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The Quarterly Journal of Mechanics and Applied Mathematics 1970 23(3):365-387; doi:10.1093/qjmam/23.3.365
© 1970 by Oxford University Press
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AN APPROXIMATE SOLUTION TO THE PROBLEM OF THE NON-UNIFORM EXPANSION OF A SPHERICAL CAVITY IN A COMPRESSIBLE ELASTIC-PLASTIC SOLID

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

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

In a previous paper (1) the authors determined the pressure required to expand a spherical cavity at a uniform rate in a compressible elastic-plastic solid. The present paper extends the previous results to the case of non-uniform cavity expansion.

The analysis is approximate and uses the previously found similarity solutions of (1) to provide a basic approximation for the unsteady problem. Correction terms are determined for the velocity field, and the pressure in the cavity is evaluated as a function of a(t), (t) and ä(t), where a(t) is the cavity radius.


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