A technique for elastic boundary value problem solutions for defects in solids is developed. The method is based on the introduction of virtual circular dislocation-disclination loops distributed continuously for satisfying the prescribed boundary conditions at free surfaces and interfaces. The set of dislocation-disclination loops which may be used as virtual ones is considered. The elastic fields and energies of the selected dislocation and disclination loops are presented. The method of the virtual circular dislocation-disclination loops is then applied to obtain the elastic fields and energies of a spherical dilatating inclusion in a plate and a half-space, of a prismatic dislocation loop parallel to free surfaces of a plate and a half-space, and the elastic fields of a twist disclination loop coaxial to a cylinder.
Virtual Circular Dislocation-Disclination Loop Technique in Boundary Value Problems in the Theory of Defects
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, September 11, 2003; final revision, December 30, 2003. Editor: R. M. McMeeking. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Journal of Applied Mechanics, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Kolesnikova, A. I., and Romanov, A. E. (June 22, 2004). "Virtual Circular Dislocation-Disclination Loop Technique in Boundary Value Problems in the Theory of Defects ." ASME. J. Appl. Mech. May 2004; 71(3): 409–417. https://doi.org/10.1115/1.1757488
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