Frictionless contact between an elastic layer on a rigid base and a circular flat-ended punch with rounded edge or a conical punch with rounded tip

The axi-symmetric frictionless indentation problem involving an elastic layer on a rigid base and a rigid indenter (punch) having either a rounded edge or a rounded tip profile has been investigated. The layer is either firmly attached to a rigid base (bonded layer) or resting without friction on a rigid base (unbonded layer). A set of asymptotic solutions for the contact pressure is derived for thin layers. Numerical and theoretical results showed good agreement.