Published Paper
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Inserted: 25 jul 2022
Last Updated: 10 nov 2026

Journal: Mechanics Research Communications
Volume: 127
Pages: 104023
Year: 2023
Doi: https://doi.org/10.1016/j.mechrescom.2022.104023
Links: PDF

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.