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Phase-field models and immersed domain finite elements for fracture simulations in complex image based geometries

Phase-field models based on the variational formulation for brittle fracture use a diffusive approximation of discontinuous cracks by a continuous phase-field. This enables the representation of complex three-dimensional crack patterns independently from a mesh and its topology by the solution of an additional differential equation. Immersed domain finite element methods use a simple unfitted Cartesian mesh for the approximation of the solution fields, while the geometry in intersected elements is captured by special quadrature techniques. This eliminates the need for time-consuming and error-prone meshing procedures and enables simulation tools that can automatically handle very complex geometries. In principle, phase-field fracture models and immersed domain finite elements strive for the same goal, i.e. representing complex geometric patterns independently of a numerical mesh.

We combine the two technologies for the fracture simulation in explicit geometric models obtained from medical imaging technologies. First, we show that crack initiation at immersed boundaries is extremely sensitive to the sawtooth pattern of the voxel data, even for image resolutions that are orders of magnitude finer than the characteristic length scale of the diffusive crack. One way to avoid this sensitivity is to use image segmentation to transfer the voxel data into a smooth surface model. However, the cost and time implications of segmentation is a major obstacle for the integration of simulations in many practical workflows. We show that the sawtooth sensitivity can also be mitigated by a local homogenization of the voxels in each intersected element based on simple averaging procedures. This approach is inexpensive and can be easily automated, so that the core advantages of immersed domain methods are maintained. We illustrate the versatility and potential of phase-field fracture models in the context of immersed domain simulations for several biomedical applications, e.g., the patient-specific fracture analysis of human teeth.

Author(s):

Dominik Schillinger    
University of Minnesota
United States

Lam H. Nguyen    
University of Minnesota
United States

Vasco Varduhn    
University of Minnesota
United States