A theoretical model of fracture of biological composites considering complex structural arrangement of microstructures

Although it is known that biological materials have remarkable fracture strength and toughness, the underlying mechanisms have not been fully understood. A key question is what effects of the structural arrangement of the microstructure are in biological materials. To address this problem, we developed a fracture model based on the fundamental solutions of the crack and rigid line inclusions in matrix to consider the roles of the complex arrangement of the microstructure. Firstly, we obtained the analytical solutions of the SIFs of three basic problems with two inclusions. These solutions revealed several fundamental toughening mechanisms of biological composites via controlling the geometric arrangement of microstructures. Then, we analyzed the fracture problem of multiple rigid lines and cracks with one-level of hierarchy of composite structure. We found that the large aspect ratio of rigid lines produces significant stress shielding effect on the main crack, but it simultaneously creates high possibility of producing local microcracks therein. Interestingly, these microcracks can significantly reduce the SIFs of the rigid lines, while only slightly increases the SIF of the main crack. Finally, we studied the effect of the hierarchical structure on the fracture toughness of biological materials. Compared with the one-level structure, the two-level hierarchy can effectively reduce the SIF of the main crack, and at the same time it becomes less sensitive to the change of the geometric parameters of the microstructures at higher level. This study may provide guidelines for the structural design of advanced biomimetic materials.