Phase-field boundary conditions for the voxel finite cell method: surface-free stress analysis of CT-based bone structures

Nguyen, L.H., Stoter, S.K.F., Baum, T., Kirschke, J.S., Ruess, M. , Yosibash, Z. and Schillinger, D. (2017) Phase-field boundary conditions for the voxel finite cell method: surface-free stress analysis of CT-based bone structures. International Journal for Numerical Methods in Biomedical Engineering, 33(12), e2880. (doi: 10.1002/cnm.2880) (PMID:28294574)

Abstract

The voxel finite cell method employs unfitted finite element meshes and voxel quadrature rules to seamlessly transfer CT data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblock to automation. We explore a phase-field based formulation for imposing traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as initial condition. Phase-field approximations of the boundary and its gradient are then employed to transfer all boundary terms in the variational formulation into volumetric terms. We show that in the context of the voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions defined over explicit sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human femur and a vertebral body.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ruess, Dr Martin
• Authors: Nguyen, L.H., Stoter, S.K.F., Baum, T., Kirschke, J.S., Ruess, M., Yosibash, Z., and Schillinger, D.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: International Journal for Numerical Methods in Biomedical Engineering
• Publisher: Wiley
• ISSN: 2040-7939
• ISSN (Online): 2040-7947
• Published Online: 11 March 2017
• Copyright Holders: Copyright © 2017 John Wiley and Sons Ltd
• First Published: First published in International Journal for Numerical Methods in Biomedical Engineering 2017
• Publisher Policy: Reproduced in accordance with the publisher copyright policy