Weak formulation of axi-symmetric frictionless contact problems with boundary elements

A boundary element formulation of the axi-symmetric elastic problem, including contact conditions for multi-domain problems, is presented in this paper and applied to the analysis of interface cracks. A weak formulation of the equilibrium and compatibility equations has been developed to allow non-conforming discretizations to be used in the contacting boundaries. In order to obtain a high accuracy in the solution (employing continuous linear elements), the singular terms appearing in the axi-symmetric boundary integral equations have been integrated analytically. The numerical analysis of a penny-shaped crack at the interface of two dissimilar materials and of a fibre-matrix debonding crack in the single fibre fragmentation test is presented.