Numerical simulation of humeral neck fractures combining phase-field models and the parallel hp-adaptive finite cell method

  • Hug, Lisa (Technical University of Munich)
  • Kollmannsberger, Stefan (Technical University of Munich)
  • Yosibash, Zohar (Tel-Aviv University)
  • Rank, Ernst (Technical University of Munich)

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The numerical simulation of crack propagation in the context of phase-field models is challenging for two main reasons. First, the regularization of the sharp crack is based on a length-scale parameter that necessitates extremely fine meshes, at least in the vicinity of the crack, to resolve the resulting crack profile fully. Secondly, a staggered solution scheme based on decoupling of the phase-field and mechanical equation is typically used which suffers from slow convergence. In a classic finite element setting, these problems can easily lead to excessive computation times already for two-dimensional examples. To reduce the computational effort and enable the solution of large-scale problems, we present a numerical framework based on a combination of a phase-field model for brittle fracture with the Finite Cell Method (FCM), multi-level hp-refinement, and parallel computing. Integrating the FCM [1] as an embedded domain approach enables the efficient simulation of complex geometries without the need to generate boundary-conforming meshes. Multi-level hp-refinement allows for a locally refined mesh that dynamically adapts to the crack path. As presented in [3], implementing the two discretization techniques in an MPI-parallel setting enables the efficient numerical solution of complex geometrical and physical problems. In the present contribution, we extend the parallel framework to the simulation of crack propagation by combining it with a phase-field model for long bones [2]. The potential of the proposed numerical framework will be investigated based on a practical example of predicting neck fractures in human humeri.