Cortical bone continuum damage mechanics constitutive model with stress triaxiality criterion to predict fracture initiation and pattern

Abstract

A primary objective of finite element human body models (HBMs) is to predict response and injury risk in impact scenarios, including cortical bone fracture initiation, fracture pattern, and the potential to simulate post-fracture injury to underlying soft tissues. Current HBMs have been challenged to predict the onset of failure and bone fracture patterns owing to the use of simplified failure criteria. In the present study, a continuum damage mechanics (CDM) model, incorporating observed mechanical response (orthotropy, asymmetry, damage), was coupled to a novel phenomenological effective strain fracture criterion based on stress triaxiality and investigated to predict cortical bone response under different modes of loading. Three loading cases were assessed: a coupon level notched shear test, whole bone femur three-point bending, and whole bone femur axial torsion. The proposed material model and fracture criterion were able to predict both the fracture initiation and location, and the fracture pattern for whole bone and specimen level tests, within the variability of the reported experiments. There was a dependence of fracture threshold on finite element mesh size, where higher mesh density produced similar but more refined fracture patterns compared to coarser meshes. Importantly, the model was functional, accurate, and numerically stable even for relatively coarse mesh sizes used in contemporary HBMs. The proposed model and novel fracture criterion enable prediction of fracture initiation and resulting fracture pattern in cortical bone such that post-fracture response can be investigated in HBMs.