Rheology Saint-Venant

It is convenient to describe these properties in terms of the following mechanical models [396] the Hooke body (an elastic spring), the Saint-Venant body modeling dry friction (a bar on a solid surface), and the Newton body (a piston in a vessel filled with a viscous fluid). By using various combinations of these elementary models (connected in parallel and/or in series), one can describe situations which are rather complex from the rheological viewpoint. 

It is well known [38, 118, 125, 280, 379] that for foam there exists a yield stress ro that classifies the types of rheological behavior of foam as follows for r < to, the foam is a solid-shaped substance, and for t > to, it is fluid-shaped. For this reason, mechanical models of foam must include the Saint-Venant body. One of the simplest macrorheological models of the foam body is shown in Figure 7.3. 

Figure 2.14 Nonlinear rheological models, (a) Saint-Venant model (b) PrandtI-Reuss model (c) Bingham model.

Nonlinear models of rheological behavior can be approximated by step functions, whereby the existence of a finite yield stress G plays a dominant role. Three typical nonlinear models include the Saint-Venant model of ideal plastic behavior, the Prandtl-Reuss model of an elastoplastic material, and the Bingham model of viscoelastic behavior. The first model can be mechanically approximated by a sliding block, the second by a Maxwell element and a sliding block in series, and the third by a dash pot damping element and a sliding block in parallel (Figure 2.14). 

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See also in sourсe #XX -- [ , ]

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