Stress concentration factors around a circular hole in two fiber reinforced materials under large deformations

Abstract

In this paper, we study the deformation and the stress concentration factor due to a small circular hole in a thin nonlinearly elastic large sheet reinforced by two families of fibers under a state of plane stress undergoing large deformations. We restrict our attention to the class of materials wherein the fibers are mechanically equivalent, rendering the body orthotropically symmetric with respect to the planes whose normals are along the angular bisectors of the angles between the fibers. Furthermore, we limit ourselves to the problems of equibiaxial, uniaxial and pure shear deformations of the body whose fibers are symmetrically oriented with respect to the Cartesian coordinate axes. These deformations indicate strong influence of the fiber angle on the stress concentration factors and a significant difference in the stress concentration factor distribution around the hole when using a constitutive relation based on a partial set of invariants (I4,I6) versus an extended constitutive relation that incorporates the full set of invariants appropriate for a body reinforced with fibers and reduces appropriately to the orthotropic linearized elastic case. We show how two constitutive relations that exhibit a similar biaxial behavior in the absence of discontinuities show noticeable differences under uniaxial and pure shear deformation with the dissimilarities magnified in the presence of discontinuities like a circular hole.