Problem of doubly periodic coated fiber reinforced composites under antiplane shear

The elastic properties of composite materials with a doubly periodic array of coated fibers under antiplane shear were studied. An analytical solution for the problem was presented by applying the Eshelby's equivalent inclusion method and Laurent 's series expansion technique as well as combining the theory of the doubly quasi-periodic Riemann boundary value problem. The expressions for the stress field and effective modulus were obtained. The comparisons with the finite element method (FEM) show the efficiency and accuracy of the present method. The influence of the coating parameters on the stress concent ration and the effective modulus of the composites was discussed. A very high stress concent ration may occur in the coating , and the stiffer and thinner the coating is , the higher the stress concent ration. A very soft or very hard coating can shield the contribution of the fiber stiffness to the effective modulus of composites.