ITM Web Conf.
Volume 49, 2022International Conference on Applied Mathematics and Numerical Methods – fourth edition (ICAMNM 2022)
|Number of page(s)||12|
|Section||Differential Equations, Dynamical Systems, Algebra, And Geometry|
|Published online||16 November 2022|
Bloch spectral analysis in the class of non-periodic laminates
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.
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
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.