Mechanical properties of mandibular and maxillary bone collagen fibrils based on nonlocal elasticity theory

In this paper, the mechanical properties of collagen fibrils in the cortical bone and cortical-trabecular bone interface of the human mandible and maxilla have been investigated. Force-indentation curves on wet collagen fibrils are taken by applying the atomic force microscopy nanoindentation technique, and the elastic modulus is measured. The distribution of stress and strain is determined by considering an elastic medium when it is deformed by a rigid cone. Afterward, by applying the nonlocal elasticity theory and the indentation parameters, the nonlocal parameter of the collagen fibrils is calculated at the nanoscale. Finally, the elastic modulus and nonlocal modulus of the collagen fibrils are compared. According to the results, the highest and lowest values of the elastic modulus of the collagen fibrils are determined in the maxillary cortical-trabecular bone interface (4.16 ± 0.18 MPa) and mandibular cortical bone (2.03 ± 0.14 MPa), respectively. In general, in collagen fibrils, this parameter is higher in the maxillary bone than in the mandibular one. In the upper and lower jaws, the elastic modulus of collagen fibrils in the cortical-trabecular bone interface is higher than that of the cortical bone. In mandibular and maxillary bone collagen fibrils, the range of nonlocal parameter and scaling parameter e₀ are computed as (0.430 ± 0.013-0.483 ± 0.011 nm) and (0.269 ± 0.006-0.302 ± 0.006), respectively. Also, the highest value of this parameter is recorded in the maxillary cortical-trabecular bone interface. The difference between the nanoscale modulus of collagen fibrils and the elastic modulus at large length scales is significant.