Uniform Stress State in Bone Structure With Residual Stress

Abstract

Residual stress and strain in living tissues have been investigated from the viewpoint of mechanical optimality maintained by adaptive remodeling. In this study, the residual stresses in the cortical-cancellous bone complex of bovine coccygeal vertebrae were examined. Biaxial strain gages were bonded onto the cortical surface, so that the gage axes were aligned in the cephalocaudal and circumferential directions. Strains induced by removal of the end-plate and the cancellous bone were recorded sequentially. The results revealed the existence of compressive residual stress in the cortical bone and tensile residual stress in the cancellous bone in both the cephalocaudal and the circumferential direction. The observed strains were examined on the basis of the uniform stress hypothesis using a three-bar model for the cephalocaudal direction and a three-layered cylinder model for the circumferential direction. In this model study, the magnitude of effective stresses, which is defined as the macroscopic stress divided by the area fraction of bone material, was found not to differ significantly between cephalocaudal and circumferential directions, although they were evaluated using independent models. These results demonstrate that the uniform stress state of the cortical-cancellous bone structure is consistent with results obtained in the cutting experiment when the existence of residual stress is taken into account.