Phase-field simulation of crack growth in cortical bone microstructure: parameter identification and comparison against experiments

Computational models are commonly used to investigate how the cortical bone microstructure affects fracture resistance; recently, phase-field models have been introduced for this purpose. However, experimentally measured material parameters for the microstructural tissues are lacking. Moreover, as no validation studies have been published, it remains unclear to what extent classical phase-field methods, assuming linear-elastic, brittle fracture, accurately represent bone. In this study, we address both these shortcomings by first applying a design-of-experiments methodology to calibrate a set of material parameters for a two-dimensional phase-field finite element model of bovine osteonal microstructure. This was achieved by comparing the outcomes from simulation to data from single-edge notched bending experiments on bovine osteonal bone and subsequent imaging of the crack path. Second, we used these parameters in new bone geometries to evaluate the parameters and the predictive performance of the model. Reasonable agreement was achieved between prediction and experiments in terms of peak load, crack initiation toughness and crack path. However, the model is unable to capture the experimentally observed gradual evolution of damage, leading to a nonlinear force response before the onset of visible crack extension. Nor does it capture the similarly observed increase in toughness with increasing crack length. These limitations are inherent to all classical phase-field methods since they originate from theories of brittle fracture, and alternative formulations are discussed. This is the first study attempting to validate classical phase-field methods in simulation of cortical bone fracture, and it highlights both potential and limitations to be addressed in future work.