Stress Concentration Near Stiff Cylindrical Inclusions under Anti-Plane Shear Loading

Analytical solutions for the problems of stress concentration near cylindrical inclusion with circular or elliptical cross section under the anti-plane shear loading are presented. The solutions are obtained in the framework of the isotropic strain gradient elasticity theory with the assumption of high stiffness of the inclusions as compared to the matrix, which corresponds to the typical properties of the fiber-reinforced composite materials. It is shown that near the thin fibers, diameter of which is comparable to the characteristic size of the matrix microstructure, the stress concentration can decrease in comparison with conventional estimates known in the theory of elasticity. For circular cylindrical inclusions, the closed-form solutions are obtained for composites with low volume fraction of inclusions and can be used for the strength prediction of composites under the longitudinal shear and for the identification of additional parameters of the strain gradient theory of elasticity.