Abstract
In this article, we studied the modeling of a hyperelastic rod during large displacements in the presence of a frictional self-contact described by the Coulomb’s law. Compared to other works the self-contact subject with friction is addressed as a problem in itself. This problem generates nonlinear constraints leading to difficulties in mathematical and numerical analysis. To relax the problem of these constraints, an augmented Lagrangian method was used. As a result, we overcame the implicit nature of the Signorini-Coulomb-self-contact formulas. We presented, on the one hand, a result of the existence of the solution. On the other hand, we have proposed an approach that can be useful for a numerical implementation of this problem.