Relaxation Derived as an Analogue to First-Order Chemical Kinetics

2 Relaxation Derived as an Analogue to First-Order Chemical Kinetics 

The simplest experiment we can visualise performing is the very rapid application of a small strain which is then maintained at a constant level. This is simply a strain-jump experiment and can be treated in an analogous fashion to a temperature or a pressure-jump experiment. The stress will follow the strain and increase to a maximum value. For an 

The time required for the stress to reduce to 1/e of the intial value 

It is a monotonically decreasing function with time, where the rate of decay is directly proportional to the stress. Using a first-order rate expression to describe the decay of stress we get the following expression  

Now in order to obtain an expression for stress in terms of time we need to integrate from the initial time t = 0, where the maximum stress j(0) is achieved, to a time t and stress a(t) later  

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