Abstract
We investigate the problem associated with two interacting circular inclusions in a composite subjected to anti-plane shear deformation. A version of the Gurtin–Murdoch model of surface/interface elasticity is incorporated into the description of the two inclusion–matrix interfaces. In contrast to previous investigations, the surface shear moduli are varied arbitrarily along the two circular interfaces. The composite is subjected to various loading mechanisms that include uniform stresses applied at infinity, uniform eigenstrains imposed on the two circular inclusions and a screw dislocation located either in the matrix or inside one of the two inclusions. Complex variable methods are used in conjunction with Fourier series expansions and matrix algebra to derive an analytical solution to the corresponding problem. The unknown coefficients in the ensuing three analytic functions are determined in an elegant manner. The size-dependent material forces acting on the two inclusions and the screw dislocation are also obtained.
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