Pressure-dependent strain gradient plasticity for micro-mechanical analyses of fibre-reinforced polymers

A new constitutive model for epoxy resins is proposed to accurately capture the micro-scale strain fields in fibre-reinforced composites. The model extends conventional plasticity by introducing strain-gradient effects through an implicit gradient formulation that accounts for pressure sensitivity and asymmetric tension/compression behaviour–critical features to represent the mechanical response of epoxies at small scales. The formulation is implemented in a commercial finite element platform through user-defined subroutines and solved via an analogy with coupled thermo-mechanical problems that include Helmholtz-type equations. The ability of the model to predict the size-dependent response and to prevent unrealistic overpredictions of strain magnitude is illustrated through the simulation of nanoindentation on neat epoxy and of the local strain field behaviour in a composite. The results are compared with experimental data, which are also used to calibrate the additional constitutive parameters through a composite Bayesian optimization strategy. The proposed framework significantly improves the predictive capabilities of micromechanical models for composite materials by incorporating scale-dependent plasticity mechanisms.