Discrete and Continuum Models for Complex Metamaterials

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.

1. Metamaterials: what is out there and what is about to come F. Dell'isola, D. Steigmann, A. Della Corte, E. Barchiesi and M. Laudato; 2. A review on some selected examples of mechanical metamaterials E. Barchiesi, F. Di Cosmo and M. Laudato; 3. A review on some selected examples of acoustic metamaterials E. Barchiesi, F. Di Cosmo and M. Laudato; 4. The pantographic metamaterial: a (not so) particular case F. Dell'isola, M. Spagnuolo, E. Barchiesi, I. Giorgio and P. Seppecher; 5. Naive model theory: its applications to the theory of metamaterials design F. Dell'isola, E. Barchiesi and A. Misra; 6. Lagrangian discrete models: applications to metamaterials F. Dell'isola, E. Turco, E. Barchiesi, F. Di Cosmo and M. Laudato; 7. Experimental methods in pantographic structures F. Dell'isola, T. Lekszycki, M. Spagnuolo, P. Peyre, C. Dupuy, F. Hild, A. Misra, E. Barchiesi, E. Turco and J. Dirrenberger; 8. Variational methods as versatile tools in multidisciplinary modelling and computation U. Andreaus and I. Giorgio; 9. Least action and virtual work principles for the formulation of generalized continuum models F. Dell'isola, P. Seppecher, L. Placidi, E. Barchiesi and A. Misra; Index.

Francesco dell'Isola is a Professor of Structural Mechanics at the Università degli Studi di Roma 'La Sapienza', Italy, and Director of the International Research Centre of Mathematics and Mechanics of Complex Systems (M&MoCS) at the University of L'Aquila.
David J. Steigmann is a Professor in the Department of Mechanical Engineering at the University of California, Berkeley.