A numerical framework to model 3-D fracture in bone tissue with application to failure of the proximal femur

• Bone can be regarded as a quasi-brittle material. Under excessive loading nonlinear fracture zones may occur ahead the crack tips, where, typically, cohesive mechanisms are activated. The finite element method provides a powerful tool to analyze fracture formations on a numerical basis, and to better understand failure mechanisms within complex structures. The present work aims to introduce a particular numerical framework to investigate bone failure. We combine the partition of unity finite element method with the cohesive crack concept, and a two-step predictor-corrector algorithm for tracking 3-D non-interacting crack paths. This approach renders a numerically efficient tool that is able to capture the strong discontinuity kinematics in an accurate way. The prediction of failure propagation in the proximal part of the femur under compressive load demonstrates the suitability of the proposed concept. A 3-D finite element model, which accounts for inhomogeneous fracture properties, was used for the prediction of the 3-D crack surface. The achieved computational results were compared with experimental data available in the literature.

Nyckelord

bone

cohesive zone model

crack initialization

crack tracking algorithm

partition of unity finite element method

strong discontinuity

variational formulation

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