The voxel finite cell method uses unfitted finite element meshes and voxel quadrature rules to seamlessly transfer computed tomography 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 used 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, ie, 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.
|Original language||English (US)|
|Journal||International Journal for Numerical Methods in Biomedical Engineering|
|State||Published - Dec 2017|
Bibliographical noteFunding Information:
D Schillinger gratefully acknowledges support from the National Science Foundation through the research grant CISE-1565997 and the NSF CAREER award no. 1651577. JS Kirschke received research grants from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 637164???ERC-2014-STG) and the German Research Foundation (BA 4085 2/1). The Minnesota Supercomputing Institute (MSI) of the University of Minnesota has provided computing resources that have contributed to the research results reported within this paper (https://www.msi.umn.edu/), which is also gratefully acknowledged.
- diffuse boundary methods
- patient-specific simulation
- voxel finite cell method