Author:
Bălilescu Loredana,Conca Carlos,Ghosh Tuhin,San Martín Jorge,Vanninathan Muthusamy
Abstract
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.
Reference12 articles.
1. Bloch wave spectral analysis in the class of generalized Hashin–Shtrikman micro-structures
2. Allaire G., Shape optimization by the homogenization method, Vol. 146 of Applied Mathematical Sciences (Springer-Verlag, New York, 2002), ISBN 0-387-95298-5
3. Tartar L., The General Theory of Homogenization, Vol. 7 of Lecture Notes of the Unione Matematica Italiana (Springer-Verlag, Berlin; UMI, Bologna, 2009), ISBN 978-3-64205194-4, http://dx.doi.org/10.1007/978-3-642-05195-1
4. Bensoussan A., Lions J.L., Papanicolaou G., Asymptotic Analysis for Periodic Structures, Vol. 5 of Studies in Mathematics and its Applications (North-Holland Publishing Co., Amsterdam-New York, 1978), ISBN 0-444-85172-0