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    STUDIA MATHEMATICA - Issue no. 2 / 2010  
         
  Article:   ANALYSIS OF A BILATERAL CONTACT PROBLEM WITH ADHESION AND FRICTION FOR ELASTIC MATERIALS.

Authors:  . 		 
       
         
  Abstract:  We consider a mathematical model which describes a contact problem between a deformable body and a foundation. The contact is bilateral and is modelled with Tresca’s friction law in which adhesion is taken into account. The evolution of the bonding field is discribed by a first order differential equation and the material’s behavior is modelled with a nonlinear elastic constitutive law. We derive a variational formulation of the mechanical problem and prove the existence and uniqueness result of the weak solution. Moreover, we prove that the solution of the contact problem can be obtained as the limit of the solution of a regularized problem as the regularizaton parameter converges to 0. The proof is based on arguments of time-dependent variational inequalities, differential equations and Banach fixed point theorem.

Key words and phrases. Elastic materials, adhesion, Tresca’s friction, fixed point, weak solution.
 
         
     
         
         
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