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

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

doi:10.1016/j.mechrescom.2022.104023

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 language	English
Article number	104023
Journal	Mechanics Research Communications
Volume	127
Early online date	9 Dec 2022
DOIs	https://doi.org/10.1016/j.mechrescom.2022.104023
Publication status	Published - Jan 2023

Keywords

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

ASJC Scopus subject areas

Civil and Structural Engineering
General Materials Science
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

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title = "Geometric modelling of polycrystalline materials: Laguerre tessellations and periodic semi-discrete optimal transport",

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.",

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note = "Funding Information: The authors thank Piet Kok, Wil Spanjer, Carola Celada-Casero and Karo Sedighiani for fruitful discussions. DPB acknowledges financial support from the EPSRC, UK grant EP/V00204X/1 . MP thanks the Centre for Doctoral Training in Mathematical Modelling, Analysis and Computation funded by EPSRC, UK grant EP/S023291/1 . Publisher Copyright: {\textcopyright} 2022 The Author(s)",

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AU - Pearce, M.

AU - Roper, S. M.

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N2 - 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.

AB - 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.

KW - Grains

KW - Laguerre diagrams

KW - Polycrystalline materials

KW - Power diagrams

KW - Semi-discrete optimal transport theory

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DO - 10.1016/j.mechrescom.2022.104023

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JO - Mechanics Research Communications

JF - Mechanics Research Communications

M1 - 104023

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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