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8 - Antiplane Shear

from Part II - Applications

Published online by Cambridge University Press:  16 December 2019

Marko V. Lubarda  and
Vlado A. Lubarda
Marko V. Lubarda
Affiliation:
University of Donja Gorica
Vlado A. Lubarda
Affiliation:
University of California, San Diego
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Summary

Antiplane shear is a type of deformation in which the only nonvanishing displacement component is the out-of-plane displacement, orthogonal to the (x,y) plane. The corresponding nonvanishing shear stresses are within that plane. For this type of deformation, the displacement is a harmonic function of (x,y), satisfying the Laplace's equation. We solve and discuss the problems of antiplane shear of a circular annulus, a concentrated line force along the surface of a half-space, antiplane shear of a medium weakened by a circular or an elliptical hole, and the problem of a medium strengthened by a circular inhomogeneity. The stress field near a crack tip under remote antiplane shear loading is derived, as well as the stress field around a screw dislocation in infinite and semi-infinite media. The stresses produced by a screw dislocation near a circular hole or a circular inhomogeneity in an infinite homogeneous medium, and the stresses produced by a screw dislocation in the vicinity of a bimaterial interface are examined.

Keywords

antiplane shearbimaterial interfacecircular inhomogeneitycrack tiphalf-spaceelliptical holeLaplace’s equationout-of-plane displacementscrew dislocationshear stress
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Chapter
Information
Intermediate Solid Mechanics , pp. 228 - 258
Publisher: Cambridge University Press
Print publication year: 2020

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