Self-healing of hierarchical materials.

We present a theoretical and numerical analysis of the mechanical behavior of self-healing materials using an analytical model and numerical calculations both based on a Hierarchical Fiber Bundle Model, and applying them to graphene- or carbon-nanotube-based materials. The self-healing process can be described essentially through a single parameter, that is, the healing rate, but numerical simulations also highlight the influence of the location of the healing process on the overall strengthening and toughening of the material. The role of hierarchy is discussed, showing that full-scale hierarchical structures can in fact acquire more favorable properties than smaller, nonhierarchical ones through interaction with the self-healing process, thus inverting the common notion in fracture mechanics that specimen strength increases with decreasing size. Further, the study demonstrates that the developed analytical and numerical tools can be useful to develop strategies for the optimization of strength and toughness of synthetic bioinspired materials.