Modelling of bone fracture and strength at different length scales: a review.

In this paper, we review analytical and computational models of bone fracture and strength. Bone fracture is a complex phenomenon due to the composite, inhomogeneous and hierarchical structure of bone. First, we briefly summarize the hierarchical structure of bone, spanning from the nanoscale, sub-microscale, microscale, mesoscale to the macroscale, and discuss experimental observations on failure mechanisms in bone at these scales. Then, we highlight representative analytical and computational models of bone fracture and strength at different length scales and discuss the main findings in the context of experiments. We conclude by summarizing the challenges in modelling of bone fracture and strength and list open topics for scientific exploration. Modelling of bone, accounting for different scales, provides new and needed insights into the fracture and strength of bone, which, in turn, can lead to improved diagnostic tools and treatments of bone diseases such as osteoporosis.

Reference point indentation study of age-related changes in porcine femoral cortical bone.

The reference point indentation (RPI) method is a microindentation technique involving successive indentation cycles. We employed RPI to measure average stiffness (Ave US), indentation distance increase (IDI), total indentation distance (TID), average energy dissipated (Ave ED), and creep indentation distance (CID) of swine femoral cortical bone (mid-diaphysis) as a function of age (1, 3.5, 6, 14.5, 24, and 48 months) and loading directions (longitudinal and transverse). The Ave US increases with animal age, while the IDI, TID, Ave ED, and CID decrease with age, for both longitudinal (transverse surface) and transverse (periosteal surface) loading directions. Longitudinal measurements generally give higher Ave US and lower IDI and TID values compared to transverse measurements. The RPI measurements show similar trends to those obtained using nanoindentation test, and ash and water content tests.

A fiber-ceramic matrix composite material model for osteonal cortical bone fracture micromechanics: solution of arbitrary microcracks interaction.

Microcracks formed in bone are due to fatigue and cyclic loading. This formation is associated with a reduction of bone resistance to fracture. However, the significance of the parameters that govern microcrack behavior is not yet fully explored. A two-dimensional micromechanical fiber-ceramic matrix composite material model of the osteonal cortical bone is presented in this paper. The solution for the edge dislocations as Green's function, is adopted to formulate a system of singular integral equations for the general microcracks in vicinity of the osteon. The effects of microstructural morphology and heterogeneity of the bone upon the fracture behavior is investigated by computing the Stress Intensity Factor (SIF) near the microcracks tips. Analysis of microcracks interaction indicates the significance of microcracks configuration in the shape of either stress amplification or stress shielding.