Modeling strain hardening in glassy polymers based on the microscopic mechanisms revealed by molecular dynamic simulations

Abstract

We perform molecular dynamics (MD) simulations to investigate the microscopic mechanisms underlying strain hardening in glassy polymers. The results reveal that strain hardening originates from heterogeneous local stretching within entangled segments of polymer chains. In each segment, the most extended bond, defined as the load-bearing bond, governs the response of the segment to mechanical deformation. Through averaging the stretch of these load-bearing bonds, a load-bearing deformation gradient is defined, which correlates with the macroscopic stress response through a neo-Hookean relation in the hardening regime. The extracted hardening modulus is independent of chain length, temperature, and strain rate, indicating that it may represent an intrinsic material constant. We further propose an evolution equation for the relaxation of entangled segments driven by the hardening stress based on MD observations. Through incorporating the load-bearing and entanglement relaxation mechanisms, a constitutive model is further developed with the ability to accurately capture the stress–strain relationship of glassy polymers across a broad range of temperatures, strain rates, and chain lengths. The work provides a unified microscopic theoretical framework for complex mechanical behavior of glassy polymers.