Generally, the mixed boundary value problems in fracture and contact mechanics may be formulated in terms of integral equations. Through a careful asymptotic analysis of the kernels and by separating nonintegrable singular parts, the unique features of the unknown functions can then be recovered. In mechanics and potential theory, a characteristic feature of these singular kernels is the Cauchy singularity. In the absence of other nonintegrable kernels, Cauchy kernel would give a square-root or conventional singularity. On the other hand, if the kernels contain, in addition to a Cauchy singularity, other nonintegrable singular terms, the application of the complex function theory would show that the solution has a non-square-root or unconventional singularity. In this article, some typical examples from crack and contact mechanics demonstrating unique applications of such integral equations will be described. After some remarks on three-dimensional singularities, the key examples considered will include the generalized Cauchy kernels, membrane and sliding contact mechanics, coupled crack-contact problems, and crack and contact problems in graded materials.
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September 2008
Special Issue Honoring Professor Fazil Erdogan’S Contributions To Mixed Boundary Value Problems Of Inhomogeneous And Functionally Graded Materials
On the Singularities in Fracture and Contact Mechanics
Fazil Erdogan,
Fazil Erdogan
Department of Mechanical Engineering and Mechanics,
Lehigh University
, Bethlehem, PA 18015
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Murat Ozturk
Murat Ozturk
Department of Mechanical Engineering and Mechanics,
Lehigh University
, Bethlehem, PA 18015
Search for other works by this author on:
Fazil Erdogan
Department of Mechanical Engineering and Mechanics,
Lehigh University
, Bethlehem, PA 18015
Murat Ozturk
Department of Mechanical Engineering and Mechanics,
Lehigh University
, Bethlehem, PA 18015J. Appl. Mech. Sep 2008, 75(5): 051111 (12 pages)
Published Online: July 11, 2008
Article history
Received:
August 31, 2007
Revised:
January 10, 2008
Published:
July 11, 2008
Citation
Erdogan, F., and Ozturk, M. (July 11, 2008). "On the Singularities in Fracture and Contact Mechanics." ASME. J. Appl. Mech. September 2008; 75(5): 051111. https://doi.org/10.1115/1.2936241
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