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Abstract
The contact problem with friction has received considerable attention
in recent years. The problem is important from the practical point of view and is hard to solve mathematically.
from the purely practical side, it is known that, there is a wide field
upon which the contact problem could be applied, such as gear teeth in
mesh, hub and shaft assemblies, and contact surfaces for transmitting loads
in rotating components. In such applications, the analysis of surface
traction at the contacting surfaces especially with friction is as important as the induced stresses within the bulk of the material or may be of greater importance according to the type of application.
from the mathematical point of view, contact problem acquires a
great importance for its nonlinearity, which arises from the change of the
boundary conditions, geometry, and material properties. The contact
constraints take the form of inequalities. Furthermore, when the friction effects are taken into consideration, the contact problem becomes a highly nonlinear one.
The present study introduces the physical concepts of the contact of
solids, the classical friction laws and the enhanced friction theories.
Moreover, the concept of the proposed non-classical friction law is
discussed. The computational model dealing with elasto-plastic contact
problems with friction is addressed.
The present study addresses the basic features of the multi-phase
contact problems and highlights the additional nonlinearity and the
difficulties to solve such type of problems. Furthermore, the consideration
of the friction effect represents a great source of non-linearity added to the previous difficulties.