杂物/基质材料。很少有其他例子证实了精心设计的框架的性能。
英文摘要：
We present a unified framework to tie overlapping meshes in solid mechanics applications. This framework is a combination of the X-FEM method and the mortar method, which uses Lagrange multipliers to fulfill the tying constraints. As known, mixed formulations are prone to mesh locking which manifests itself by the emergence of spurious oscillations in the vicinity of the tying interface. To overcome this inherent difficulty, we suggest a new coarse-grained interpolation of Lagrange multipliers. This technique consists in selective assignment of Lagrange multipliers on nodes of the mortar side and in non-local interpolation of the associated traction field. The optimal choice of the coarse-graining spacing is guided solely by the mesh-density contrast between the mesh of the mortar side and the number of blending elements of the host mesh. The method is tested on two patch tests (compression and bending) for different interpolations and element types as well as for different material and mesh contrasts. The optimal mesh convergence and removal of spurious oscillations is also demonstrated on the Eshelby inclusion problem for high contrasts of inclusion/matrix materials. Few additional examples confirm the performance of the elaborated framework.
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