| Issue |
ITM Web Conf.
Volume 49, 2022
International Conference on Applied Mathematics and Numerical Methods – fourth edition (ICAMNM 2022)
|
|
|---|---|---|
| Article Number | 02001 | |
| Number of page(s) | 12 | |
| Section | Differential Equations, Dynamical Systems, Algebra, And Geometry | |
| DOI | https://doi.org/10.1051/itmconf/20224902001 | |
| Published online | 16 November 2022 | |
Bloch spectral analysis in the class of non-periodic laminates
1
Department of Mathematics and Informatics, University of Pites¸ti, Str. Târgu din Vale nr. 1, 110040 Pites¸ti, Arges¸, Romania.
2
Departamento de Ingeniería Matemática, Centro de Modelamiento Matemático, UMR 2071 CNRSUChile, Casilla 170/3 Correo 3, Santiago, Chile.
3
Centro de Biotecnología y Bioingeniería, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile.
4
Centre For Applicable Mathematics, Tata Institute of Fundamental Research, Post Bag 6503, GKVK Post, Bangalore 560065, India.
5
Department of Mathematics, IIT-Bombay, Powai, Mumbai- 400076, India.
* e-mail: smaranda@dim.uchile.cl
** e-mail: cconca@dim.uchile.cl
*** e-mail: imaginetuhin@gmail.com
**** e-mail: jorge@dim.uchile.cl
† e-mail: muthu.vanni@gmail.com
In this work, we introduce Bloch waves to study the homogenization process in a class of simple laminates which are obtained as a particular Hashin-Shtrikman microstructure involving translations and dilations in only one direction. This makes this class of microstructures non necessarily periodic in the direction of lamination. We derive explicit formulae for the Bloch wave spectral representation of the homogenized coefficients.
Key words: Homogenization / Laminates / Hashin-Shtrikman / Spectral analysis / Bloch waves
© The Authors, published by EDP Sciences, 2022
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