摘要：Bone and other natural material exhibit a combination of strength and toughness that far exceeds that of synthetic structural materials. Bone's toughness is a result of numerous extrinsic and intrinsic toughening mechanisms that operate synergistically at multiple length scales to produce a tough material. At the system level however no theory or organizational principle exists to explain how so many individual toughening mechanisms can work together. In this paper, we utilize the concept of phonon localization to explain, at the system level, the role of hierarchy, material heterogeneity, and the nanoscale dimensions of biological materials in producing tough composites. We show that phonon localization and attenuation, using a simple energy balance, dynamically arrests crack growth, prevents the cooperative growth of cracks, and allows for multiple toughening mechanisms to work simultaneously in heterogeneous materials. In turn, the heterogeneous, hierarchal, and multiscale structure of bone (which is generic to biological materials such as bone and nacre) can be rationalized because of the unique ability of such a structure to localize phonons of all wavelengths.
