Shape memory property of amorphous polymer networks. Mechanical model

The shape memory property of amorphous polymer networks is the result of two intrinsic properties of these materials: 1) The viscoelasticity and 2) the time-temperature superposition property. This can be proven by characterizing the material linear viscoelasticity and time-temperature superposition with DMA (dynamic mechanical analysis) tests and by introducing these properties in a TRS (thermo-theologically simple) finite strain model. We used Simo’s model that is a generalized Maxwell model defined in finite strain including the time-temperature superposition. We used this model because it is already implemented in Abaqus finite element code and therefore easy to use. Doing so we have been able to predict the strain recovery and stress recovery presented in the experimental posts 1 and 2. Why this is working albeit the applied storage strain is large and the material parameters are estimated in infinitesimal strain? Because the time-temperature superposition recorded at infinitesimal strain applied to large strain too as long as the material is not in the glassy state showing yield.

Prediction of shape recovery obtained in torsion show very good representation of the experimental data based on parameters fitted on linear viscoelasticity DMA tests added of the hyperelastic stress-strain response of the material in the rubbery state (obtained with a mere uniaxial tension tests at high temperature and slow strain rate). The heating ramp dependance is very well reproduced.

Predictions of strain and stress recoveries in uniaxial tension (figure below) show also very good representation of the experimental data. The only prediction that is not very satisfactory is for the stress recovery of a sample submitted to large strain (50%)  at a temperature of 45 °C in the glass transition. It is anticipated that at such a temperature and such a high strain, the molecular motion are different than what is observed in the rubbery state and therefore which may explain discrepancy between the model and the experiments.

If interested you can find more on the model and an input file for Abaqus in:

J. Diani, P. Gilormini, C. Frédy, I. Rousseau, 2012. Predicting thermal shape memory of crosslinked network polymers from linear viscoelasticity, International Journal of Solids and Structures, 49, 793-799.
S. Arrieta, J. Diani, P. Gilormini, 2014. Experimental characterization and thermoviscoelastic modeling of strain and stress recoveries of an amorphous polymer network,  Mechanics of Materials,  68, 95-103.