#### Document Type

Article

#### Publication Date

1997

#### DOI

10.1016/s0895-7177(97)00091-5

#### Publication Title

Mathematical and Computer Modelling

#### Volume

25

#### Issue

12

#### Pages

11-18

#### Abstract

Motivated by the increased use of fibre-reinforced materials, we illustrate how the effective elastic modulus of an isotropic and homogeneous material can be increased by the insertion of rigid inclusions. Specifically 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 difference between its faces, see Figure 1. it should be noted that the problem posed is equivalent to that of the uniform antiplane shear problem for an infinite two-dimensional material containing a staggered array 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 form solution given in terms of integrals of Weierstrassian 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.

#### Original Publication Citation

Kerr, G., Melrose, G., & Tweed, J. (1997). Antiplane shear of a strip containing a staggered array of rigid line inclusions. *Mathematical and Computer Modelling, 25*(12), 11-18. doi:10.1016/s0895-7177(97)00091-

#### Repository Citation

Kerr, G.; Melrose, G.; and Tweed, J., "Antiplane Shear of a Strip Containing a Staggered Array of Rigid Line Inclusions" (1997). *Mathematics & Statistics Faculty Publications*. 144.

https://digitalcommons.odu.edu/mathstat_fac_pubs/144

## Comments

Elsevier open archive. Copyright © 1997 Elsevier Science Ltd.