Elastic aftereffect Kelvin model

The key point in the rheological classification of substances is the question as to whether the substance has a preferred shape or a natural state or not [19]. If the answer is yes, then this substance is said to be solid-shaped otherwise it is referred to as fluid-shaped [508]. The simplest model of a viscoelastic solid-shaped substance is the Kelvin body [396] or the Voigt body [508], which consists of a Hooke and a Newton body connected in parallel. This model describes deformations with time-lag and elastic aftereffects. A classical model of viscoplastic fluid-shaped substance is the Maxwell body [396], which consists of a Hooke and a Newton body connected in series and describes stress relaxation. 

Such process is referred to as the elastic aftereffect and can be found in solid-like systems that reveal an elastic behavior. Elastic aftereffect is mechanically reversible the removal of applied stress results in gradual decrease of strain to zero due to the energy stored in the elastic element. The object thus restores its original shape. At the same time, in contrast to the case of a truly elastic body, the deformation of an object that follows Kelvin s model is thermodynamically irreversible due to the dissipation of energy in the... 

At lowest shear stresses the behavior of bentonite clays may be the same as that of a solid-like system with high viscosity, which is consistent with the Kelvin model and corresponds to region I. The investigation of relaxation properties of coagulation structures forming in these moderately concentrated dispersions of bentonite clays revealed the existence of an elastic aftereffect at low shear stresses. This aftereffect is related to mutual coorientation of anisometric particles that are capable of taking part in rotational Brownian motion without any rupture of contacts. Consequently, the nature of elastic aftereffect is entropic. In such systems high viscosities are related... 

The elastic aftereffect is encountered in solid-like systems with an elastic behavior. The elastic behavior is reversible when the stress is removed, the strain drops gradually to zero, that is, the initial shape of the body is restored, using the energy stored by the elastic element. However, in contrast to true elastic behavior, the elastic aftereffect is thermodynamically irreversible the dissipation of energy takes place in the viscous element. The damping of mechanical oscillations in rubber, caused by harmonic stresses, is the example of a process conforming to the Kelvin model. 

As seen in Figure 3.21, a complete rheological curve contains four characteristic regions. Region I corresponds to low stresses under which the system may demonstrate a solid-like behavior with high viscosity (Kelvin model). This case is characteristic of the already mentioned bentonite clays. The studies of relaxation structures in moderately concentrated suspensions of bentonite clays indicated the appearance of elastic aftereffect at low shear stresses. This effect has an entropic nature, as it is associated with the... 

The processes involved in the elastic aftereffect can be described by a simple rheological model consisting of two Kelvin s elements connected in series, as shown in Figure 3.32a. It is worth emphasizing here that this model is applicable only in the region of low shear stresses, below the onset of Schwedow s creep. From this model, one gets the following values for the slow and fast elastic strain moduli ... 

FIGURE 3.32 The corresponding rheological models describing two stages of the elastic aftereffect. The two Kelvin elements connected in series (a) G, and strains are replaced with a single elasticity modulus, G i (b). 

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