A variationally consistent formulation of the thermo-mechanically coupled problem with non-associative viscoplasticity for glassy amorphous polymers

This study presents a variationally consistent formulation of the thermo-mechanically coupled problem with non-associative viscoplasticity for glassy amorphous polymers. First, the decomposition of the equivalent plastic strain is carried out to derive the variational consistent evolution law of the shear yield strength with reference to the analogous approach taken for formulating the Armstrong-Frederick model. Second, an alternative form of the dual viscoplastic dissipation potential is proposed to recast the principle of maximum plastic dissipation for viscoplasticity to be of the same form of rate-independent plasticity with the introduction of the extended yield function. Third, we address the optimization problem relevant to the thermo-mechanically coupled behavior of glassy amorphous polymers within the incremental variational framework with the help of the parameterization of flow rules. 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 the monolithic method under the condition that the material behavior is stable. 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. Numerical examples are presented to demonstrate the capability of the proposed formulation in simulating actual compression tests conducted on a PMMA specimen that exhibits complex thermo-mechanically coupled phenomena.