A Simple Model of the Treloar—Kearsley Instability

The Treloar—Kearsley instability is studied in the framework of membrane theory. The phenomenon considered is the bifurcation of an equibiaxial stretch of a thin square elastic sheet, in equilibrium under equibiaxial dead loads, to a rectangle at a critical value of the load. The membrane setting, in which the sheet is regarded as an elastic surface, leads to sharper results on the stability of equilibria than those delivered by conventional elasticity theory. Further, definite conclusions can be drawn under weaker constitutive hypotheses. These are illustrated through the use of a particular strain-energy function which renders the analysis nearly trivial.