Antiplane Shear of a Strip Containing a Periodic Array of Rigid Line Inclusions

Abstract

Motivated by the increased use of fiber-reinforced materials, the authors illustrate how the effective elastic modulus of an isotropic material can be increased by the insertion of rigid inclusions. Specifically, the authors consider the two-dimensional antiplane shear problem for a strip of material. The strip is reinforced by introducing a periodic array of ribbon-like, rigid inclusions perpendicular to the faces of the strip. The strip is then subjected to a prescribed uniform displacement difference between its faces. The problem is reduced in standard fashion to a mixed-boundary value problem in a rectangular domain, whose closed-form solution, given in terms of integrals of Jacobian elliptic functions, is obtained via triple sine series techniques. The effective shear modulus of the reinforced strip can now be calculated and compared with the shear modulus of a strip without inclusions. Also obtained are the stress singularity factors at the end tips of the inclusions. Numerical results are presented for several different reinforcement geometries.