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Performing an energy balance on a viscoelastic material undergoing shear can be far from straightforward, a point which is not always recognized in the rheological literature. It is difficult to recommend a text where the matter is dealt with clearly and fully. The most complete analysis is that of Tschoegl [1], from which the following is mainly taken.
During a rheological experiment, a body is supplied with mechanical energy. A full energy balance would consider the resulting in changes in kinetic, surface, potential, thermal and all other forms of energy within the sample. But rheology is concerned only with the deformation and rate of deformation of materials, and the contributions from most of these other forms of energy are considered to be negligible. In other words the sample is considered to have constant volume and surface area. The change in kinetic energy arising from its acceleration from rest is ignored, and it is considered to be in constant thermal equilibrium with its surroundings. The heating effect of the thermal energy generated is also ignored. 
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