Rotational self-friction problem of elastic rods

Abstract The aim of this paper is to extend the modeling of a hyperelastic rod undergoing large displacements with tangential self-friction to their modeling with rotational self-friction. As well as the discontinuity of contact force into a contact region not known in advance, taking into account the effects of friction in this problem type underlies more serious modeling, mathematical and numerical analysis difficulties. In this paper, we present an accurate modeling of rotational and tangential self-friction with Coulomb's law and also describe an augmented Lagrangian method to present a weak variational formulation approach of this problem. We then use the minimization method of the total energy to present an existence result of solution for the nonlinear penalized formulation. Finally, we give the linearization and the finite-element discretization of the weak variational formulation that can be useful for a numerical implementation.