Linear viscoelastic behavior definition

It is now easy to understand why the viscoelastic behavior of filled vulcanizates at large strains is so complex and why it is so difficult to investigate in definitive manner. None of the processes responsible for stress-softening occur instantaneously (16,182), nor can they generally be expected to obey the time-temperature relationships of linear viscoelasticity. Since time-temperature superposition is no longer applicable,... 

Since by definition the viscoelastic material in shear exhibits both the behavior governed by equation 6 and than represented by equation 8, the constitutive relation for the linear viscoelastic solid can be written as... 

Mechanical testing procedures in common use involve other patterns of stress history than the simple creep and relaxation experiments on which the definitions of the transient viscoelastic functions are based, and the sinusoidally varying stress which is inherent in the definitions of the so-called dynamic properties. Certain relations between the behavior under coniplicated conditions and the basic viscoelastic functions are presented here together with some related problems. They are limited to linear viscoelastic systems and hence small strains, but in some cases could be extended to describe larger deformations, especially for simple extension. 

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