The Boltzmann superposition principle BSP

Boltzmann extended the idea of linearity in viscoelastic behaviour to take account of the time dependence He assumed that, in a creep experiment  

This leads to the following interpretation of the creep compliance J t) any incremental stress Act applied at time t results in an incremental strain Ae(t) at a later time t given by Ae(t) = aJ t — t ), where t — t is the time that has elapsed since the application of Act. 

As an example, fig. 7.5 illustrates a two-step loading programme. The dashed curve shows the strain Acti J t — tj) that would have been present at time t 2 if the second step in stress Act2 had not been applied at tj. The actual strain is this strain plus the strain Act2 J t — t ) produced by the second step in stress applied at ti- 

It is easy to generalise to a multi-step loading programme  

5 A two-step creep experiment. See the text for explanation and symbols. 

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