A Nitsche type method for stress fields calculation in dissimilar material with interface crack

This work deals with the crack problem simulation in dissimilar media. It proposes a new numerical method derived from a Nitsche approach for handling interface conditions in the elasticity equations. The Nitsche method, introduced to impose weakly essential boundary conditions in the scalar Laplace operator, has been then worked out more generally and transferred to continuity conditions. We propose here an extension of this method to the Navier-Lame equations. We derive a variational formulation that provides the solution in terms of displacements field in the case of a crack existence in a plate domain Ω, made of several different layers characterized by different material properties. We formulate the method for both the homogeneous and the dissimilar material domains and report some numerical experiments.