Asymptotic simulation of imperfect bonding in periodic fibre-reinforced composite materials under axial shear
Asymptotic simulation of imperfect bonding in periodic fibre-reinforced composite materials under axial shear
复制标题
轴向剪切下周期性纤维增强复合材料不完美粘接的渐近模拟
DOI：
10.1016/j.ijmecsci.2007.04.002
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发表时间：
2007
影响因子：
7.3
通讯作者：
D. Weichert
中科院分区：
文献类型：
--
作者：
I. Andrianov;V. Bolshakov;V. Danishevs’kyy;D. Weichert
提出了一种模拟复合材料非理想界面结合的渐近方法。我们在基体和夹杂物之间引入一个体积分数为c（3）、无量纲刚度为λ（3）的柔性粘结层，导出这种三组分结构的解，然后设c（3）→0，λ（3）→0。在渐近极限中，根据λ（3）/c（3）的比值，可以模拟不同程度的界面响应。本文研究了含正方形和六边形圆柱形夹杂的弹性纤维增强复合材料的轴向剪切问题。进行分析的基础上的渐近均匀化方法，细胞的问题是解决使用的基本原则的边界形状摄动技术。得到了有效剪切模量的近似解析解，并得到了界面脱粘程度对微观应力场的影响。所开发的解决方案是有效的所有值的组分的体积分数和性质。特别地，它们在局部应力的快速振荡的情况下工作良好（例如，在密集堆积的完全刚性夹杂物的情况下），而许多其它常用的方法可能面临计算困难。
An asymptotic approach for simulation of the imperfect interfacial bonding in composite materials is proposed. We introduce between the matrix and inclusions a flexible bond layer of a volume fraction c(3)and of a non-dimensional rigidity λ(3), derive a solution for such three-component structure, and then set c(3)→0, λ(3)→0. In the asymptotic limit depending on the ratio λ(3)/c(3)different degrees of the interface's response can be simulated. A problem of the axial shear of elastic fibre-reinforced composites with square and hexagonal arrays of cylindrical inclusions is considered. The performed analysis is based on the asymptotic homogenization method, the cell problem is solved using the underlying principles of the boundary shape perturbation technique. As a result, we obtain approximate analytical solutions for the effective shear modulus and for the stress field on micro level depending on the degree of the interfacial debonding. Developed solutions are valid for all values of the components’ volume fractions and properties. In particular, they work well in cases of rapid oscillations of local stresses (e.g., in the case of densely packed perfectly rigid inclusions), while many of other commonly used methods may face computational difficulties.