8. Conclusion

Discreet contact friction models with 1D and 2D sliding surfaces have been implemented in*Code_Aster*. These models that can be used with STAT_NON_LINE and DYNA_NON_LINE are available under DEFI_CONTACT.

The proposed models are based on the meshes of the surfaces coming into contact and make it possible to transcribe node to node the conditions of contact and friction between the surfaces after discretization of the corresponding variational formulation. The method then extends easily from small trips to large trips. In fact, the absence of use of finite elements, between the surfaces that may come into contact, avoids the great distortion of the latter, in the case of large displacements. It is then possible to use either direct node-to-node link conditions for initially compatible meshes, or weighted node-to-node link conditions using a master-slave projection approach for incompatible meshes.

In the case of 1D sliding surfaces, it was possible to develop an algorithm using only Lagrange multipliers. The finite convergence of this type of algorithm is proved for the unilateral contact without friction and in the case with friction for low values of the Coulomb friction coefficient. In the case of 2D sliding surfaces, the friction contact is treated by regularization.