Geometric modelling of polycrystalline materials: Laguerre tessellations and periodic semi-discrete optimal transport

D. P. Bourne, M. Pearce, S. M. Roper

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Abstract

In this paper we describe a fast algorithm for generating periodic RVEs of polycrystalline materials. In particular, we use the damped Newton method from semi-discrete optimal transport theory to generate 3D periodic Laguerre tessellations (or power diagrams) with cells of given volumes. Complex, polydisperse RVEs with up to 100,000 grains of prescribed volumes can be created in a few minutes on a standard laptop. The damped Newton method relies on the Hessian of the objective function, which we derive by extending recent results in semi-discrete optimal transport theory to the periodic setting.
Original languageEnglish
Article number104023
JournalMechanics Research Communications
Volume127
Early online date9 Dec 2022
DOIs
Publication statusPublished - Jan 2023

Keywords

  • Grains
  • Laguerre diagrams
  • Polycrystalline materials
  • Power diagrams
  • Semi-discrete optimal transport theory

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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