A Model of Couple Stress Effect Upon the Transverse Stiffness of a Fiber-Reinforced Material

The purpose of this paper is to demonstrate the possible effect of couple stresses on the transverse elastic moduli of anisotropic composite material systems. Couple stress theory considers that within an elastic body, the surface of each element of material is subjected not only to normal and tangential stress components but also to a moment component designated as a couple stress, thus introducing another elastic constant of the material. The necessary theory of elasticity needed for this purpose is developed and extended from the available classical theory found in the literature. The model considered is a uniaxially loaded infinitely long rectangular cell of composite material with a circular fiber located at the center. The stress and displacement fields thus developed in the composite cell are for the plane strain case. A numerical solution for the transverse elastic stiffness of the composite material as a function of the elastic constants, including the moduli of curvature, of the fiber and the matrix is developed. The results thus obtained are compared with those of classical theory.