In this paper, a finite element method is proposed to analyze the microscopic and macroscopic mechanical behaviors of heterogeneous media with randomly distributed inclusions. A simple mesh partitioned the domain into regular quadrilateral or triangular elements, where one element may contain two phases. An assumed stress hybrid formulation is implemented in the finite element model and the functional is derived for an element containing two phases. Numerical examples were used to study the microscopic and macroscopic properties of the composites, such as the effective modulus, to validate of the proposed model. The results show that the proposed multiphase hybrid stress finite element model can accurately measure the stress fields of materials with arbitrary microstructural distributions and improve computational efficiency by about 30 to 1500 times in comparison with the traditional displacement based finite element method.

中文翻译：

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基于简单网格的非均质介质多相混合应力有限元分析

本文提出了一种有限元方法来分析夹杂物随机分布的非均质介质的微观和宏观力学行为。一个简单的网格将域划分为规则的四边形或三角形元素，其中一个元素可以包含两个相位。在有限元模型中实现了假设的应力混合公式，并为包含两个相的元素导出了函数。通过数值算例研究了复合材料的微观和宏观性能，例如有效模量，以验证所提出的模型。