Hierarchical composites that combine microscopic fibers and carbon nanotubes (CNTs) offer opportunities to further improve mechanical properties. Motivated by the experimental evidence that the spatial distribution of CNTs has a significant effect on the strength and toughness of these composites, we developed a novel modelling tool to help us explore mechanisms of strengthening and toughening in an efficient way. The spatial position and orientation of CNTs are chosen as design variables and their optimization is performed on the example of a unidirectional fiber-reinforced composite (FRC) subjected to transverse tensile loading. The model relies on the use of genetic algorithm and finite element method. Our modelling results show that the CNT network with an optimized morphology suppresses stress concentrations in the matrix near the fibers. The optimized morphology is shown to activate a new strengthening and toughening mechanism—diffusion of damage at micro-scale. It allows substantial increase in the consumption of the strain energy by matrix cracking, delocalization of damage, and with it, improvement of the strength and toughness. When the network morphology of 1.0 wt% of CNTs is optimized, the strength and toughness are increased by 49% and 65%, respectively, compared to the pristine FRC. The same amount of homogenously distributed CNTs in the composite leads to only 2% of the strength increase accompanied by a 13% decrease in toughness. The work emphasizes the importance of optimizing spatial position and orientation of CNTs for the strength and toughness improvements of composites.
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