Correspondence principle, viscoelastic contact

The conclusion is also valid for viscoelastic bodies - if the non-inertial approximation applies. This follows immediately by invoking the Classical Correspondence Principle. Our object in this section is to generalize the result to the case of two viscoelastic bodies in contact. 

In chapter 1, the properties of the viscoelastic functions are explored in some detail. Also the boundary value problems of interest are stated. In chapter 2, the Classical Correspondence Principle and its generalizations are discussed. Then, general techniques, based on these, are developed for solving non-inertial isothermal problems. A method for handling non-isothermal problems is also discussed and in chapter 6 an illustrative example of its application is given. Chapter 3 and 4 are devoted to plane isothermal contact and crack problems, respectively. They utilize the general techniques of chapter 2. The viscoelastic Hertz problem and its application to impact problems are discussed in chapter 5. Finally in chapter 7, inertial problems are considered. 

In the case of viscoelastic materials, very few studies have been done, because of the complexity of their formulation. The situation is much simpler when the principle of correspondence (12) applies, that is when the domain where the boundary conditions apply, does not depend on time. Thus, for sufficiently small displacements, leading to constant dimension of the contact area, the previous equation can be generalised for viscoelastic materials. 

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