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Extended multiscale finite element method for mechanical analysis of heterogeneous materials

ISSN号：0567-7718
期刊名称：Acta Mechanica Sinica
时间：2010.12.12
页码：899-920
分类：O343.6[理学—固体力学;理学—力学] O241.82[理学—计算数学;理学—数学]
作者机构：[1]State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology,Dalian 116024,China
相关基金：supported by the National Natural Science Foundation（10721062 11072051 90715037 10728205 91015003 51021140004）; the Program of Introducing Talents of Discipline to Universities（B08014）; the National Key Basic Research Special Foundation of China（2010CB832704）.
相关项目：饱和多孔介质拟静力耦合分析的两尺度有限元方法

作者： Zhang, H. W.|Wu, J. K.|Lu, J.|Fu, Z. D.|

关键词：非均质材料, 有限元法, 多尺度, 力学分析, 周期性边界条件, 数值实验, 有限元分析, 力学问题, Extended multiscale finite element method, Heterogeneous material, Base function, Downscaling computation

中文摘要：

一个扩大多尺度的有限元素方法(EMsFEM ) 为在弹性解决异构的材料的机械问题被开发。方法的内在的想法是数字地构造多尺度的基础功能在多尺度的有限元素分析捕获粗糙的元素的小规模的特征。根据我们的存在工作为周期捆绑材料，异构的材料系统地被介绍的为连续统的基础函数的构造方法。这样，为库的构造的边界条件的选择工作的数字实验表演在多尺度的解决方案的精确性上有大影响边界条件的不同类型被建议。发达方法的效率和精确性被验证，有不同边界条件的结果与周期、随机的异构的微观结构通过广泛的数字例子被验证。另外，方法的一致性测试数字地被执行。结果证明 EMsFEM 罐头有效地象反应一样获得异构的结构的宏反应在微规模，特别在周期的边界条件下面。

英文摘要：

An extended multiscale finite element method （EMsFEM） is developed for solving the mechanical problems of heterogeneous materials in elasticity.The underlying idea of the method is to construct numerically the multiscale base functions to capture the small-scale features of the coarse elements in the multiscale finite element analysis.On the basis of our existing work for periodic truss materials, the construction methods of the base functions for continuum heterogeneous materials are systematically introduced. Numerical experiments show that the choice of boundary conditions for the construction of the base functions has a big influence on the accuracy of the multiscale solutions, thus,different kinds of boundary conditions are proposed. The efficiency and accuracy of the developed method are validated and the results with different boundary conditions are verified through extensive numerical examples with both periodic and random heterogeneous micro-structures.Also, a consistency test of the method is performed numerically. The results show that the EMsFEM can effectively obtain the macro response of the heterogeneous structures as well as the response in micro-scale,especially under the periodic boundary conditions.

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