tailieunhanh - Báo cáo hóa học: VISCOELASTIC FRICTIONLESS CONTACT PROBLEMS WITH ADHESION

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: VISCOELASTIC FRICTIONLESS CONTACT PROBLEMS WITH ADHESION | VISCOELASTIC FRICTIONLESS CONTACT PROBLEMS WITH ADHESION MOHAMED SELMANI AND MIRCEA SOFONEA Received 16 December 2005 Revised 8 March 2006 Accepted 9 March 2006 We consider two quasistatic frictionless contact problems for viscoelastic bodies with long memory. In the first problem the contact is modelled with Signorini s conditions and in the second one is modelled with normal compliance. In both problems the adhesion of the contact surfaces is taken into account and is modelled with a surface variable the bonding field. We provide variational formulations for the mechanical problems and prove the existence of a unique weak solution to each model. The proofs are based on arguments of time-dependent variational inequalities differential equations and a fixed point theorem. Moreover we prove that the solution of the Signorini contact problem can be obtained as the limit of the solutions of the contact problem with normal compliance as the stiffness coefficient of the foundation converges to infinity. Copyright 2006 M. Selmani and M. Sofonea. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction The adhesive contact between deformable bodies when a glue is added to prevent relative motion of the surfaces has received recently increased attention in the mathematical literature. Basic modelling can be found in 7 9 12 17 . Analysis of models for adhesive contact can be found in 1-6 10 and in the recent monographs 15 16 . An application of the theory of adhesive contact in the medical field of prosthetic limbs was considered in 13 14 there the importance of the bonding between the bone-implant and the tissue was outlined since debonding may lead to decrease in the persons ability to use the artificial limb or joint. The novelty in all the above papers is the introduction of a surface internal variable