Models and Analysis of Quasistatic Contact
Variational Methods
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15 Result(s)
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Mircea Sofonea
Physics
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Book
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Chapter
1 Introduction
Considerable progress has been achieved recently in modeling and mathematical analysis of various processes involved in contact between deformable bodies. Indeed, a general Mathematical Theory of Contact Mecha...
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Chapter
5 A Detailed Representative Problem
In the previous three chapters various constitutive laws for the behaviour of the material and different contact conditions were described in some detail. In this chapter we take the next step and assemble, in...
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Chapter
10 Slip or Temperature Dependent Frictional Contact
The frictional contact problems which have been described up to now contained a constant friction coefficient, although, as was described in Sect. 2.7, in many applications it depends on the slip speed, on the...
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Chapter
7 Elastic Contact
Existence results for the problem of quasistatic contact between an elastic material and a reactive foundation were first obtained in [18] and [19]. In both papers the normal compliance contact condition was e...
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Chapter
12 Contact with Damage
We describe new results dealing with contact problems for materials that may undergo internal damage, resulting from strains and stresses which lead to the opening and growth of microscopic cracks. The damage ...
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Chapter
14 Conclusions, Remarks and Future Directions
This monograph shows clearly that the branch of the Mathematical Theory of Contact Mechanics which deals with quasistatic processes has made an impressive progress in the last decade. Indeed, from a handful of...
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Chapter
4 Thermodynamic Derivation
In this chapter we present a short review of thermodynamic principles and potentials and describe their use in derivation of general thermomechanical conditions and equations, as applied to processes involved ...
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Chapter
6 Mathematical Preliminaries
Part II provides mathematical formulations of the models, the assumptions that underlie them, their weak or variational formulations and the statements of the results. Each chapter also describes representativ...
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Chapter
8 Viscoelastic Contact
We describe results for contact problems involving viscoelastic materials. It will be seen that adding viscosity to the models leads to a substantial increase in the regularity or the smoothness of the solutio...
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Chapter
13 Dynamic, One-Dimensional and Miscellaneous Problems
The previous part of this monograph makes it clear that the branch of the Mathematical Theory of Contact Mechanics, which deals with quasistatic problems, has been develo** and expanding rapidly. Other branc...
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Chapter
3 Additional E.ects Involved in Contact
More is involved in contact than just friction, although it is the main process. Indeed, during a contact process elastic or plastic deformations of the surface asperities may happen. Also, some or all of the ...
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Chapter
9 Viscoplastic Contact
We describe contact problems for viscoplastic materials in which once the stress reaches the so-called yield limit the deformation becomes irreversible. Metals behave as viscoplastic materials, for instance, d...
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Chapter
2 Evolution Equations, Contact and Friction
Contact processes take place on the surface, and, therefore, are described by boundary conditions. However, these are the boundaries or surfaces of mechanical bodies or structures, and one has to describe the ...
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Chapter
11 Contact with Wear or Adhesion
In this chapter we present results on models of frictional contact when the wear of the contacting surfaces is taken into account. The importance of the control and minimization of the wear of industrial parts...
