A mixed variational formulation of a contact problem with wear

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).

Mircea Sofonea
Laboratoire de Mathématiques et Physique, Université de Perpignan

Flavius Patrulescu
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Ahmad Ramadan
Laboratoire de Mathématiques et Physique, Université de Perpignan

viscoplastic material, frictional contact, normal compliance, unilateral constraint, wear, mixed variational formulation, history-dependent operator, weak solution

M. Sofonea, F. Pătrulescu, A. Ramadan, A mixed variational formulation of a contact problem with wear, Acta Appl. Math., vol. 153 (2018), pp. 125-146.

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3745733

1380.74089

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