Multi-scale finite element analysis of porous materials and components by asymptotic homogenization theory and enhanced mesh superposition method
Multi-scale finite element analysis of porous materials and components by asymptotic homogenization theory and enhanced mesh superposition method
复制标题
利用渐进均质化理论和增强网格叠加法对多孔材料和构件进行多尺度有限元分析
DOI：
10.1088/0965-0393/11/2/303
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
Y. Okuno
中科院分区：
文献类型：
--
作者：
N. Takano;M. Zako;Y. Okuno
为了分析异质材料和部件的宏观和微观行为，研究了多尺度计算方法。尽管渐近均质化理论是近十年来解决各种多尺度问题的主要工具，但其对微观晶胞周期性的假设以及无法考虑尺度效应导致该理论的应用受到限制。这些问题应该得到克服，因为先进材料经常用作接头或层压部件，并且必须分析界面裂纹问题。为此，提出了一种新的多尺度有限元方法，该方法将增强网格叠加法与渐近均匀化理论结合使用。有限元网格叠加法使用全局网格和任意叠加到全局网格上的局部网格。增强的方法允许对两个网格采用不同的本构定律。仍然发挥了均质化理论基于复杂微观结构准确预测均质化材料模型的优势。全局网格采用均质材料模型，而局部网格则根据成分的材料特性考虑微观异质性和裂纹。描述了所提出方法的公式、建模策略、实现和数值精度。数值例子中研究了多孔陶瓷。
To analyse the macroscopic and microscopic behaviours of heterogeneous materials and components, a multi-scale computational method is studied. Although asymptotic homogenization theory has been the main tool during the last decade to solve various multi-scale problems, the assumption of the periodicity of the microscopic unit cell and the incapability of considering the scale effect have resulted in the limitations to this theory's applications. These problems should be overcome because advanced materials are often used as joint or laminated components and the interface crack problem must be analysed. For this sake, a novel multi-scale finite element method is proposed that uses the enhanced mesh superposition method together with the asymptotic homogenization theory. The finite element mesh superposition method uses the global mesh and the local mesh that is superimposed arbitrarily onto the global mesh. The enhanced method allows the adoption of different constitutive laws for the two meshes. The advantage of the homogenization theory to predict the homogenized material model accurately based on the complex microstructure is still utilized. The homogenized material model is used for the global mesh, whilst the microscopic heterogeneity and the crack are considered in the local mesh with the material properties of the constituents. The formulation, modelling strategy, implementation and numerical accuracy of the proposed method is described. A porous ceramic is studied in the numerical example.