Evaluation of the relaxation modules from the response to a constant rate of strain followed by a constant strain

The stress response σ(t) to a constant rate of strain $ \dot \varepsilon $ ε during the period 0 < t ≤ t^* and to the constant strain ε^* $ ( = \dot \varepsilon t*) $ thereafter is considered in terms of the Boltzmann superposition principle. When t ≤ t^*, the data directly give the constant‐rate modulus F (t) ≡ σ(t)/ε(t), which can be converted straightforwardly into the relaxation modulus E(t). Results from illustrative calculations show that a reduction in the relaxation rate effects a decrease in [σ(t^*)/ε^*]/E(t^*) and also in the time at which [σ(t)/ε^*]/E(t) becomes essentially unity. To evaluate E(t) at t > t^*, F(t) is first obtained from σ(t) and F(t − t^*) by using a derived equation similar to that presented by Meissner. Thereafter, F(t) is transformed into E(t). For illustration, E(t) for a rubbery solid is evaluated over some 2.5 decades of time from its response to a strain rate of 0.25 min⁻¹ for 0.40 min and thereafter to the attained strain of 0.10 for 5.4 min.