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 W1,2-quasiconvex.
|Number of pages||10|
|Journal||Quarterly Journal of Mechanics and Applied Mathematics|
|Publication status||Published - Aug 1997|