A note on the stability of certain deformations of compressible nonlinearly elastic media

Abstract.

The main stability result established in [15] (according to which a plane strain equilibrium solution of a harmonic material which satisfies the tension-extension condition is globally stable for boundary conditions of place and zero body forces if and only if a weakened form of the Baker-Ericksen inequality is satisfied at this particular solution) is extended in two different directions. Firstly, it is shown that this stability result holds not only for plane strain but also for three-dimensional deformations and secondly, for the case when the sum of principal stretches is constant, it is shown (following [17] where such a result was obtained within the context of a discussion regarding the plane strain radial inflation of hollow cylinders) that if for boundary conditions of place and zero body forces a certain equilibrium solution is stable relative to the harmonic materials, then it is also stable relative to a certain generalization of these materials.