IJPAM: Volume 78, No. 8 (2012)

BOUNDARY INTEGRALS WITH VECTOR POTENTIALS
APPLIED TO MATRIX INCLUSION PROBLEM

S.I. Zaman
Department of Mathematics and Statistics
Sultan Qaboos University
P.O. Box 36, Post Code 123, Muscat, OMAN


Abstract. The inclusion problems arise in a natural way in some solid-state phase changes. These changes have metallurgical significance. For instance, the austenite-martensite transformation in steel manufacture can be regarded as an inclusion problem. Martensite plates can be considered as an elastic inclusion within the matrix, that generates misfit stresses similar to the generation of classical thermoelastic stresses by temperature gradients, and with equally significant physical effects. Eshelby [#!Eshelby!#] formulated the stress field generated by an ellipsoidal elastic inclusion within an infinite elastic continuum with the use of imagined operations of cutting, space filling and welding. These usages are essentially an intuitive application of Somigliana’s formula which is a vector analogue of Green’s formula as implied by Jaswon and Symm [#!Jassym!#]. Boundary Integral method is well suited to achieve efficient numerical solutions for wide variety of problems involving a thin interface between a finite and infinite medium. Some numerical results are obtained.

Received: July 1, 2012

AMS Subject Classification: 74B10

Key Words and Phrases: linear elasticity, vector potentials, boundary integral equation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 8