Stress relaxation recovery after partial

In an experiment which combines stress relaxation and recovery, sudden shear strain 70 is applied to a viscoelastic liquid at time t = ti, and stress relaxation is observed until a time r = 0 at which there is still some residual stress. Then the stress is removed and the decreasing strain is observed as a function of time. It is given by 5 

All the relations in Sections B to F above may be regarded as originating in the Boltzmann superposition principle or the constitutive equation of Chapter 1, equation 7. The foundation of the theory has also been related to the principles of linear irreversible thermodynamics. It has been pointed out by Meixner that certain other postulates are taken for granted. Many of the specific predictions 

Relations among the linear viscoelastic functions with numbers of equations (in this chapter unless otherwise specified). 

The relations among the various types of linear viscoelastic functions are summarized in Fig. 3-9 with equation numbers identified. The equation numbers for calculation of viscoelastic constants are identified in Table 3-1. 

For further details on the theory of linear viscoelasticity, the treatise of Tschoegl may be consulted. 

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As with the elastic solid we can see that as the stress is applied the strain increases up to a time t = t. Once the stress is removed we see partial recovery of the strain. Some of the strain has been dissipated in viscous flow. Laboratory measurements often show a high frequency oscillation at short times after a stress is applied or removed just as is observed with the stress relaxation experiment. We can replace a Kelvin model by a distribution of retardation times ... 

Compressive creep tests allow measurement of strain as a function of time when a constant stress is applied. These can be conducted at several stress levels for aerogel of various densities. Loads are removed at the end of the creep test, and strains as a function of time are monitored to determine the recovery behavior. Compressive relaxation tests can be conducted at different strain levels. The relaxation functions determined at the same strain level at different temperatures can be shifted horizontally to determine whether a master curve can be formed for use to determine the long-term behavior. Recovery behavior after relaxation can also be characterized by monitoring the stress as a function of time after removing partially the step strain. For aerogels that contain polymers such as X-aerogels... 

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