Hierarchical multi-scale models for mechanical response prediction of highly filled elastic-plastic and viscoplastic particulate composites

Though a vast amount of literature can be found on modelling particulate reinforced composites and suspensions, the treatment of such materials at very high volume fractions V-f (> 90%), typical of high performance energetic materials, remains a challenge. The latter is due to the very wide particle size distribution needed to reach such a high value of V-f. In order to meet this challenge, multiscale models that can treat the presence of particles at various scales are needed. This study presents a novel hierarchical multiscale method for predicting the effective properties of elasto-viscoplastic polymeric composites at high V-f. Firstly, simulated microstructures with randomly packed spherical inclusions in a polymeric matrix were generated. Homogenised properties predicted using the finite element (FE) method were then iteratively passed in a hierarchical multi-scale manner as modified matrix properties until the desired filler V-f was achieved. The validated hierarchical model was then applied to a real composite with microstructures reconstructed from image scan data, incorporating cohesive elements to predict debonding of the filler particles and subsequent catastrophic failure. The predicted behaviour was compared to data from uniaxial tensile tests. Our method is applicable to the prediction of mechanical behaviour of any highly filled composite with a non-linear matrix, arbitrary particle filler shape and a large particle size distribution, surpassing limitations of traditional analytical models and other published computational models.