Discrete and Continuum Models for Complex Metamaterials

✍ Scribed by Francesco dell'Isola (editor), David J. Steigmann (editor)

• Publisher: Cambridge University Press
• Year: 2020
• Tongue: English
• Leaves: 409
• Category: Library

✦ Synopsis

Bringing together contributions on a diverse range of topics, this text explores the relationship between discrete and continuum mechanics as a tool to model new and complex metamaterials. Providing a comprehensive bibliography and historical review of the field, it covers mechanical, acoustic and pantographic metamaterials, discusses Naive Model Theory and Lagrangian discrete models, and their applications, and presents methods for pantographic structures and variational methods for multidisciplinary modeling and computation. The relationship between discrete and continuous models is discussed from both mathematical and engineering viewpoints, making the text ideal for those interested in the foundation of mechanics and computational applications, and innovative viewpoints on the use of discrete systems to model metamaterials are presented for those who want to go deeper into the field. An ideal text for graduate students and researchers interested in continuum approaches to the study of modern materials, in mechanical engineering, civil engineering, applied mathematics, physics, and materials science.

✦ Table of Contents

Contents
List of Contributors
Part I: Designing Complex (Meta) Materials: Results and Perspectives
1 Metamaterials: What Is Out There and What Is about to Come
1.1 Technology and Science: A Two-way Interaction
1.2 The Importance of a Universal Terminology
1.3 The Relation between Mechanics’ Fundamental Hypotheses and Existing Technology
1.5 Discrete and Continuous: An Attempt at a Twenty-First-Century Methodological Position
1.4 Three Approaches to Accomplish the Objective
1.6 Mission Statement: Examples of Possible Implementations
1.7 Standard Methods and Related Challenges in Material Designing
1.8 Surface-Related Effects in Micro- and Nano-structured Materials
1.9 An Example: Pantographic Structures
1.10 Final Thoughts before Moving On
2 A Review of Some Selected Examples of Mechanical and Acoustic Metamaterials
2.1 Mechanical Metamaterials
2.2 Acoustic Metamaterials
3 Pantographic Metamaterial: A (NotSo) Particular Case
3.1 Introduction
3.2 Modeling Pantographic Structures: A Rèsumè of Results Obtained
3.3 Conclusion
Part II: Mathematical and Numerical Methods
4 Naive Model Theory: Its Applications to the Theory of Metamaterials Design
4.1 Introduction
4.2 Morphisms
4.3 Mathematical Models of Physical Phenomena
4.4 Relation between Mathematics, Science, and Technology
4.5 A Digression on Mathematics and Mechanics
4.6 Materials or Metamaterials? A Dichotomy?
4.7 Data-Driven or Theory-Driven? Final Epistemological Reflections Motivated by the Desire to Design Novel Metamaterials
5 Lagrangian Discrete Models: Applications to Metamaterials
5.1 Introduction
5.2 Lagrangian Formulation of Mechanics
5.3 Continuous and Discrete Modeling in Modern Mechanics
5.4 Hencky-Type Model for Pantographic Metamaterials
5.5 Towards 3D Models: Hencky-Type Model for Elastica
5.6 Conclusions and Perspectives
6 Experimental Methods in Pantographic Structures
6.1 Introduction
6.2 Design and Manufacturing
6.3 Comparison between Experimental Measurements and Numerical Simulations
6.4 Damage and Failure in Pantographic Fabrics
6.5 Validations via Image Correlation
6.6 Conclusion
7 Variational Methods as Versatile Tools in Multidisciplinary Modeling andComputation
7.1 Variational Principles: A Powerful Tool
7.2 Applications in Biomechanics
7.3 Applications in Materials Science
7.4 Applications in Vibration Damping
8 Least Action and Virtual Work Principles for the Formulation of Generalized ContinuumModels
8.1 Introduction and Historical Background
8.2 Why Look for the Historical Roots of Variational Principles and Calculus of Variation?
8.3 Pluralitas non est ponenda sine necessitate (John Duns Scoto 1265–1308)
8.4 Lex parsimoniae: “Law of Parsimony.” Balance Laws or Variational Principles for Generalized Continua?
8.5 More about Action Functionals
8.6 The Principle of Virtual Work
8.7 Appendix
Index