December  2013, 6(6): 1599-1608. doi: 10.3934/dcdss.2013.6.1599

Prolegomena to studies on dynamic materials and their space-time homogenization

1. 

Université Pierre et Marie Curie, Institut Jean Le Rond d'Alembert, UMR CNRS 7190, Case 162, Tour 55, 4 place Jussieu, 75252 Paris Cedex 05, France, France

Received  June 2012 Revised  September 2012 Published  April 2013

This short contribution aims at introducing the notion of dynamic materials (as initiated by Blekhman and Lurie) and the corresponding allied techniques of homogenization and asymptotic analysis. Main role is played by the canonical conservation laws of energy and wave momentum - the latter most often ignored in the field of continuum mechanics - as follows from an application of the celebrated theorem of E. Noether.
Citation: Gerard A. Maugin, Martine Rousseau. Prolegomena to studies on dynamic materials and their space-time homogenization. Discrete & Continuous Dynamical Systems - S, 2013, 6 (6) : 1599-1608. doi: 10.3934/dcdss.2013.6.1599
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show all references

References:
[1]

(Russian) Doklady Akademii Nauk, 371 (2000), 182-185. doi: 10.1134/1.171720.  Google Scholar

[2]

Physics Reports, 49 (1979), 1-89; Original Russian in Usp. Fiz. Nauk, 126 (1978), 553-563. doi: 10.1016/0370-1573(79)90052-8.  Google Scholar

[3]

Advances in Mechanics and Mathematics, 15, Springer, New York, 2007.  Google Scholar

[4]

Zeit. Angew. Math. Mech., 89 (2009), 333-340. doi: 10.1002/zamm.200800185.  Google Scholar

[5]

J. Math. Analysis and Applications, 355 (2009), 180-194. doi: 10.1016/j.jmaa.2009.01.031.  Google Scholar

[6]

Applied Mathematics and Mathematical Computation, 3, Chapman & Hall, London, 1993.  Google Scholar

[7]

CRC Series: Modern Mechanics and Mathematics, CRC Press, Boca Raton, FL, 2011.  Google Scholar

[8]

J. Math. Pures Appl. (9), 92 (2009), 232-262. doi: 10.1016/j.matpur.2009.04.002.  Google Scholar

[9]

Johns Hopkins University Press, Baltimore, MD, 2011.  Google Scholar

[10]

Arch. Appl. Mechanics, 81 (2011), 925-942. doi: 10.1007/s00419-010-0461-4.  Google Scholar

[11]

Papers from the course held in Udine, July 1-5, 1985, Lecture Notes in Physics, 272, Springer-Verlag, Berlin, 1987. doi: 10.1007/3-540-17616-0.  Google Scholar

[12]

in "Handbuch der Physik, Vol. III/1" (ed. S. Flügge), Springer-Verlag, Berlin, 1960. Google Scholar

[13]

Physics-Uspekhi, 39 (1996), 983-1007. Google Scholar

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