A method of fully implicit coupled analyses for thermoset resin subjected to cure based on variationally consistent formulation for finite thermo-viscoelasticity

A variationally consistent formulation is presented to devise a method of fully implicit analysis for predicting thermo-mechanically coupled behavior of thermosetting resin subjected to cure in finite strain theory. To characterize the finite thermo-viscoelasticity coupled with cure kinetics, the dual dissipation potential (DDP) is originally defined in the thermodynamically consistent formulation, which begins with the definition of stored energy. The governing equations are derived as stationary conditions of the relevant total energy rate potential containing internal energy, and viscous and curing DDPs, and then discretized in time and space in order. In the temporal discretization process within a time interval, we utilize the function form of the equilibrium temperature obtained from the Legendre-Fenchel transformation of internal energy. The obtained time discretized equations are spatially discretized by means of the standard finite element method. The present formulation results in a fully implicit algorithm with separate systems of governing equations that can be solved in a monolithic manner. Two representative numerical examples are presented to demonstrate that, while allowing relatively large time increments, the devised analysis method provides a more realistic prediction than the previous method formulated within the framework of small strain theory.