The main purpose of this study was to examine, modelling and optimization the fracture toughness and the fracture energy of bisphenol-A epoxy resin reinforced by silica nano-particles. Three different approaches including Gene Expression Programming (GEP), Response Surface Method (RSM) and, Decision Tree Method (DTM) have been employed to predict the effects of particle size and the weight fraction of nano-particles on the mentioned parameters. Three sizes of the nano-particles with the mean diameters of 17 nm, 25 nm and 65 nm up to 6 wt% have been used. The two general series of the nano-composites consisting of unimodal and bimodal particle size systems have been investigated. Experimental and modelling results showed that the Young’s modulus, the fracture toughness and the fracture energy increased in all composites by the addition of the silica nano-particles and also by increasing the silica weight percent. In addition, it was observed that the particle size had no considerable effect on the properties. Mixed use of particles with different sizes in a composite also showed a negligible synergy effect on the Young’s modulus and the fracture characteristics. The addition of these nano-particles did not have a significant effect on the yield strength of composites. Moreover, the best modelling approach is selected and optimized values resulted by Particle Swarm Optimization (PSO). The fracture surface was examined to understand the role of nanoparticles on toughening mechanisms by SEM.

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