Stress concentration and effective stiffness of aligned fiber reinforced composite with anisotropic constituents
Stress concentration and effective stiffness of aligned fiber reinforced composite with anisotropic constituents
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DOI：
10.1016/j.ijsolstr.2008.05.009
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发表时间：
2008-09
影响因子：
3.6
通讯作者：
V. Kushch;I. Sevostianov;L. Mishnaevsky
中科院分区：
文献类型：
--
作者：
V. Kushch;I. Sevostianov;L. Mishnaevsky
本文讨论了各向异性单向纤维增强复合材料的局部应力场和有效弹性性能的计算问题。为了这个目的，已经利用了代表性的单位单元方法。复合材料的微观几何形状由含有多个圆形纤维的单元胞的周期性结构来建模。纤维的数量足以解释复合材料的微观结构统计。提出了一种基于多极展开技术的细观应力场精确级数解的新方法。该方法结合了叠加原理、复势技术和特殊函数论中的一些新结果。一个适当的选择的潜力和新的结果，他们的系列扩展允许一个减少的多连通域的边值问题，一个普通的，适定的线性代数方程组。这种减少提供了高的数值效率的开发方法。通过对应变场和应力场的解析平均，得到了有效刚度张量分量的精确表达式。
The paper addresses the problem of calculation of the local stress field and effective elastic properties of a unidirectional fiber reinforced composite with anisotropic constituents. For this aim, the representative unit cell approach has been utilized. The micro geometry of the composite is modeled by a periodic structure with a unit cell containing multiple circular fibers. The number of fibers is sufficient to account for the micro structure statistics of composite. A new method based on the multipole expansion technique is developed to obtain the exact series solution for the micro stress field. The method combines the principle of superposition, technique of complex potentials and some new results in the theory of special functions. A proper choice of potentials and new results for their series expansions allow one to reduce the boundary-value problem for the multiple-connected domain to an ordinary, well-posed set of linear algebraic equations. This reduction provides high numerical efficiency of the developed method. Exact expressions for the components of the effective stiffness tensor have been obtained by analytical averaging of the strain and stress fields.