Hierarchical composites: Analysis of damage evolution based on fiber bundle model

A computational model of multiscale composites is developed on the basis of the fiber bundle model with the hierarchical load sharing rule, and employed to study the effect of the microstructures of hierarchical composites on their damage resistance. Two types of hierarchical materials were considered: "hierarchical tree" (bundles-of-bundles of fibers) and self-similar particle and fiber reinforced composite (in which reinforcements at each scale level represents composites in turn consisting of lower level reinforcements and matrix). For the case of the hierarchical tree ("bundle-of-bundles" material), it was observed that the increase in the amount of hierarchy levels leads to the lower strength of material. In the self-similar fiber reinforced matrix materials, as differed from the hierarchical trees, the damage resistance of the hierarchical materials increases with increasing the amount of hierarchy levels. The effect of mixed fiber and particle reinforcement on the damage resistance of the hierarchical composites is investigated as well.