Axisymmetric contact and crack problems for an initially stressed neo-Hookean elastic layer

A solution of the contact problem for an initially stressed neo-Hookean infinite layer is obtained. The layer is assumed to be bonded to a rigid foundation. The punch is taken to be axisymmetric and in particular, the conical and cylindrical shapes of the punch are considered in detail. The expression for the total load applied to the punch to maintain a given displacement is obtained. We have also considered the penny-shaped crack in the layer under an initial stress. The crack is taken to lie in the central plane of the layer. The surfaces of the layer are considered to be either stress free or fixed. Expressions for the stress intensity factors are obtained. Numerical values of the physical quantities are exhibited graphically.