Kelvin-Voigt body

Earlier in the theory of viscoelasticity many rheological models with combinations of the Maxwell and the Voigt - Kelvin bodies were considered (see Freudental and Geiringer [1]). These models have constitutive laws for stresses o j and strains eij which include time derivatives of arbitrary order. 

In which element or model for a viscoelastic body will the elastic response be retarded by viscous resistance (a) Maxwell or (b) Voigt-Kelvin ... 

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. 

Maxwell bodies are obtained if Hookean and Newtonian bodies are connected in series (Figure 11-11). The Kelvin or Voigt model, on the other hand, contains Hookean and Newtonian bodies in a parallel arrangement (Figure 11-11). The Maxwell body is a model for relaxation phenomena and the Kelvin body is a model for retardation processes. 

If the creep experiment is extended to infinite times, the strain in this element does not grow indefinitely but approaches an asymptotic value equal to tq/G. This is almost the behavior of an ideal elastic solid as described in Eq. (11 -6) or (11 -27). The difference is that the strain does not assume its final value immediately on imposition of the stress but approaches its limiting value gradually. This mechanical model exhibits delayed elasticity and is sometimes known as a Kelvin solid. Similarly, in creep recovery the Maxwell body will retract instantaneously, but not completely, whereas the Voigt model recovery is gradual but complete. 

The compliance J t) at any time was described by a six-element model made up of an instantaneous compliance, two Kelvin-Voigt bodies, and Newtonian compliance (Sherman 1970) ... 

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