ON EXTREME THINNING AT THE NOTCH TIP OF A NEO-HOOKEAN SHEET

The deformation and stress fields around the apex of a notch (in an in finite, thin and incompressible sheet of neo-Hookean material) are inv estigated. General far-field loading and conditions ensuring vanishing tractions at the notch faces are considered. For certain notch angles , the sheet can exhibit a singular asymptotic mechanical behaviour, ch aracterized by unbounded in-plane stresses, accompanied by transversal extreme thinning. The problem, which is formulated within the nonline ar elastostatic plane stress theory, is governed by a quasilinear syst em of two partial differential equations of the second order with resp ect to the two in-plane components of the unknown deformation. An asym ptotic analysis is performed to extract a solution from such a system. As the notch angle varies, emphasis is placed on the degree of singul arity of the Cauchy stress fields as well as on the behaviour of the t ransverse stretch at the apex.