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 ε ε during the period 0 < t ≤ t * and to the constant strain ε * ( = ε 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.