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The Quarterly Journal of Mechanics and Applied Mathematics 2003 56(4):483-491; doi:10.1093/qjmam/56.4.483
© 2003 by Oxford University Press
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On Isotropic, Frame-Invariant, Polyconvex Strain-Energy Functions

David J. Steigmann1

( 1 Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA )

We discuss the problem of generating polyconvex and coercive strain-energy functions for isotropic elastic solids. Such functions meet the main requirements of Ball's fundamental existence theory. We demonstrate that a formulation based on the principal invariants of the right stretch tensor, which has advanced analytical work to a considerable degree, furnishes a natural setting for this purpose. It is shown that this formulation is amenable to numerical treatment in that it does not require explicit polar decompositions or eigenanalysis. We thus adapt to a computational setting a formulation of isotropic finite elasticity theory which has been highly successful in analytical studies.

Received 5 August 2002. Revised 10 January 2003.


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