SOME NEW IMPLICATIONS OF CERTAIN CONSTITUTIVE INEQUALITIES IN PLANE ISOTROPIC ELASTICITY

In plane isotropic elasticity a strengthened form of the Ordered-Force s inequality is shown to imply that the restriction of the strain-ener gy function to the class of deformation gradients which share the same average of the principal stretches is bounded from below by the strai n energy corresponding to the conformal deformations in this class. Fo r boundary conditions of place, this property (together with a certain version of the Pressure-Compression inequality) is then used (i) to s how that the plane radial conformal deformations are stable with respe ct to all radial variations of class C-1 and (ii) to obtain explicit l ower bounds for the total energy associated with arbitrary plane radia l deformations. For the same type of boundary conditions and together with a different version of the Pressure-Compression inequality, an an alogous property in plane isotropic elasticity (established in [3] und er the assumption that the material satisfies a strengthened form of t he Baker-Ericksen inequality and according to which the restriction of the strain-energy function to the class of deformation gradients whic h share the same determinant is bounded from below by the strain energ y corresponding to the conformal deformations in that class) is used ( i) to show that the plane radial conformal deformations are stable wit h respect to all variations of class C-1 and (ii) to obtain explicit l ower bounds for the total energy associated with any plane deformation .