含双周期不等长刚性线材料有效反平面剪切模量研究

研究无限介质中含双周期刚性线夹杂复合材料的反平面问题,其基本胞元含有四条不同长度的刚性线夹杂。运用椭圆函数和保角变换理论,获得了该问题严格的闭合解。利用微结构的周期性和平均应力/应变定理得到了复合材料有效反平面剪切模量的精确公式。由结果的特殊情形可以得到一系列有意义的解答。数值结果给出了该类非均匀材料有效反平面剪切模量随微结构参数变化的规律。精确解可以为其它数值和近似方法提供有价值的参考。

EFFECTIVE MODULUS OF COMPOSITE MATERIALS WITH DOUBLY PERIODIC RIGID LINE INCLUSIONS OF UNEQUAL LENGTH SUBJECT TO ANTIPLANE SHEAR

Composite materials with doubly periodic rigid line inclusions under antiplane shear in an infinite medium are discussed. Its representative cell contains four rigid lines of unequal size. By using the elliptic function and conformal transformation theory, a close form solution to this problem is obtained. The effective antiplane shear modulus of the composite material is derived using the periodicity of the microstructure and the average stress/strain theorem. A series of meaningful solutions for various arrays of periodic rigid lines can be obtained as special cases. Numerical results demonstrate the variations of the effective antiplane shear modulus of such heterogeneous materials with microstructure parameters. The present close form solution can also provide benchmark solution for other numerical or approximate methods.