Thermo-chemo-mechanical model and variational multiscale framework for material and geometric evolution in frontal polymerization

Abstract

This paper presents a thermodynamically consistent model for thermo-chemo-mechanical processes in frontal polymerization (FP). The model consists of cure kinetics, heat transfer, and finite strain kinematics of nonlinear inelastic solid undergoing finite deformation. The constitutive relations are derived by enforcing non-negative entropy production which implies the existence of cure induced inelastic processes during material property evolution. Rapid curing triggered by thermo-chemical processes results in traveling reaction fronts that traverse the domain, and material properties evolve across these fronts on short time scales, accompanied with chemical expansion/contraction of the constituents. Complexity of the process increases with increased rate of chemical reaction, increased rate of mass transport, and large mechanical deformations. Evolving nonlinearities and coupled thermo-chemo-mechanical effects give rise to spatially localized phenomena that exhibit shear bands, steep gradients, and boundary and/or internal layers. The presence of interfacial effects can also trigger jumps in the fields, leading to further classification as mathematically non-smooth mixed-field problems. These modeling issues require mathematical formulations that can handle rapidly evolving material nonlinearity as well as steep traveling gradients. A stabilized finite element method that is based on the Variational Multiscale (VMS) framework is employed. A unique attribute of the VMS framework is the derivation of the residual-based fine-scale models that represent subgrid scale physics. These models enhance the stability of the numerical method as well as the accuracy of the computed physics. Several test cases are presented that investigate the mathematical attributes of the constitutive model for FP, and the role of enhanced stability and higher spatial accuracy of the proposed stabilized method in free-form printing with evolving polymerization front.