Dual formulation of a quasistatic viscoelastic contact problem with tresca's friction law

B. Awbl (1) , M. Shillor (2) , M. Sofonea (1)

1 LTS - Laboratoire de Théorie des Systèmes
2 Department of Mathematics and Statistics

We consider quasistatic evolution of a viscoelastic body which is in bilateral frictional contact with a rigid foundation, We derive two variational formulations for the problem: the primal formulation in terms of the displacements and the dual formulation in terms of the stress field. We prove the existence of a unique solution to each one and establish the equivalence between the two variational formulations. We also prove the continuous dependence of the solution on the friction yield limit.

Mots clés: Quasistatic bilateral frictional contact; Viscoelastic constitutive law; Dual problem; Fixed point; Tresca's law of friction

Domaines: Mathématiques [math]

B. Awbl, M. Shillor, M. Sofonea. Dual formulation of a quasistatic viscoelastic contact problem with tresca's friction law. Applicable Analysis, 2001, 79 (1-2), pp.1-20. ⟨10.1080/00036810108840949⟩. ⟨hal-01352587⟩