Standard linear viscoelastic solid

Note 3 Comparison with the general definition of a linear viscoelastic behaviour shows that the polynomial P(D) and Q D) are of order one, go = afpi, a = PiiP and po = adai. Hence, the standard linear viscoelastic solid is a solid (ago>0) having instantaneous elasticity (/"(D) and 0(D) are of the same order). 

Note 4 The standard linear viscoelastic solid may be represented by ... 

Note 5 The standard linear viscoelastic solid can be used to represent both creep and stress relaxation in materials in terms of single retardation and relaxation times, respectively. 

Note 3 The relaxation time of a standard linear viscoelastic solid is r= /p( = P a. ... 

It is apparent therefore that the Superposition Principle is a convenient method of analysing complex stress systems. However, it should not be forgotten that the principle is based on the assumption of linear viscoelasticity which is quite inapplicable at the higher stress levels and the accuracy of the predictions will reflect the accuracy with which the equation for modulus (equation (2.33)) fits the experimental creep data for the material. In Examples (2.13) and (2.14) a simple equation for modulus was selected in order to illustrate the method of solution. More accurate predictions could have been made if the modulus equation for the combined Maxwell/Kelvin model or the Standard Linear Solid had been used. 

There are several models to describe the viscoelastic behavior of different materials. Maxwell model, Kelvin-Voigt model, Standard Linear Solid model and Generalized Maxwell models are the most frequently applied. 

Since neither model adequately describes the behavior of real viscoelastic materials, a combination of the classic elements is often made to gain closer representation. The most common configuration is called the standard linear solid4 configuration, and it is illustrated in Figure 6.6. A more accurate representation of actual behavior can be obtained by a composite of multiple elements of the standard linear solid configuration into a multi-element model (Figure 6.7) with an array of coefficients for each element. 

Figure 5.14 Common viscoelastic models a) Voigt/Kelvin model b) Zener model/standard linear solid.

Voigt element n. This is a Voight model which is a component, together with other Voight or Maxwell components, of a more complex viscoelastic model system, such as the standard linear solid. 

A response closer to that of a real polymer is obtained by adding a second spring of modulus in parallel with a Maxwell unit (Figure 4.12). This model is known as the standard linear solid and is usually attributed to Zener [2]. It provides an approximate representation to the observed behaviour of polymers in their viscoelastic range. In creep, both springs extend, so that... 

Fig. 3 Common viscoelastic models (a) Maxwell, (b) Kelvin-Voigt, (c) Wiechert, (d) Kelvin, and (e) standard linear solid...

We have shown (Section 5.2.7) tliat the standard linear solid, a three-component spring and dashpot model, provides to a first approximation a description of linear viscoelastic behaviour. Eyring and his colleagues [52] assumed that the deformation of a polymer was a thermally activated rate process involving the motion of segments of chain molecules over potential barriers, and modified the standard linear solid so that the movement of the dashpot was governed by the activated process. The model, which now represents non-linear viscoelastic behaviour, is useful because its parameters include an activation energy and... 

In the small viscoelasticity approximation, however, the entirely explicit formula (3.8.15), or for standard linear solid, (3.8.16), can be given for lubricated contact. The expression for a more general spectrum model is a sum of terms of the form given by (3.8.16). 

A three-parameter model, the Zener element or standard linear solid (SLS), has been used to represent viscoelastic behavior in certain solids. Two equivalent forms of the SLS are ... 

Fig. 5.7 Mechanical models used to represent the viscoelastic behaviour of polymers, (a) Maxwell model, (b) Voigt model, (c) Standard linear solid.

Figure 1- Standard Linear Solid Model for Viscoelastic Deformation of Polymers...

In the previous chapter, it was pointed out how the chemical structure of polymers influences their mechanical properties. The glass transition temperature and the rate of cooling from the melt determine whether the polymer will be a hard, stiff material, or a soft flexible material. These qualitative differences can be quantifled by measuring standard mechanical properties. The student, generally, is introduced to the subject of mechanical behavior through the study of linear elastic metals that exhibit solid behavior at normal operating temperatures and conditions. However, this study of polymers reveals that polymers exhibit fluid as well as solid behavior and are viscoelastic and viscoplastic at room temperature. The mechanical properties of polymers are strain rate sensitive and highly temperature dependent. 

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