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arXiv 0802.0511cond-mat.mtrl-scicond-mat.stat-mech
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基于细观结构的弹性功能梯度材料建模:一维情况

Microstructure-based modeling of elastic functionally graded materials: One dimensional case

Zahra Sharif-Khodaei, Jan Zeman

摘要:

功能梯度材料(FGM)是一种两相复合材料,其微观结构不断变化以适应性能要求。传统上,功能梯度材料的整体行为已被确定使用局部平均技术或给定的材料特性的平滑变化。尽管这些模型在计算上是有效的,但它们的有效性和准确性仍然值得怀疑,因为与底层微观结构(包括其随机性)的联系尚不清楚。在本文中,我们提出了一个建模策略的线弹性分析的功能梯度材料系统的基础上现实的微观结构模型。在随机Hashin-Shtrikman变分原理的框架下,对功能梯度材料的整体响应进行了研究。为了允许有限体的分析,最近推出的离散方案的基础上的有限元法和边界元法获得统计的局部领域。有代表性的数值例子,比较这两种方案的性能和精度。为了深入了解这些方法之间的相似性和差异,并尽量减少技术性,在一维设置中进行分析。

英文摘要:

Functionally graded materials (FGMs) are two-phase composites with continuously changing microstructure adapted to performance requirements. Traditionally, the overall behavior of FGMs has been determined using local averaging techniques or a given smooth variation of material properties. Although these models are computationally efficient, their validity and accuracy remain questionable, since a link with the underlying microstructure (including its randomness) is not clear. In this paper, we propose a modeling strategy for the linear elastic analysis of FGMs systematically based on a realistic microstructural model. The overall response of FGMs is addressed in the framework of stochastic Hashin-Shtrikman variational principles. To allow for the analysis of finite bodies, recently introduced discretization schemes based on the Finite Element Method and the Boundary Element Method are employed to obtain statistics of local fields. Representative numerical examples are presented to compare the performance and accuracy of both schemes. To gain insight into similarities and differences between these methods and to minimize technicalities, the analysis is performed in the one-dimensional setting.

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