Incremental variational formulation of time evolution of cure-degree along with viscoelasticity for thermosetting resins

In the thermodynamically consistent formulation of the material behavior of thermosetting resins subjected to curing, a dual dissipation potential (DDP) for the cure state is originally derived in conjunction with that for viscoelasticity, and the free energy combined with these DDPs is applied to the incremental variational framework (IVF) to construct an algorithm to efficiently solve the equilibrium problem. By the introduction of the ‘cure’ multiplier as an internal variable to the cure’s DDP, a flow rule for the degree of cure (DOC), which is equivalent to the stationary condition of the Legendre-Fenchel transformation, is defined as a constraint condition for the rate of change of the total energy in the IVF. The flow condition of the DOC for the prescribed flow rule that is analogous with that of viscoplasticity is transformed along the lines of Perzyna’s viscoplastic over-stress theory and is therefore fully consistent with the vairational structure of mathematical theory for plasticity. As a result, the governing equation for the global equilibrium and the constitutive equations for local material behavior, which correspond to the stationary conditions of the rate of change of the total energy within the IVF, are also variationally consistent so that all the state variables can be implicitly solved in the numerical scheme. The verification analysis is carried out to confirm that the proposed method provides the same numerical result with that obtained by the conventional framework.