Internal viscosity model, yield stresses

For a food whose flow behavior follows the Casson model, a straight line results when the square root of shear rate, (y), is plotted against the square root of shear stress, (cr) , with slope Kc and intercept Kqc (Figure 2-2). The Casson yield stress is calculated as the square of the intercept, ctoc = (Kocf and the Casson plastic viscosity as the square of the slope, r]ca = The data in Figure 2-2 are of Steiner (1958) on a chocolate sample. The International Office of Cocoa and Chocolate has adopted the Casson model as the official method for interpretation of flow data on chocolates. However, it was suggested that the vane yield stress would be a more reliable measure of the yield stress of chocolate and cocoa products (Servais et al., 2004). 

We have already seen in Section 11.3.4 that yield can be modelled using the Eyring process. Many workers [19,49-56] have considered that the applied stress induces molecular flow much along the lines of the Eyring viscosity theory where internal viscosity decreases with increasing stress. The basic equation for the plastic strain rate has been given as Equation... 

Non-linear constitutive equations are developed for highly filled polymeric materials. These materials typically exhibit an irreversible stress softening called the "Mullins Effect." The development stems from attempting to mathematically model the failing microstructure of these composite materials in terms of a linear cumulative damage model. It is demonstrated that p order Lebesgue norms of the deformation history can be used to describe the state of damage in these materials and can also be used in the constitutive equations to characterize their time dependent response to strain distrubances. This method of analysis produces time dependent constitutive equations, yet they need not contain any internal viscosity contributions. This theory is applied to experimental data and shown to yield accurate stress predictions for a variety of strain inputs. Included in the development are analysis methods for proportional stress boundary valued problems for special cases of the non-linear constitutive equation. 

To account for the nonideal nature of real soUds and liquids, the theory of Unear viscoelasticity provides a generaUzation of the two classical approaches to the mechanics of the continuum-that is, the theory of elasticity and the theory of hydromechanics of viscous Uquids. Simulation of the ideal boundary properties elastic and viscous requires mechanical models that contain a combination of the ideal element spring to describe the elastic behavior as expressed by Hooke s law, and the ideal element dash pot (damper) to simulate the viscosity of an ideal Newton Uquid, as expressed by the law of internal friction of a liquid. The former foUows the equation F = D -x (where F = force, x = extension, and D = directional force or spring constant). As D is time-invariant, the spring element stores mechanical energy without losses. The force F then corresponds to the stress a, while the extension x corresponds to the strain e to yield a = E - e. 

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