On uniqueness and stability in the theory of finite elastic strain

Abstract It is shown that there is a direct relation between the criterion for stability of an elastic solid in a state of finite strain and the criterion for a unique solution to the associated boundary-value problem set by given velocities and nominal traction-rates on its surface. The criteria are obtained in a particularly simple form through a convenient choice of stress and strain variables. A suggestive connexion exists between the structure of the criteria and the idea of functional convexity in relation to the strain-energy density; this concept is explained in detail. Finally, the stability limit is characterized by eigenfunctions, or adjacent positions of equilibrium.