ANTIPLANE SHEAR OF A STRIP CONTAINING A STAGGERED ARRAY OF RIGID LINEINCLUSIONS

Motivated by the increased use of fibre-reinforced materials, we illus trate how the effective elastic modulus of an isotropic and homogeneou s material can be increased by the insertion of rigid inclusions. Spec ifically we consider the two-dimensional antiplane shear problem for a strip of material. The strip is reinforced by introducing two sets of ribbon-like, rigid inclusions perpendicular to the faces of the strip . The strip is then subjected to a prescribed uniform displacement dif ference between its faces, see Figure 1. it should be noted that the p roblem posed is equivalent to that of the uniform antiplane shear prob lem for an infinite two-dimensional material containing a staggered ar ray of rigid inclusions (see [1] for a review of antiplane problems in the literature). The problem is reduced in standard fashion [2-6] to a mixed boundary value problem in a rectangular domain, whose closed f orm solution given in terms of integrals of Weierstrassian Elliptic fu nctions, is obtained via triple sine series techniques. The effective shear modulus of the reinforced strip can now be calculated and compar ed 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 g eometries.