| Abstract: |
The contact problem with friction has received considerable attention in recentyears. The problem is important from both physical and mathematical points ofVIew. from the purely physical side, it is known that, there is a wide fieldupon which the contact problem could be applied, such as gear teeth in mesh, huband shaft assemblies, contact surfaces for transmitting loads in rotatingcomponents, etc. . In such applications, the analysis of surface traction at thecontacting surfaces especially with friction is as important as the induced stresseswithin the bulk of the material or may be of greater importance according to thetype of the application.On the other side, and from the mathematical point of view, the contact problemacquires a great importance for its nonlinear characteristics which arise from thechange of the boundary conditions, the geometry, and the material properties.The contact constraints take the form of inequalities. Furthermore, if the frictioneffects are taken into consideration, the contact problem becomes a highlynonlinear one.The present study presents the physical concepts of the contact of solids, theclassical friction laws and the general friction theories. Moreover, the concept ofthe proposed non classical friction law is discussed. The computational modeldealing with the contact problems with friction is presented.However, many computational models have been developed for conformal or nonconformal contact problems, but nothing is developed for the multi-phase contactproblems which constitute both con formal and non conformal contact regions.The present study addresses the basic features of the multi-phase contactproblems and highlights the additional non linearities and the difficulties to solvesuch type of problems. Furthermore, the consideration of the friction effectrepresents a great source of non linearity added to the previous difficulties .
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