Necessary conditions at the boundary for minimizers in finite elasticity
Pointwise algebraic conditions on the elasticity tensor are derived which are necessary for a deformation to be a local minimizer of the energy of an elastic body subjected to dead loads. In particular it is shown that the Legendre-Hadamard condition, Agmon's condition and a new condition derived by the authors are necessary conditions. It is also shown that the three aforementioned conditions are sufficient for the nonnegative of the second variation of the energy of a homogeneous deformation of a homogeneous body that has the shape of a half-ball with the deformation prescribed on the curved surface of the body.
scientific article; zbMATH DE number 3970
scientific article