Maxwellian Fluids; Viscoelastic Solids

Abstract

Maxwellian fluids are viscous fluids possessing certain elastic properties which yield so-called normal stress effects (Weissenberg effects). The latter are very reminiscent of the properties of solids. On the other hand, the viscoelastic solids are elastic solids which, in addition, possess certain viscous properties. Both classes of materials have no sharp dividing line and, from the point of view of the construction of the thermodynamical model, should be considered jointly. However, this is not done for both historical and practical reasons. We shall also not do so in this chapter. Its first part is devoted to the construction of a model of the Maxwellian fluid. It is done “almost” by means of extended thermodynamics, as explained earlier in this book. There is, however, a deviation from the method in the construction of the constitutive relations for the sources. On the other hand, the extended thermodynamics of viscoelastic solids is an illustration of the method without any deviations, but it shall only be presented very briefly in the second part of this chapter.