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On two-scale adaptive FE analysis of micro-heterogeneous media with seamless scale-bridging

机译:无缝尺度桥接微尺度异质介质的两尺度自适应有限元分析

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In principle, two approaches are possible for resolving strong material micro-heterogeneity: one approach is to adopt homogenization with the underlying assumption of scale separation, whereas the other approach is to completely resolve the fine scale(s) in a single-scale computation. The point of departure for this paper is a recently proposed algorithm for scale-transition such that the two extreme approaches are bridged in a "seamless" fashion. Numerical homogenization is carried out locally, where needed, based on the relation of the macro-scale mesh diameter to the typical length scale of the subscale structure. Moreover, the macroscale mesh adaptivity is driven by an estimation of discretization errors. In the present paper, we generalize this procedure by introducing two-scale adaptivity, whereby subscale discretization errors are viewed as model errors from the macroscale perspective. Numerical examples, adopting elastic-plastic subscale material properties, illustrate the principle and the effectiveness of the adaptive procedure.
机译:原则上,有两种方法可以解决强的材料微观异质性:一种方法是采用均质化,并基于尺度分离的基本假设,而另一种方法是在单尺度计算中完全解析精细尺度。本文的出发点是最近提出的比例转换算法,以至于两种极端方法以“无缝”方式被桥接。基于宏观尺度网格直径与子尺度结构的典型长度尺度之间的关系,在必要时在本地进行数值均质化。此外,宏观网格自适应性由离散化误差的估计驱动。在本文中,我们通过引入两尺度适应性来概括该过程,从而从宏观尺度将子尺度离散化误差视为模型误差。数值示例采用了弹塑性子尺度的材料特性,说明了自适应程序的原理和有效性。

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