中文摘要：

采用一种新型的杂交元模型和一种单胞模型来解决周期分布多边形夹杂角部的奇异性应力相互干涉的问题。新型杂交元模型是基于广义Hellinger-Reissner变分原理建立的，其中奇异性应力场分量和位移场分量是采用有限元特征分析法的数值特征解得到的。使用当前的新型杂交元模型，只需要在夹杂角部邻域的周界上划分一维单元．避免了像传统有限元模型那样需要划分高密度二维单元。文中给出了代表奇异性应力场强度的夹杂角部广义应力强度因子数值解，并考虑材料属性、夹杂尺寸和夹杂位置关系的影响。算例中，考虑了夹杂和基体完全接合的情况，并给出了考核例。结果表明：当前模型能得到高精度数值解，且收敛性好；与传统有限元法和积分方程方法相比，该模型更具有通用性，为非均质材料的细观力学分析打下了基础。

英文摘要：

This paper deals with the stress interaction problem of periodic polygonal inclusions under far field tension by using a novel hybrid finite element model and a unit cell model. The novel hybrid finite element method is established based on the general Hellinger-Reissner variational principle for an inclusion corner tip domain, in which components of stress and displacement fields are expressed by numerical eigensolusions obtained from an ad hoc finite element eigenanalysis method. Due to the use of present finite element method, only boundaries of a inclusion corner tip domain need to be discretized, i. e. , 2D meshes with high density are avoided. Generalized stress intensity factors which represent the intensities of stress fields at the corners of inclusions are systematically calculated with varying the material type, shape and arrangement of polygonal inclusions. In numerical examples, the inclusion-matrix interfaces are assumed to be perfectly bonded, and some numerical results are compared with existing results. The present method is found to be yield rapidly converging numerical solutions with high accuracy. Relative to the conventional finite element method, even the boundary integral equation method, the method is more versatile, attractive and potentially very useful in the analysis of micromechanics of heterogeneous materials.