Boltzmann Superposition Principle in Relaxation Experiments

Let us assume that a viscoelastic material undergoes the following shear strain history — Qi), and Ae(02)/f(t — 02)- Let us assume further 

As indicated above, cancelation of a given perturbation is interpreted by the material as if a perturbation of opposite sign were applied on it. The Boltzmann superposition principle can be expressed in a generalized way by 

For a material with a history of discrete isotropic deformations, the evolution of the hydrostatic pressure with time can be written as 

If the values of A8(0,) are very small, the time dependence of the shear stress in Eq. (5.42) can be expressed by the relationship 

This equation, however, does not give a good account of the histories in which the strain remains constant during a given interval of time, because in 

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