Pseudo-grain discretization and full Mori Tanaka formulation for random heterogeneous media: Predictive abilities for stresses in individual inclusions and the matrix
Pseudo-grain discretization and full Mori Tanaka formulation for random heterogeneous media: Predictive abilities for stresses in individual inclusions and the matrix
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随机异质介质的伪晶粒离散化和完整 Mori Tanaka 公式：单个夹杂物和基体中应力的预测能力
DOI：
10.1016/j.compscitech.2013.08.009
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
W. Paepegem
中科院分区：
文献类型：
--
作者：
Atul K. Jain;S. Lomov;Y. Abdin;I. Verpoest;W. Paepegem
为了模拟短纤维复合材料的损伤，复合材料的有效性能以及单个夹杂物和基体中的应力都是必需的。平均场定理常用于计算复合材料的有效性质，其中最常用的是Mori-Tanaka公式。由于Mori-Tanaka公式偶尔会出现数学和物理上的可容许性问题，文献中提出了伪粒离散化的Mori-Tanaka公式(PGMT)。本文研究了完全Mori-Tanaka公式和PGMT公式对单个夹杂物和基质中的应力以及夹杂物相中的平均应力的预测能力。将夹杂物和基体内部的平均应力与各种构型的全尺寸有限元模型的解进行了比较。可以看出，即使Mori-Tanaka的基本假设被报道过于简单化，Mori-Tanaka公式对单个包裹体中的平均应力的预测也很好，而PGMT的预测在所有情况下都有明显的偏差。用这两种方法预测的矩阵应力非常相似。整个包裹体阶段的平均应力也非常接近。必须使用Mori-Tanaka公式作为首选的均化方案。
Both effective properties of composite and the stresses in the individual inclusions and in the matrix are necessary for modelling damage in short fibre composites. Mean field theorems are usually used to calculate the effective properties of composite materials, most common among them is the Mori–Tanaka formulation. Owing to occasional mathematical and physical admissibility problems with the Mori–Tanaka formulation, a pseudo-grain discretized Mori–Tanaka formulation (PGMT) was proposed in literature. This paper looks at the predictive capabilities for stresses in individual inclusions and matrix as well as the average stresses in inclusion phase for full Mori–Tanaka and PGMT formulation for 2D planar distribution of orientation of inclusions. The average stresses inside inclusions and the matrix are compared to solutions of full-scale finite element (FE) models for a wide range of configurations. It was seen that the Mori–Tanaka formulation gave excellent predictions of average stresses in individual inclusions, even when the basic assumptions of Mori–Tanaka were reported to be too simplistic, while the predictions of PGMT were off significantly in all the cases. The predictions of the matrix stresses by the two methods were found to be very similar to each other. The average value of stress averaged over the entire inclusion phase was also very close to each other. The Mori–Tanaka formulation must be used as the first choice homogenization scheme.