Axial pulling of a neo-Hookean fiber embedded in a generalized neo-Hookean matrix

In this paper, we study the mechanical behavior of a slightly compressible neo-Hookean fiber, which is subjected to an axial pullout displacement, embedded in a slightly compressible generalized neo-Hookean matrix. We study three different boundary value problems containing both fully and partially embedded fibers. We study the effect of material and geometric parameters on the force required to axially displace the fiber, the shear stress at the interface and in the interior of the fiber-matrix system, and the norm of the Green-St. Venant strain. We found an interesting result in that the maximum shear stress occurs in the interior of the matrix when the shear modulus of the fiber is comparable to that of the matrix. Furthermore, as the fiber and matrix becomes more compressible, the maximum shear stress decreases.