On the stability of asymmetric deformations of a symmetrically-tensioned elastic sheet

Abstract

Bifurcation from a symmetrically to an unsymmetrically deformed homogeneous configuration of a plane incompressible isotropic elastic membrane subject to equal in-plane tensions is examined. Critical values of the tension at which bifurcation occurs are obtained for a general form of strain-energy function, and the nature of the deformation in the neighbourhood of the critical point is studied in detail. The stability of the global unsymmetric bifurcation branch is assessed. and secondary branching into either a homogeneous or a non-homogeneous mode of deformation is found to be possible under certain conditions.