Stability of the equilibrium of an elastic ring in the presence of radial shear (Q1062806)

An exact formulation of the nonlinear theory of elasticity is used to study the problem of bifurcation of equilibrium in a circular annulus. It is assumed that the inner boundary is rigidly clamped and tangential stresses act on the outer boundary. The material considered is isotropic and incompressible, with elastic Mooney potential. The subcritical state is determined from the exact solution of the problem of shear under finite deformations. After separating the variables in the equations of neutral equilibrium, the problem is reduced to a system of ordinary differential equations. The critical value of the tangential load intensity is determined by numerical methods.