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Boundary integral equations for the scattering of elastic waves by elastic inclusions with thin interface layers (1992)

Martin, P. A.

Springer

Journal of nondestructive evaluation 11 (1992), S. 167-174

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ISSN: 1573-4862

Keywords: Elastic waves ; interface layers ; inclusions ; boundary integral equations ; uniqueness

Source: Springer Online Journal Archives 1860-2000

Topics: Electrical Engineering, Measurement and Control Technology , Mathematics

Notes: Abstract Elastic waves are scattered by an elastic inclusion. The interface between the inclusion and the surrounding material is imperfect: the displacement and traction vectors on one side of the interface are assumed to be linearly related to both the displacement vector and the traction vector on the other side of the interface. The literature on such inclusion problems is reviewed, with special emphasis on the development of interface conditions modeling different types of interface layer. Inclusion problems are formulated mathematically, and uniqueness theorems are proved. Finally, various systems of boundary integral equations over the interface are derived.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00566407

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A normal crack in an elastic half-space with stress-free surface (1993)

Martin, P. A. ; Päivärinta, L. ; Rempel, S.

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 16 (1993), S. 563-579

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ISSN: 0170-4214

Keywords: Mathematics and Statistics ; Applied Mathematics

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics

Notes: The problem of an elastic half-space with stress-free surface and a crack of arbitrary shape with prescribed displacements or tractions is reduced to an equivalent system of integral equations on the crack. For a pressurized crack in a plane perpendicular to the free surface, a scalar integral equation is derived. In properly chosen function spaces, unique solvability of the integral equation and regularity of solutions for regular data are proven.