【摘要】 研究无限介质中矩形排列双周期圆柱形夹杂的纵向剪切问题.利用Eshelby等效夹杂理论并结合双周期与双准周期解析函数工具,为这类考虑夹杂相互影响的问题提供了一个严格又实用的分析方法,求得了问题的全场级数解.作为退化情形得到单夹杂问题的经典解答,双周期孔洞、双周期刚性夹杂及单行(列)周期弹性夹杂等问题也可作为特殊情况被解决.数值结果揭示了这类非均匀材料力学性质随微结构参数变化的规律.更多还原

【Abstract】 An infinite elastic solid containing a doubly periodic rectangular array of cylindrical inclusions under longitudinal shear is dealt with. By using Eshelby’s effective inclusion method, and combining the theory of doubly periodic and doubly quasi-periodic analytical functions, a rigorous and effective method for the problem considering the interaction among inclusions is presented, and the solution in series is obtained. The classic solution for a single inclusion is rearrived at as a degenerate case. The problems of doubly periodic voids, doubly periodic rigid inclusions and single periodic elastic inclusions are also solved as special cases. Numerical results disclose the influences of microstructure of a material on its mechanics properties, which include the non-uniformity of stress in inclusions caused by interaction of inclusions, non-monotonic variation of stress concentration coefficient with inclusion volume fraction in a square array and contrary dependence of stress concentration coefficient on inclusion spacings in two directions in a rectangle array.更多还原