Recursive grain remapping scheme for phase-field models of additive manufacturing

Alexander F. Chadwick*, Peter W. Voorhees

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The phase-field method is an attractive tool in modeling microstructural evolution due to rapid solidification under additive manufacturing conditions, but typical polycrystalline models are prone to grain coalescence. Grain tracking and remapping schemes can eliminate artificial coalescence and increase the number of grains and crystallographic orientations that may be considered in a simulation, but previous tracking and remapping schemes may not efficiently capture the complex grain morphologies that form during additive manufacturing. A new recursive scheme is derived from a binary tree of axis-aligned bounding boxes that can efficiently represent columnar and irregularly shaped grains. We demonstrate the power of this approach by simulating microstructures with hundreds to thousands of grains and quantify the reduction in the number of order parameters required to represent the microstructure. The new scheme leads to orders of magnitude fewer computational resources as compared to the naïve paradigm of one grain per order parameter, and also offers a substantial improvement over algorithms derived from bounding spheres.

Original languageEnglish (US)
Pages (from-to)3093-3110
Number of pages18
JournalInternational Journal for Numerical Methods in Engineering
Issue number13
StatePublished - Jul 15 2022


  • additive manufacturing
  • finite difference method
  • materials science
  • phase-field method

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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