Equilibrium strain

The fundamental equations treated in structural analyses are the mechanical equilibrium, strain-displacement relation, and stress-strain relation. The equilibrium equations in an elementary volume can be expressed ... 

After the equilibrium strain has been reached, if the applied load is increased there is no further change of strain with time but if it is decreased, the strain again decreases with time. As with force-temperature experiments there is a detectable change in mass between runs to indicate solvent loss. 

Fig. 5 shows the remaining two parameters, the equilibrium strain e and its derivative with respect to pressure. Cp. as function of p. The line is the smoothed derivatic e of the data points, plotted on the right axis. The fact that it falls on the data for 8p shows that the fit parameters are consistent with each other. 

Fig, 5 Equilibrium strain Eq axis, squares) and its derivative (line, right axis) as well as the parameter Cp (circles, right axis) as function of pressure. 

Smaller equilibrium strains than those for thixotropic systems Larger equilibrium strains than those for viscoelastic systems... 

In section 7.2.1 the idea of a relaxation time is made explicit through the assumption that, in the simplest relaxation, the material relaxes to its equilibrium strain or stress on application of a stress or strain in such a way that the rate of change of strain or stress is proportional to the difference between the fully relaxed value and the value at any instant. A similar assumption is made in the present section for the relaxation of polarisation on application of an electric field. 

The Voigt model will exhibit a creep compliance which will start from zero and asymptotically approach a constant deformation known as the equilibrium strain. The Maxwell model, on the other hand, will eventually creep at a constant rate. 

When the stress is suddenly applied in a creep test, only the dashpot offers an initial resistance to deformation, so the initial slope of the strain versus time curve is xjf]. As the element is extended, the spring provides an increasingly greater resistance to further extension, so the rate of creep decreases. Eventually, the system comes to equilibrium with the spring alone supporting the stress (with the rate of strain zero, the resistance of the dashpot is zero). The equilibrium strain is simply xJG. Quantitatively, the response is an exponential rise. 

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