A Mixed Variational Formulation of a Contact Problem with Wear

Mircea Sofonea (1) , Flavius Pătrulescu (2) , Ahmad Ramadan (1)

1 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations
2 Tiberiu Popoviciu Institute of Numerical Analysis

We consider a mathematical model which describes the sliding frictional contact between a viscoplastic body and an obstacle, the so-called foundation. The process is quasistatic, the material’s behavior is described with a viscoplastic constitutive law with internal state variable and the contact is modelled with normal compliance and unilateral constraint. The wear of the contact surfaces is taken into account, and is modelled with a version of Archard’s law. We derive a mixed variational formulation of the problem which involve implicit history-dependent operators. Then, we prove the unique weak solvability of the contact model. The proof is based on a fixed point argument proved in Sofonea et al. (Commun. Pure Appl. Anal. 7:645–658, 2008), combined with a recent abstract existence and uniqueness result for mixed variational problems, obtained in Sofonea and Matei (J. Glob. Optim. 61:591–614, 2014).

Mots clés: Ciscoplastic material; Frictional contact; Normal compliance; Unilateral constraint; Wear; Mixed variational formulation; History-dependent operator; Weak solution

Domaines: Mathématiques [math]

Mircea Sofonea, Flavius Pătrulescu, Ahmad Ramadan. A Mixed Variational Formulation of a Contact Problem with Wear. Acta Applicandae Mathematicae, 2017, ⟨10.1007/s10440-017-0123-4⟩. ⟨hal-01627028⟩