Book contents
- Frontmatter
- Contents
- List of Contributors
- Part I Designing Complex (Meta)Materials: Results and Perspectives
- Part II Mathematical and Numerical Methods
- 4 Naive Model Theory: Its Applications to the Theory of Metamaterials Design
- 5 Lagrangian Discrete Models: Applications to Metamaterials
- 6 Experimental Methods in Pantographic Structures
- 7 Variational Methods as Versatile Tools in Multidisciplinary Modeling and Computation
- 8 Least Action and Virtual Work Principles for the Formulation of Generalized Continuum Models
- Index
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
- Frontmatter
- Contents
- List of Contributors
- Part I Designing Complex (Meta)Materials: Results and Perspectives
- Part II Mathematical and Numerical Methods
- 4 Naive Model Theory: Its Applications to the Theory of Metamaterials Design
- 5 Lagrangian Discrete Models: Applications to Metamaterials
- 6 Experimental Methods in Pantographic Structures
- 7 Variational Methods as Versatile Tools in Multidisciplinary Modeling and Computation
- 8 Least Action and Virtual Work Principles for the Formulation of Generalized Continuum Models
- Index
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.
- Type
- Chapter
- Information
- Discrete and Continuum Models for Complex Metamaterials , pp. 327 - 394Publisher: Cambridge University PressPrint publication year: 2020
- 16
- Cited by