考虑周期微结构分布特征的Mori-Tanaka方法

利用两点间应变Green函数张量概念所建立的应变场积分方程, 推导了两相复合材料中夹杂的应变集中张量。该张量较之传统Mori-Tanaka (MT)法采用的由稀疏法导出的应变集中张量, 增加了一个与夹杂体积分数和分布相关的项, 并由此发展了考虑周期微结构分布特征的MT法。传统的MT法虽然能很好地预测正六角形分布圆截面纤维增强复合材料等的有效模量, 但不能反映正方形分布时的四方对称性特征, 本文作者所发展的方法弥补了这方面的不足, 并且所预报的有效刚度和柔度仍然保持了原MT方法所具有的自洽特性。最后通过与双周期有限元计算结果的对照验证了本文方法的精度。 

A modified Mori-Tanaka method considering the doubly periodic distribution of inclusions

The strain concentration tensor for the inclusions in a two-phase composite is derived from the strain field integral equation based on the concept of the so called strain Green tensor. In contrast with the traditional Mori- Tanaka (MT) strain concentration tensor derived with the dilute method, such a strain concentration tensor includes a term related to the volume fraction and distribution of inclusions, whereby a modified Mori-Tanaka method considering the doubly periodic microstructural characteristics is developed. The traditional MT method has proven to be quite accurate in predicting the effective moduli of fiber reinforced composites with the hexagonal array of cylindrical fibers; however, it can not represent square symmetric effective properties of composites with a square array of fibers. The present method gets rid of such a drawback, and provides compact expressions for the effective stiffness and compliance tensors with the same self-consistency as the traditional MT method. A comparison with finite element calculations demonstrates the efficiency and accuracy of the present method.