Constitutive Modeling of Vitrimers and Their Nanocomposites Based on Transient Network Theory

In recent years, vitrimers have emerged as significant alternatives to traditional thermosets because of their self-healing and reprocessing capabilities at temperatures higher than their topological freezing temperature (Tv) and thermoset-like properties at lower temperatures. In the present work, we have developed a constitutive model based on the transient network theory (TNT), building upon the statistical mechanics of evolving polymer networks, to characterize the time- and temperature-dependent mechanical response of vitrimers. We propose a deformation-dependent evolution of the bond exchange reaction (BER) kinetics in the networks under finite deformation to explain the nonlinear viscoelasticity observed in vitrimer’s short-term mechanical behavior. In addition, the long-term diffusion-driven chain dynamics are incorporated using a constant-rate kinetic term influencing the slower mobility of the cross-linked network. We further extend this theory to predict the mechanical response of vitrimer composites (vitrimers added with nanoparticle fillers). We numerically implement the theory in a commercial finite element package by writing a user material subroutine (UMAT) and assess the model’s ability to capture the mechanical response of various vitrimers. Careful calibration strategies have been adopted for the model parameters based on the underlying micromechanics of the vitrimer networks, as evident from the experiments. The model predictions are validated against various experimental responses, such as stress relaxation, loading–unloading, and creep at different temperatures.