A numerical method for homogenization in non-linear elasticity
A numerical method for homogenization in non-linear elasticity
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DOI：
10.1007/s00466-006-0097-y
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发表时间：
2007-04
影响因子：
4.1
通讯作者：
I. Temizer;T. Zohdi
中科院分区：
文献类型：
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作者：
I. Temizer;T. Zohdi
在这项工作中，非均质材料在弹性背景下的均匀化，其中寻求非均质材料的有效本构行为。同时考虑了线弹性和非线性弹性体系。均化过程的核心是确定非均质材料的统计代表性体积元素(RVE)。在线性区域，研究了这种辨识的各个方面，并引入了一种数值方案来确定RVE的大小。通过引入应力-应变状态表征参数，将线性区域的方法扩展到非线性区域。其次，讨论了材料映射的概念及其在有限元方法中的实现，材料映射是在离散意义上标识材料的本构行为。然后利用数值识别的RVE计算非线性弹性非均质材料的有效材料图，从而实现材料的均匀化。结果表明，使用材质图对非均质结构进行宏观分析可以显著减少计算时间。
In this work, homogenization of heterogeneous materials in the context of elasticity is addressed, where the effective constitutive behavior of a heterogeneous material is sought. Both linear and non-linear elastic regimes are considered. Central to the homogenization process is the identification of a statistically representative volume element (RVE) for the heterogeneous material. In the linear regime, aspects of this identification is investigated and a numerical scheme is introduced to determine the RVE size. The approach followed in the linear regime is extended to the non-linear regime by introducing stress–strain state characterization parameters. Next, the concept of a material map, where one identifies the constitutive behavior of a material in a discrete sense, is discussed together with its implementation in the finite element method. The homogenization of the non-linearly elastic heterogeneous material is then realized through the computation of its effective material map using a numerically identified RVE. It is shown that the use of material maps for the macroscopic analysis of heterogeneous structures leads to significant reductions in computation time.