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In a private communication with D. M. Barnett, W. D. Nix presented a series of numerical computations in which he calculated the net interaction force between two skew dislocations separated by a distance h that are parallel to the traction-free surface of an isotropic elastic half-space. Nix drew a series of conclusions from his numerical computations including the independence of the net interaction force on the distance h. In seeking the extension of Nix's conclusions to half-spaces of arbitrary anisotropy, Barnett called Nix's original set of results 'Nix's Theorem'. In this paper, using the Stroh octet formalism, we derive new explicit and real form expressions for the net interaction force between two skew dislocations with generalized Burgers vectors, separated by a distance h, in an infinite anisotropic piezoelectric space, in a half-space and in a bimaterial. Each dislocation undergoes finite discontinuities in displacements and in electric potential across the slip plane. The net interaction force is yet again found independent of the separation distance. For an infinite space and half-space with a traction-free and charge-free surface, the net interaction force is found independent of the second component of each of the two generalized Burgers vectors and vanishes when only the second component of one generalized Burgers vector is nonzero and the remaining three components are zero. [ABSTRACT FROM AUTHOR]

We study the anti-plane deformations of a linearly elastic bimaterial. One phase of the bimaterial is weakened by a finite crack with surface elasticity perpendicular to the interface and is also subjected to a screw dislocation. The surface elasticity is incorporated by using a version of the continuum-based surface/interface model of Gurtin and Murdoch. By considering a distribution of screw dislocations and line forces on the crack, the interaction problem is reduced to two decoupled first-order Cauchy singular integro-differential equations, which can be numerically solved by means of the Chebyshev polynomials and the collocation method. The associated problem of a mode III Zener-Stroh crack perpendicular to a bimaterial interface is also solved. [ABSTRACT FROM AUTHOR]

The elastostatic bending of an arbitrarily loaded bimaterial plate with a circular interface is analysed. It is shown that the deflections in the composite solid are directly related to the deflection in the corresponding homogeneous material by integral and differential operators. It is further shown that, by a simple transformation of elastic constants, the Airy stress function induced in the composite by a stretching singularity can be deduced from the deflection induced by a bending singularity. This result is significant for reduction of mathematical labour and for systematic construction of solutions for more complex structures with circular geometry. [ABSTRACT FROM AUTHOR]