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The Quarterly Journal of Mechanics and Applied Mathematics 1993 46(4):545-568; doi:10.1093/qjmam/46.4.545
© 1993 by Oxford University Press
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ANTIPLANE DYNAMIC CRACK PROPAGATION IN A NON-HOMOGENEOUS VISCOELASTIC STRIP

C. ATKINSON and N. D. APARICIO

( Department of Mathematics, Imperial College of Science London SW7 2AZ )

A semi-closed solution to the problem of antiplane crack propagation along an inhomogeneous viscoelastic strip is obtained. The material is assumed to be isotropic and with symmetrical viscoelastic properties on each side of the crack as well as symmetrical distribution of the density. The procedure is similar to that applied by the first author and C. H. Popelar for homogeneous materials which involves a change to a moving system of reference, application of the Laplace and Fourier transforms and use of the Wiener-Hopf technique with the help of Cauchy's theorem. Expressions for the Laplace transform in time of the stress-intensity factors as a function of crack-tip speed and material parameters are obtained, and are used to calculate the stress-intensity factor for the steady-state case. In some interesting cases, a verification using energy considerations was possible. Finally, a numerical example using data for ‘polyurethane’ is discussed.


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