Viscoelasticity mechanical analogues

Whilst obtaining this is the ultimate goal for many rheologists, in practice it is not possible to develop such an expression. However, our mechanical analogues do allow us to develop linear constitutive equations which allow us to relate the phenomena of linear viscoelastic measurements. For a spring the relationship is straightforward. When any form of shear strain is placed on the sample the shear stress responds instantly and is proportional to the strain. The constant of proportionality is the shear modulus... 

Simple viscoelastic models can mimic the phenomena mentioned in Table 7.1. Although the models are inadequate at high stress levels, they aid understanding, and are the basis for more complex treatments. They are mechanical analogues of viscoelastic behavioui constructed using the linear mechanical elements shown in Table 7.2. They are linear because the equations relating the force f and the extension x only involve the first power of both the variables. 

In Debye s model of dielectric relaxation, the polarisation process has a single relaxation time. The model has both electrical circuit and viscoelastic model analogues (Fig. 12.14). The electrical circuit is the dual of the mechanical model, because the voltages across the capacitor and resistor... 

It is rather complex to describe viscoelastic behaviors mathematically. We will only focus here the simple, but representative Maxwell model for viscoelastic liquids. A mechanical analogue of a Maxwell liquid model is obtained by a serial combination of a spring and a dashpot see Fig. lc(l). If the individual strain rates of the spring and the dashpot, respectively, are 4oiid liquid > then the total strain rate e is given by the sum of these two components ... 

Fig. 1. Mechanical analogues for viscoelastic behaviour of poiymers (f = flow h.e. = highly elastic ret. = retardation o.e. = ordinary elastic)...

In a mechanical model, each spring or dashpot represents a mechanical analogue to the response of the material. However, the most complex mechanical model may not be able to describe polymer concrete. In the case of rPET polymer concrete, the Maxwell and Kelvin models have elements which allow representation of the viscoelastic response. A combination of these two models in series satisfactorily describes the creep response of rPET polymer concrete. This multiparameter model is shown in Figure 4.12. 

On the nano-scale, the discrete moleculai structure of the polymer has to be considered. Segmental immobilization seems to be the primary reinforcing mechanism in true polymer nanocomposites at temperatures near and above the Tg. Reptation model and simple percolation model were used to describe immobilization of chains near solid nanopaiticles and to explain the peculiarities in the viscoelastic response of polymers near solid surfaces of lar ge polymer-inclusion contact areas. The inteiphase in the continuum sense does not exist at the nano-scale when relaxation processes in individual discrete chains are taken into account and the chains with retarded reptation catr be considered forming the iirterphase analogue irr the discrete matter. For a common polymer, all the chains in the composite are immobilized when the internal filler-matrix interface area reached about 42 m per 1 g of the nanocomposite. 

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