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The Quarterly Journal of Mechanics and Applied Mathematics 1970 23(3):349-363; doi:10.1093/qjmam/23.3.349
© 1970 by Oxford University Press
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SIMILARITY SOLUTION FOR THE RAPID UNIFORM EXPANSION OF A CYLINDRICAL CAVITY IN A COMPRESSIBLE ELASTIC-PLASTIC SOLID

R. J. M. CROZIER and S. C. HUNTER

( Department of Applied Mathematics and Computing Science, University of Sheffield )

In a previous paper (1) the authors gave the solution to the problem of the dynamic expansion of a spherical cavity at a uniform rate in a compressible elastic-plastic solid.

The present paper is concerned with the parallel problem for a cylindrical cavity. As for the spherical case, the situation in which the cavity radius expands at a uniform speed V0 from zero radius yields to a similarity solution in which stress, density and particle velocity are functions of a single variable {eta} = r/t. In the present paper t is time (as in (1)) while r is now the cylindrical polar coordinate r = (x2+y2)1/2.

The principal result of the paper is the calculation of the cavity pressure P as a function of V0. For sufficiently small V0 an analytic solution is obtained; for the larger values of V0, P is determined numerically.


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