Local uniqueness and continuation of solutions for the discrete Coulomb friction problem in elastostatics

Patrick Hild (1) , Yves Renard (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 MIP - Mathématiques pour l'Industrie et la Physique

This work is concerned with the frictional contact problem governed by the Signorini contact model and the Coulomb friction law in static linear elasticity. We consider a general nite dimensional setting and we study local uniqueness and smooth or nonsmooth continuation of solutions by using a generalized version of the implicit function theorem involving Clarke's gradient. We show that for any contact status there exists an eigenvalue problem and that the solutions are locally unique if the friction coe cient is not an eigenvalue. Finally we illustrate our general results with a simple example in which the bifurcation diagrams are exhibited and discussed

Mots clés: local uniqueness; unilateral contact; Coulomb friction; Clarke’s gradient; bifurcation

Domaines: Analyse numérique [math.NA]

Patrick Hild, Yves Renard. Local uniqueness and continuation of solutions for the discrete Coulomb friction problem in elastostatics. Quarterly of Applied Mathematics, 2005, 63, pp.553-573. ⟨10.1090/S0033-569X-05-00974-0⟩. ⟨hal-00690592⟩