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8 - Least Action and Virtual Work Principles for the Formulation of Generalized Continuum Models

from Part II - Mathematical and Numerical Methods

Published online by Cambridge University Press:  20 February 2020

Edited by
Francesco dell'Isola  and
David J. Steigmann
Francesco dell'Isola
Affiliation:
Università degli Studi di Roma 'La Sapienza', Italy
David J. Steigmann
Affiliation:
University of California, Berkeley
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Summary

Generalized continua represent a class of models whose potential applicability seems to have been underestimated. The mathematical structure of these models is discussed and the reasons why it has been underestimated are made clear. Their importance in the theory of metamaterials is highlighted and their potential impact on future technological applications is carefully argued. It is shown how the original ideas of Lagrange and Piola can be developed by using the modern tools of differential geometry, as formulated by Ricci and Levi-Civita. It has to be concluded that variational principles are the most powerful tool also in the mathematical modeling of metamaterials.

Keywords

leastactionvirtualworkprinciplegeneralizedcontinuummodelmetamaterialgeometry
Type
Chapter
Information
Discrete and Continuum Models for Complex Metamaterials , pp. 327 - 394
Publisher: Cambridge University Press
Print publication year: 2020

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