Model Analogies of Linear Viscoelastic Behavior

MECHANICAL MODEL ANALOGIES OF LINEAR VISCOELASTIC BEHAVIOR 

For example, when the Maxwell model, Fig. 1 -9, is subjected to a stress relaxation experiment as in Fig. 1 -4, the force on each spring-dashpot pair relaxes exponentially expressed in terms of the modulus analogy, we have the contribution of the /th pair to the modulus, G, t), given by 

It was pointed out by Poincare that if a physical phenomenon can be represented by one mechanical model it can also be represented by many other models. Thus, springs and dashpots could be arranged in many different patterns, as dis- 

Equations 7 and 9 are two of many possible expressions of the Boltzmann superposition principle that the effects of mechanical history are linearly additive, where the stress is described as a function of rate of strain history or alternatively the strain is described as a function of the history of rate of change of stress. Many early treatises have elaborated on the effects of different sequences of stressing or straining according to this principle, and it has been tested by a variety of experiments. The procedure may be illustrated by some characteristic sequences of stress history. 

We take first a trivial example of just two events in stress history, continuing to omit the subscripts 21 but with the understanding tha the deformation is simple shear. If a stress is applied at t = 0 and an additional stress gb is applied at t. = ti, the total strain at time t is found by applying equation 9 to be 

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D. MECHANICAL MODEL ANALOGIES OF LINEAR VISCOELASTIC BEHAVIOR... 

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