Some generalized anti-plane strain problems for an inhomogeneous elastic halfspace

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This paper develops a generalized formulation of the theory of anti-plane deformations of a linear elastic solid, the Lamé constants of which depend on a single spatial variable. The generalized theory is applied to the study of a generalized screw dislocation, a semi-infinite crack and a finite crack located in a halfspace region where the elastic inhomogeneity is depth dependent. The problems examined in this paper are relevant to the modelling of cracks located in inhomogeneous geological materials and the study of surface defects associated with functionally graded materials.

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