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    STUDIA MATHEMATICA - Issue no. 1 / 2009  
         
  Article:   A FRICTIONLESS ELASTIC-VISCOPLASTIC CONTACT PROBLEM WITH NORMAL COMPLIANCE, ADHESION AND DAMAGE.

Authors:  LAMIA CHOUCHANE, LYNDA SELMANI.
 
       
         
  Abstract:  We study a quasistatic frictionless contact problem with normal compliance, adhesion and damage for elastic-viscoplastic material. The adhesion of the contact surfaces is modeled with a surface variable, the bonding field, whose evolution is described by a first order differential equation. The mechanical damage of the material, caused by excessive stess or strains, is described by a damage function whose evolution is modeled by an inclusion of parabolic type. We provide a variational formulation of the problem and prove the existence and uniqueness of a weak solution. The proofs are based on time-dependent variational equalities, classical results on elliptic and parabolic variational inequalities, differential equations and fixed point arguments.

Key words and phrases: quasistatic process, elastic-viscoplastic material, damage, normal compliance,adhesion, weak solution, variational equality, ordinary differential equation, fixed point.
 
         
     
         
         
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