This study presents a thermo-mechanical coupled variational update for glassy amorphous polymers and investigates how the mechanical entropy change influences the thermo-mechanical behaviors of glassy amorphous polymers. The evolution of the viscoplastic strain associated with the intermolecular resistance is modeled by the co-operative model proposed by Richeton et al. (2007), while the strain-softening behavior is represented by the evolution law of shear yield strength originally proposed by Boyce et al. (1988). These models are, in particular, formulated in accordance with the Perzyna type viscoplastic regularization theory and derived as the pseudo dual dissipation potential along with parameterization of flow rules (Mosler and Bruhns, 2010). On the other hand, the strain hardening associated with the entropic resistance is modeled by the alternative phenomenological hyperelastic model because the non-Gaussian network model is not appropriate for the modeling of entropy change in the sense of unsteady heat conduction. Then, the thermo-mechanical coupled problem is established with the incremental variational formulation for non-associative viscoplasticity (Matsubara and Terada, Preprint), so that the effect of entropy change is naturally involved in our present model.

Thanks to the achieved variational consistency, the mathematical model derived by the proposed formulation can enjoy several benefits for ensuring the stability of the strongly coupled discretized equations. In addition, since the present formulation does not require the time derivative of the shear yield strength, the resulting evolution equation accommodates the time variations of temperature in terms of its material properties, implying that it is amenable to various thermal processes other than isothermal ones.

The entropy in our present model is constructed as the sum of elastic, viscoplastic, and pure thermal parts. Among these, the elastic and viscoplastic parts are often neglected because they are thought to have little contributions to temperature change. However, once the material undergoes large deformation, the viscoplastic part of entropy associated with the entropic resistance drastically increases in response to the further deformation. For this reason, the non-negligible temperature reduction occurs, so that the stress rising arises faster than that in the isothermal condition because of the temperature dependence of the limiting chain extensibility. This study investigates such a problem quantitatively and tries to settle by the introduction of a correction factor proposed by Bartels et al. (2015) which means the contribution ratio between energy storage and dissipation.

The comparative study with the results of Arruda et al. (1995) is conducted to verify the performance of our present model and to investigate the effect of mechanical entropy change.


A Thermo-Mechanical Coupled Variational Update for Glassy Amorphous Polymers in Consideration of the Effect of Mechanical Entropy Change

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Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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