Elastic component

The component with the lower viscosity tends to encapsulate the more viscous (or more elastic) component (207) during mixing, because this reduces the rate of energy dissipation. Thus the viscosities may be used to offset the effect of the proportions of the components to control which phase is continuous (2,209). Frequently, there is an intermediate situation where a cocontinuous or interpenetrating network of phases can be generated by careflil control of composition, microrheology, and processing conditions. Rubbery thermoplastic blends have been produced by this route (212). 

One of the most important conclusions from this is that since both the viscous and the high elastic components of deformation depend on both time and temperature, the total deformation will depend on time and temperature. Since this fact has been shown to be an important factor affecting many polymer properties it is proposed to consider the background to this in greater detail in the following section. 

The spring is the elastic component of the response and obeys the relation... 

Example 2.14 A plastic is subjected to the stress history shown in Fig. 2.45. The behaviour of the material may be assumed to be described by the Maxwell model in which the elastic component = 20 GN/m and the viscous component r) = 1000 GNs/m. Determine the strain in the material (a) after u seconds (b) after 1/2 seconds and (c) after 3 seconds. 

J7 In a tensile test on a plastic, the material is subjected to a constant strain rate of 10 s. If this material may have its behaviour modelled by a Maxwell element with the elastic component f = 20 GN/m and the viscous element t) = 1000 GNs/m, then derive an expression for the stress in the material at any instant. Plot the stress-strain curve which would be predicted by this equation for strains up to 0.1% and calculate the initial tangent modulus and 0.1% secant modulus from this graph. 

To add to this picture it should be realised that so far only the viscous component of behaviour has been referred to. Since plastics are viscoelastic there will also be an elastic component which will influence the behaviour of the fluid. This means that there will be a shear modulus, G, and, if the channel section is not uniform, a tensile modulus, , to consider. If yr and er are the recoverable shear and tensile strains respectively then... 

The analytic validity of an abstract parallel elastic component rests on an assumption. On the basis of its presumed separate physical basis, it is ordinarily taken that the resistance to stretch present at rest is still there during activation. In short, it is in parallel with the filaments which generate active force. This assumption is especially attractive since the actin-myosin system has no demonstrable resistance to stretch in skeletal muscle. However, one should keep in mind, for example, that in smooth muscle cells there is an intracellular filament system which runs in parallel with the actin-myosin system, the intermediate filament system composed of an entirely different set of proteins, (vimentin, desmin, etc.), whose mechanical properties are essentially unknown. Moreover, as already mentioned, different smooth muscles have different extracellular volumes and different kinds of filaments between the cells. 

It is implicit in the idea of a series elastic component that there should be a lag between the activation of the contractile apparatus and the rise of force measured between the ends of the muscle. The observed time lag is also commensurate with the idea that the series component is largely due to the crossbridges themselves. 

FIGURE 28.9 Idealized cyclic stress-strain curve, showing the fuU viscoelastic curve together with its elastic component. (Redrawn from Andrew, C., Introduction to Rubber Technology, Knovel e-book publishers, 1999.)... 

Returning to Eq. (1) and considering the response of a biomaterials to an imposed stress in a relatively slow process (long process time, tp and low Deborah number, De), the elastic component, the second term, of Eq. (1) will be small and the wall material is likely to behave in a viscous manner. Thus Eq. (1) reduces to ... 

Rayleigh Scattering of the Phonons Due to the Elastic Component of Ripplon-Phonon Interaction... 

APPENDIX A RAYLEIGH SCATTERING OF THE PHONONS DUE TO THE ELASTIC COMPONENT OF RIPPLON-PHONON INTERACTION... 

The plastic deformation of a member terminates with its rupture which normally occurs at the smallest section of the neck formed due to plastic instability. After being loaded into the plastic range, if the member is unloaded before plastic instability occurs then the elastic component of the strain can be recovered. This is a consequence of the atoms returning to... 

In the molten state polymers are viscoelastic that is they exhibit properties that are a combination of viscous and elastic components. The viscoelastic properties of molten polymers are non-Newtonian, i.e., their measured properties change as a function of the rate at which they are probed. (We discussed the non-Newtonian behavior of molten polymers in Chapter 6.) Thus, if we wait long enough, a lump of molten polyethylene will spread out under its own weight, i.e., it behaves as a viscous liquid under conditions of slow flow. However, if we take the same lump of molten polymer and throw it against a solid surface it will bounce, i.e., it behaves as an elastic solid under conditions of high speed deformation. As a molten polymer cools, the thermal agitation of its molecules decreases, which reduces its free volume. The net result is an increase in its viscosity, while the elastic component of its behavior becomes more prominent. At some temperature it ceases to behave primarily as a viscous liquid and takes on the properties of a rubbery amorphous solid. There is no well defined demarcation between a polymer in its molten and rubbery amorphous states. 

Figure 18. (A) Fourier transformation spectra of the time trace of surface pressure for the steady loop (see Figure 17). Top real part (elastic component), bottom imaginary part (viscous component). (B) Inverted Fourier Spectra for the real and imaginary parts.

For a viscoelastic solid, the loss modulus which reflects the viscous processes in the material is unaffected by the presence of a spring without a dashpot. The storage modulus includes the elastic component G(0) ... 

It is a complex quantity. The phase lag ( > between the stress and the strain determines the real part G (the elastic component) and the imaginary part G" (the loss component) ... 

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