A class of integro-differential variational inequalities with applications to viscoelastic contact

✍ Scribed by M. Sofonea; A. Rodríguez-Arós; J.M. Viaño

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 813 KB
• Volume: 41
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/j.mcm.2004.01.011

✦ Synopsis

We consider a class of abstract evolutionary variational inequalities arising in the study of frictional contact problems for linear viscoelastic materials with long-term memory. First, we prove an abstract existence and uniqueness result, by using arguments of evolutionary variational inequalities and Banach's fixed-point theorem. Next, we study the dependence of the solution on the memory term and derive a convergence result. Then, we consider a contact problem to which the abstract results apply. The problem models a quasistatic process, the contact is bilateral and the friction is modeled with Tresca's law. We prove the existence of a unique weak solution to the model and we provide the mechanical interpretation of the corresponding convergence result. Finally, we extend these results to the study of a number of quasistatic frictional problems for linear viscoelastic materials with long-term memory.