A mean-field shear transformation zone theory for amorphous polymers

The complex nonlinear constitutive behavior of amorphous polymers has been extensively investigated in numerous experiments, displaying a strong dependence on the thermal history and loading path. Theoretical models have been proposed to conjoin the underlying mechanisms to certain aspects of mechanical features, such as yielding, strain hardening, physical aging, and the Bauschinger effect. However, an urgent need for theoretical understanding capable of fulfilling the comprehensive predictions of the featured constitutive behaviors of amorphous polymers is to be addressed. In this paper, we develop a micromechanical mean-field shear transformation zone (STZ) model to systematically describe the stress responses of amorphous polymers. The dynamics of STZ is affected by the nonequilibrium structural state described by effective temperature and also related to the anisotropic internal structure induced by the microscopical deformation. Our model exhibits the ability to fully capture the behaviors of amorphous polymers in constant rate/ switch rate loading, creep, relaxation, and loading-unloading-reloading cycles. The model is further verified by reproducing the Bauschinger effect in experiments, which remains a challenge to other widely used models. Our results show that the deformation-induced material polariza-tion, in the form of an anisotropic distribution of STZs, is the governing mechanism of the Bauschinger effect. This work establishes a comprehensive relationship between the microscopic mechanisms and the constitutive behaviors of deforming amorphous polymers, which advances the fundamental understanding of complex mechanical behaviors in amorphous glassy polymers.