Numerical simulation of strain-softening behavior of glass-filled polymer composites: Comparison of two-dimensional and three-dimensional analyses using Arruda-Boyce and Three-Network viscoplastic models

Most polymers and stiff-filler reinforced polymer composites exhibit post-yield strain-softening characteristics under large deformation mechanical loading. Singh et al. [Polymer Composites, 40 (12), pp. 4726–4741, 2019] conducted compression tests on glass-filled epoxy composites, altering the shape and volume percent of the glass fillers, and observed a dominant strain-softening tendency immediately after the yield stress values. This study aims to capture the post-yield strain-softening characteristics of glass-filled epoxy composites reported by Singh et al. using finite element analysis (FEA). Arruda - Boyce (AB) and Three Network (TN) viscoplastic constitutive material models are used as matrix behavior to perform numerical simulations on two-dimensional and three-dimensional representative volume elements (RVEs), where spherical (circular in 2D) and milled/cylindrical (rectangular in 2D) fillers are randomly positioned and oriented inside. When the calibrated AB and TN models were used to simulate the stress-strain response of the pristine matrix, both models numerically converged and were in good agreement with the experimental results. However, when filler-reinforced polymer composites are considered, the simulations using the AB model become unstable and fail to converge soon after the yield stress (at small strain values) is reached. Whereas simulations using the TN model take a short period to converge to large strain values compared to the former model. The existence of an extra elastic-viscoplastic network in the TN model improves stability in the model's strain-softening zone, allowing for faster numerical convergence. Therefore, the TN model can be used to simulate the strain-softening behavior of both pristine and stiff-filler-reinforced polymer composites under large deformations. The true stress versus true strain data retrieved from the FEA of the two-dimensional and three-dimensional simulations using the TN model were compared with experimental data. When the TN constitutive model was used in three-dimensional simulations instead of the AB viscoplastic model, the elastic modulus, yield stress, and post-yield strain-softening characteristics of the spherical particle and milled fibre epoxy composites were shown to predict the experimental data rather well.