An FFT-based approach for Bloch wave analysis: application to polycrystals

Segurado, Javier; Lebensohn, Ricardo A.

doi:10.1007/s00466-021-02055-9

Title: An FFT-based approach for Bloch wave analysis: application to polycrystals

Journal Article · 23 July 2021 · Computational Mechanics

DOI: https://doi.org/10.1007/s00466-021-02055-9 · OSTI ID:1827584

^[1];

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Universidad Politécnica de Madrid, Madrid (Spain); IMDEA Materials Institute, Madrid (Spain)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

A method based on the Fast Fourier Transform is proposed to obtain the dispersion relation of acoustic waves in heterogeneous periodic media with arbitrary microstructures. The microstructure is explicitly considered using a voxelized Representative Volume Element (RVE). The dispersion diagram is obtained solving an eigenvalue problem for Bloch waves in Fourier space. To this aim, two linear operators representing stiffness and mass are defined through the use of differential operators in Fourier space. The smallest eigenvalues are obtained using the implicitly restarted Lanczos and the subspace iteration methods, and the required inverse of the stiffness operator is done using the conjugate gradient with a preconditioner. The method is used to study the propagation of acoustic waves in elastic polycrystals, showing the strong effect of crystal anistropy and polycrystaline texture on the propagation. It is shown that the method combines the simplicity of classical Fourier series analysis with the versatility of Finite Elements to account for complex geometries proving an efficient and general approach which allows the use of large RVEs in 3D.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: Spanish Ministry of Education; USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1827584

Report Number(s):: LA-UR--21-22889

Journal Information:: Computational Mechanics, Journal Name: Computational Mechanics Journal Issue: 5 Vol. 68; ISSN 0178-7675

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
Elastic waves
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Title: An FFT-based approach for Bloch wave analysis: application to polycrystals

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