Identification of a crushable foam material model and application to strength and damage prediction of human femur and vertebral body

• A crushable foam material model for bone was proposed and identified.
• The material model was compared to experiments and a reference for a large number of femora and vertebral body samples.
• Good predicted strength and fracture location were achieved.
• The material model is simple, easy to use and can be applied in future studies.

Finite element (FE) models allow quantitative predictions of bone strength and fracture location and, thus, became increasingly popular for assessing fracture risk or effectiveness of osteoporosis therapies. However, predictions crucially depend on the used material models, which are usually complex and rely on a large number of parameters. Therefore, the goal of this study was to propose a simple crushable foam (CF) material model and to perform an extensive comparison with data from the literature.Material parameters of the CF plasticity model were identified based on previously published yield stress data. Voxel-based FE models of thirty-six femora pairs and thirty-eight vertebral bodies were generated from QCT images. The femora models were analyzed with boundary conditions simulating one-legged stance and fall on the greater trochanter. The vertebral body models were subjected to uniaxial compression. Load-displacement curves, ultimate forces and damage distributions computed with the CF material model were compared to a reference material model as well as to in vitro experiments.The result showed that the FE models with CF material provided reasonable quantitative predictions of the ultimate forces measured in the experiments (R2>0.80R2>0.80). Comparison of the FE results obtained with CF and reference material model showed very similar outcomes regarding ultimate force, load-displacement behavior and damage patterns for all investigated anatomical sites and loading conditions.In conclusion, the identified CF material model provided good strength and damage predictions, required only few material parameters and is already implemented in many commercial FE solvers. Thus, it can be easily used in other studies.