Numerical homogenization of heterogeneous and cellular materials utilizing the finite cell method
Numerical homogenization of heterogeneous and cellular materials utilizing the finite cell method
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DOI：
10.1007/s00466-012-0681-2
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发表时间：
2012-10-01
影响因子：
4.1
通讯作者：
Rank, Ernst
中科院分区：
文献类型：
--
作者：
Duester, Alexander;Sehlhorst, Hans-Georg;Rank, Ernst
本文提出了一种新的数值均匀化方法来处理多孔和非均匀材料。该程序是基于有限单元法，这是适用于有效地离散的有效材料性能计算的代表性体积元素。我们的均匀化的起点可能是计算机辅助设计的异质材料或三维计算机断层扫描（CT扫描）的标本的利益。一个全自动离散的有限单元，应用分层扩展过程来控制离散误差，是用来解决相应的边值问题，在均匀化过程中出现的。特别强调的是边界条件的数值处理。为此，我们应用窗口方法，它可以被解释为一个变种的自洽方法。从多孔材料到纤维增强复合材料的几个数值例子将被提出，证明我们的方法的效率。均质化程序也将应用于泡沫，其CT扫描可用。
We present a new approach for the numerical homogenization of cellular and heterogeneous materials. The procedure is based on the finite cell method, which is applied to efficiently discretize representative volume elements for which effective material properties are computed. The starting point for our homogenization might be either a computer-aided design of a heterogeneous material or a three-dimensional computer tomography (CT-scan) of the specimen of interest. A fully automatic discretization in terms of finite cells, applying a hierarchic extension process to control the discretization error, is utilized to solve the corresponding boundary value problems arising during the homogenization. Special emphasis is placed on the numerical treatment of boundary conditions. To this end we apply the window method, which can be interpreted as a variant of the self-consistency method. Several numerical examples ranging from porous materials to fiber-reinforced composites will be presented, demonstrating the efficiency of our approach. The homogenization procedure will be also applied to a foam, a CT-scan of which is available.