ON A MINIMUM PROPERTY IN NONLINEAR ELASTICITY

In plane, isotropic, elasticity a certain version of the Baker-Ericksen inequalities is shown to imply that the stored energy corresponding to any purely distortional deformation originating from a given undistorted (ground) state must be greater than the stored energy of that ground state. Together with some additional assumptions this minimum property is then shown to entail that (i) the ratio of the (plane, cross-sectional) areas of the deformed and undeformed configurations tends to unity in the stored-energy measure as the loading on the surface of the body tends to zero and (ii) a certain radical cavitating deformation is unstable when the body is subject to uniform, compressive, boundary displacement.