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On the theory of plane strain in finitely deformed compressible materials

Published online by Cambridge University Press:  24 October 2008

R. Hill
R. Hill
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Extract

In solid mechanics an outstanding lacuna is a general method for solving problems of plane strain for materials other than classically elastic, or visco-elastic, or rigid–plastic. Even with restriction to incrementally linear response, and to infinitesimal deformations superimposed on uniform pre-strains, there is no body of theory with the scope and power of the complex variable approach in isotropic elasticity. This lack has been highlighted recently by the growing interest in bifurcation phenomena in finitely deformed materials. So far, all analytical solutions to plane boundary-value problems with bifurcations (1,2,3,4) have relied on a separation-of-variables technique, which succeeds only for certain types of data.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 1 , July 1979 , pp. 161 - 178
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

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