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By A. S. Nowick

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4) it will be shown t h a t the equality also holds w h e n / a n d vary relatively slowly over a b r o a d range of time, regardless of t h e m a g nitude of the relaxation strength. I n the most general cases, however, E q . 2-2) m u s t be used to provide t h e implicit relation between t h e creep a n d stress relaxation functions. 3 Relation s b e t w e e n Quasi-Stati c a n d D y n a m i c Propertie s I n order to relate t h e creep function to t h e dynamic response functions a 0eitot. / ι ( ω ) or J 2(co) we make use of E q .

T h e purpose of this chapter is to show t h e validity of this last statement a n d to derive t h e interrelationships a m o n g t h e various response functions. + T h e utility of these functions is that they represent simply a strain (in the case of J x and J 2) or a stress (in the case of Mx and M2) in a specified experiment. T h e quantity is essentially a ratio of two strains or of two stresses, while | J | is the square root of the sum of squares of two strains. T h e latter quantities do not permit one to take advantage of the simplicity inherent in the linear equations of anelasticity as easily as do the selected functions.

W i t h the aid of E q . 1-1) w h e n all coefficients except a 0> a ly and bx are zero, and the equation is divided t h r o u g h by a 0. Like E q . 2-1) for the Voigt model, this result involves j u s t one m o r e t e r m t h a n the case of ideal elasticity which, in fact, is obtained in t h e limit of τ - * o o . Expressions for the creep function and the stress relaxation function can easily be derived from E q . 2-2). However, it is already clear t h a t the Maxwell model does not describe an anelastic material, since it displays steady viscous creep, rather t h a n the recoverable creep characteristic of anelasticity.

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