Numerical method for stress fields calculation in dissimilar elastic material with initial crack in axially symmetrical geometry

This work deals with the crack problem simulation in dissimilar material. We propose a new numerical approach, based on a modified Nitsche's variational formulation, to handle the interface conditions in the Navier-Lame equations between two or more axially symmetrical sub domains, characterized by different material constants. This gives a numerical method easy to implement, that is able to solve problems in domains with cracks, where the stress fields tend to infinity. We present the variational formulation which provides the solution in terms of displacements field in the case of a crack existence for axisymmetric plate domain O made of several different layers characterized by different material properties.