双周期分布圆环形截面夹杂反平面问题的解析方法

An analytical method for bi-periodic arrays of annular cross-section inclusions under antiplane shear

研究含双周期分布圆环形截面弹性夹杂的无限大介质在远场均匀反平面应力下的弹性响应。通过在双周期圆环形区域内引入非均匀本征应变,将双周期非均匀介质问题转化为带有双周期非均匀本征应变的均匀介质问题,结合双周期函数和双准周期Riemann边值问题理论,获得了该问题弹性场的级数形式解答。作为一个应用,利用该解答预测了含双周期圆环形截面夹杂复合材料的有效纵向剪切模量。数值结果表明,在相同夹杂体积分数下,含圆环形截面夹杂的复合材料比含圆形截面夹杂的复合材料拥有更高的有效纵向剪切模量。

An infinite elastic solid containing a bi-periodic parallelogrammic array of annular cross-section inclusions under antiplane shear is dealt with. By introducing eigensrtains in bi-periodic annular regions, the problem of hi-periodic inclusions is transformed into ones of homogeneous materials with bi-periodic eigenstrains. Combined with theories of hi-period function and hi-quasi-periodic Riemann boundary value problem, the series form solutions of elastic field in each region are obtained. As an application, the ef- fective longitudinal shear modulus of composite materials containing such a hi-periodic annular cross-see- tion inclusions are predicted by the average field theory. Numerical results show that composite materi- als with annular cross-section inclusions have higher effective longitudinal shear modulus than that of composite materials with circular cross-section inclusions on the condition of the same inclusion volume fraction.