Meeting Abstract
Ligaments are over ten-fold softer than the bones that they attach to. Such mismatched materials, with large differences in their Young’s modulus, suffer from high stress concentrations at the interface and are therefore prone to failure. Nevertheless, ligament-bone attachments are remarkably robust, and it has been suggested that the robustness is because of a transitional zone with graded mineralization, leading to intermediate material properties. We evaluate this hypothesis using analytical and computational analyses of a 2D elastic model for the interface, and find a scaling law for the optimal size of the transitional zone. Although any gradation of the Young’s modulus alleviates the interfacial stress concentration, we find that some gradation profiles do so more effectively. Finally, by analyzing the maximal stress direction in the vicinity of the interface, we propose a previously unreported functional advantage for the fanned shape of ligaments near the interface, and the anisotropic nature of ligaments because of oriented collagen fibers. Collagen fibers have a higher tensile strength than the ligament matrix. Therefore, aligning these fibers parallel to the maximal stress directions is effective at preventing shear-driven failure at the interface. The fanned geometry near the interface and the anisotropic tensile strength of ligaments both achieve this function. In summary, our analyses point to three main features of biological material interfaces for improving their robustness, namely, a graded transitional zone whose size scales as a function of the interface width, a fanned geometry and anisotropic tensile strength. Preliminary evidence from published data support these predictions, and we propose future measurements of ligament-bone interfaces from different species and sizes.
