An adaptive multiscale resolution strategy for the finite deformation analysis of microheterogeneous structures
An adaptive multiscale resolution strategy for the finite deformation analysis of microheterogeneous structures
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DOI：
10.1016/j.cma.2010.06.013
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发表时间：
2011-09
影响因子：
7.2
通讯作者：
I. Temizer;P. Wriggers
中科院分区：
文献类型：
--
作者：
I. Temizer;P. Wriggers
在微异构域上提出的问题的标准齐次化公式在解场中观察到高度局部化变化的区域中提供了较低级别的精度。为了解决一般非弹性宏观结构的有限变形分析的这种精度损失，开发了一种尺度适应策略，其中在指定的感兴趣区域中追求从均质描述到显式微观结构分辨率的过渡。在高阶均化技术的推动下，基于均化溶液的后处理步骤识别适应区，并对应于具有高应变梯度的区域。为了避免使用近似显式宏观本构方程带来的建模误差，采用了基于数据库和直接多层有限元计算的精确均匀化方法。整个方法是在二维环境下研究的，其中特别关注底层的多尺度网格分辨率，并通过三维问题进行了额外的演示。数字观察提出了一个具有代表性的适应区的概念，在这个适应区内可以评估规模适应的影响。
Standard homogenized formulations of problems posed on microheterogeneous domains provide a lower order of accuracy in regions where highly localized variations are observed in the solution fields. In order to account for this loss of accuracy for the finite deformation analysis of generally inelastic macrostructures, a scale adaptation strategy is developed where a transition from a homogenized description to an explicit microstructural resolution is pursued in designated zones of interest. Motivated by higher-order homogenization techniques, the adaptation zones are identified based on a post-processing step on the homogenized solution and correspond to regions with high strain-gradients. In order to avoid modeling errors emanating from the use of approximate explicit macroscale constitutive formulations, an exact homogenization procedure based on databased and direct multilevel finite element computations is employed. The overall methodology is investigated in a two-dimensional setting where special attention is paid to the underlying multiscale mesh resolution and additionally demonstrated with a three-dimensional problem. Numerical observations suggest the concept of a representative adaptation zone within which scale adaptation effects can be assessed.