Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Dynamically accelerating cracks part 2: a finite length mode III crack in elastic material


Authors: Tanya L. Leise and Jay R. Walton
Journal: Quart. Appl. Math. 59 (2001), 601-614
MSC: Primary 74R10
DOI: https://doi.org/10.1090/qam/1866550
MathSciNet review: MR1866550
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Abstract: We consider a dynamically accelerating, finite length, mode III crack in an infinite elastic body. This initial boundary value problem has the nature of a free boundary problem since the crack tip motion is a priori unknown and must be found as part of the solution after imposition of a fracture criterion. Using an analog to a Dirichlet-to-Neumann map, we reduce the fracture problem to integrodifferential equations along the boundary that, for simplicity, we combine with a stress intensity factor fracture criterion. This approach has the advantage of being applicable to cases of multiple cracks as well as, in principle, to mode I cracks and to cracks in viscoelastic materials.


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DOI: https://doi.org/10.1090/qam/1866550
Article copyright: © Copyright 2001 American Mathematical Society


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