A New Curing-Dependent Viscoelastic Constitutive Model and Stress-Increment Equations for Numerical Simulation Predicting the Cure-Induced Stress of Epoxy Resin

A cure-dependent viscoelastic constitutive model is developed to describe the stress response of epoxy resin during curing. The progressive formation of the load-carrying network is represented phenomenologically through cure-dependent equilibrium and Maxwell-branch stiffness functions. A one-dimensional history-integral equation is derived and extended to non-isothermal conditions by incorporating temperature-dependent stiffness and reduced-time effects. Explicit stress-increment equations are then obtained for one-dimensional and three-dimensional isotropic materials and implemented in ABAQUS through a UMAT. Two idealized numerical cases are used to verify the consistency between the UMAT results and direct constitutive calculations. An illustrative encapsulation model further shows that different assumptions regarding the curing-dependent stiffness factor produce substantial differences in peak and final stresses. An additional cooling-rate sensitivity analysis shows that increasing the cooling rate increases the magnitude of the final compressive stress because less time is available for viscoelastic relaxation. A formal tensorial extension is also provided for anisotropic thermosetting materials, although it is not numerically assessed. The present results constitute constitutive and numerical verification rather than material-specific experimental validation.