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The Quarterly Journal of Mechanics and Applied Mathematics 2005 58(3):333-347; doi:10.1093/qjmam/hbi027
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Q. Jl Mech. Appl. Math, Vol. 58. No. 3 © The Author 2005. Published by Oxford University Press 2005; all rights reserved. For Permissions, please email: journals.permissions@oupjournals.org

Perturbation of a dynamic crack in an infinite strip

N. V. Movchan1, A. B. Movchan1,** and J. R. Willis2

( 1 Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, 2 Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Cambridge CB3 0WA )

** abm{at}maths.liv.ac.uk

This paper presents an asymptotic analysis of a dynamic problem of two-dimensional elasticity for a crack propagating in an infinite strip. The sides of the elastic strip are subjected to Dirichlet boundary conditions. The crack motion is considered as a steady, constant speed propagation, upon which is superposed a small dynamic perturbation of the crack path, in both horizontal and vertical directions. A Wiener–Hopf problem is solved to evaluate the corresponding dynamic weight functions. Asymptotic representations for the stress-intensity factors are given in terms of the ‘crack-path-perturbation function’, the second-order asymptotics of the weight functions and the applied load. These results are then used in the analysis of the crack stability.

Received 20 April 2004. Revise 22 November 2004.


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