A computational approach to handle complex microstructure geometries
A computational approach to handle complex microstructure geometries
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DOI：
10.1016/s0045-7825(03)00346-3
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发表时间：
2003-07
影响因子：
7.2
通讯作者：
N. Moës;Mathieu Cloirec;P. Cartraud;J. Remacle
中科院分区：
文献类型：
--
作者：
N. Moës;Mathieu Cloirec;P. Cartraud;J. Remacle
在构件的多尺度分析中，通常需要求解具有复杂几何形状的微结构。在本文中，我们使用扩展有限元法（X-FEM）来解决涉及复杂的几何尺度。X-FEM允许使用不一定匹配问题的物理表面的网格，同时保留经典有限元方法的精度。对于材料界面，这是通过引入新的富集策略来实现的。虽然网格不需要符合物理表面，但它需要足够精细以捕获这些表面的几何形状。一个简单的算法描述自适应细化网格，以满足这一几何要求。两相复杂胞元周期均匀化的数值实验验证了X-FEM的准确性和简单性。
In multiscale analysis of components, there is usually a need to solve microstructures with complex geometries. In this paper, we use the extended finite element method (X-FEM) to solve scales involving complex geometries. The X-FEM allows one to use meshes not necessarily matching the physical surface of the problem while retaining the accuracy of the classical finite element approach. For material interfaces, this is achieved by introducing a new enrichment strategy. Although the mesh does not need to conform to the physical surfaces, it needs to be fine enough to capture the geometry of these surfaces. A simple algorithm is described to adaptively refine the mesh to meet this geometrical requirement. Numerical experiments on the periodic homogenization of two-phase complex cells demonstrate the accuracy and simplicity of the X-FEM.