A novel phase field method for modeling the fracture of long bones

Rilin Shen, Haim Waisman*, Zohar Yosibash, Gal Dahan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


A proximal humerus fracture is an injury to the shoulder joint that necessitates medical attention. While it is one of the most common fracture injuries impacting the elder community and those who suffer from traumatic falls or forceful collisions, there are almost no validated computational methods that can accurately model these fractures. This could be due to the complex, inhomogeneous bone microstructure, complex geometries, and the limitations of current fracture mechanics methods. In this paper, we develop a novel phase field method to investigate the proximal humerus fracture. To model the fracture in the inhomogeneous domain, we propose a power-law relationship between bone mineral density and critical energy release rate. The method is validated by an in vitro experiment, in which a human humerus is constrained on both ends while subjected to compressive loads on its head, in the longitudinal direction, that lead to fracture at the anatomical neck. CT scans are employed to acquire the bone geometry and material parameters, from which detailed finite element meshes with inhomogeneous Young modulus distributions are generated. The numerical method, implemented in a high performance computing environment, is used to quantitatively predict the complex 3D brittle fracture of the bone and is shown to be in good agreement with experimental observations. Furthermore, our findings show that the damage is initiated in the trabecular bone-head and propagates outward towards the bone cortex. We conclude that the proposed phase field method is a promising approach to model bone fracture.

Original languageEnglish
Article numbere3211
JournalInternational Journal for Numerical Methods in Biomedical Engineering
Issue number8
StatePublished - Aug 2019


FundersFunder number
Division of Science Technology and Innovation
New York State Empire State Development
National Institutes of Health1G20RR030893-01
Columbia University
Empire State Development's Division of Science, Technology and InnovationC090171
China Scholarship Council201606120064


    • crack propagation
    • humerus fracture
    • phase field method
    • proximal


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