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The Quarterly Journal of Mechanics and Applied Mathematics 1997 50(3):427-433; doi:10.1093/qjmam/50.3.427
© 1997 by Oxford University Press
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STABILITY OF THE ELASTIC ENERGY IN STAR-SHAPED DOMAINS

K. ZHANG

( Department of Mathematics, Heriot-Watt University Riccarton, Edinburgh, EH14 4AS )

For pure displacement boundary value problems of compressible hyperelastic materials with affine boundary values and small body forces, we show that the energy of any smooth solution is close to the energy of that of the affine mapping given by the boundary condition. The energy of any minimizer is also close to that of the affine mapping provided that the minimizer exists. The main assumptions are that the reference configuration is star-shaped and the stored energy function is strongly W12-quasiconvex.


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