Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A new method for solving dynamically accelerating crack problems. I. The case of a semi-infinite mode $ {\rm III}$ crack in elastic material revisited

Authors: J. R. Walton and J. M. Herrmann
Journal: Quart. Appl. Math. 50 (1992), 373-387
MSC: Primary 73M25; Secondary 73D99
DOI: https://doi.org/10.1090/qam/1162281
MathSciNet review: MR1162281
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Presented here is a new method for constructing solutions to dynamically accelerating, semi-infinite crack problems. The problem of a semi-infinite, anti-plane shear (mode III) crack accelerating dynamically in an infinite, linear, homogeneous, and isotropic elastic body has been solved previously by Freund and Kostrov. However, their methods are based upon the construction of a certain Green's function for the ordinary two-dimensional wave equation and do not generalize to either the opening mode problem in elastic material or viscoelastic material. What is presented here is a new approach based upon integral transforms and complex variable techniques that does, in principle, generalize to both the opening modes of deformation and viscoelastic material. Moreover, the method presented here produces directly, for the mode III crack, a simple closed form expression for the crack-face profile for arbitrary applied crack-face tractions. Generalizations to opening modes of deformation and viscoelastic material produce integral equations for the crack-face displacement profile that in some cases admit closed form solutions and otherwise can be solved numerically. In contrast, the method of Freund and Kostrov yields, in mode III, an expression for the stress in front of the crack, but for opening modes provides only the stress intensity factor.

References [Enhancements On Off] (What's this?)

  • [1] R. Burridge, An influence function for the intensity factor in tensile fracture, Internat. J. Engng. Sci. 14, 725-734 (1976)
  • [2] L. B. Freund, Dynamic fracture mechanics, Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, Cambridge, 1990. MR 1054375
  • [3] G. Goleniewski, PhD Dissertation, University of Bath, 1988
  • [4] B. V. Kostrov, Unsteady propagation of longitudinal shear cracks, Appl. Math. Mech. 30, 1241-1248 (1966)
  • [5] J. R. Willis, Accelerating cracks and related problems, Elasticity, Mathematical Methods and Applications, G. Eason and R. W. Ogden eds., Ellis Horwood Ltd., Chichester, 1990, pp. 397-409

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73M25, 73D99

Retrieve articles in all journals with MSC: 73M25, 73D99

Additional Information

DOI: https://doi.org/10.1090/qam/1162281
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society