Discrete and Continuum Models for Complex Metamaterials PDF Download

Author: Francesco dell'Isola
Publisher: Cambridge University Press
ISBN: 1107087732
Category : Science
Languages : en
Pages : 409

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Book Description
Explores the relationship between discrete and continuum mechanics as a tool to model new and complex metamaterials. Including a comprehensive bibliography and historical review of the field, and a pedagogical mathematical treatment, it is ideal for graduate students and researchers in mechanical and civil engineering, and materials science.

Author: Francesco dell'Isola
Publisher: Cambridge University Press
ISBN: 1108850189
Category : Science
Languages : en
Pages : 409

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Book Description
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.

Author: Bilen Emek Abali
Publisher: Springer Nature
ISBN: 3030504646
Category : Science
Languages : en
Pages : 484

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Book Description
This book presents a selection of cutting-edge methods that allow readers to obtain novel models for nonlinear solid mechanics. Today, engineers need more accurate techniques for modeling solid body mechanics, chiefly due to innovative methods like additive manufacturing—for example, 3D printing—but also due to miniaturization. This book focuses on the formulation of continuum and discrete models for complex materials and systems, and especially the design of metamaterials. It gathers outstanding papers from the international conference IcONSOM 2019

Author: François Willot
Publisher: Springer
ISBN: 9783031586644
Category : Mathematics
Languages : en
Pages : 0

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Book Description
The present book contains the proceedings of the 14th International Symposium on Continuum Models and Discrete Systems (CMDS14) held in Paris in June 2023. It contains 21 contributions that cover a broad range of topics in the wide field of mechanics and physics of heterogeneous media for discrete and continuous systems, from image analysis to models of random structures and to homogenization. The sessions in the CMDS conference series cover, in particular, the modeling of complex heterogeneous systems and metamaterials, structures and composites with extreme properties, deformable solids with microstructures, generalized continua, fracture and defect dynamics, fatigue, design of structured and architectured materials, micro and nanostructures, thermodynamics, transport theory and multiphysics coupling and methods ranging from homogenization theories to optimal design and machine-learning frameworks. Papers in the present volume are organized according to the following six main topics: probabilistic models, homogenization, solid mechanics, architectured materials, optics and metamaterials, machine learning methods.

Author: Antonio J. Schiavone
Publisher:
ISBN:
Category : Continuum mechanics
Languages : en
Pages : 0

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Book Description
The group of materials classified as "metamaterials" have accrued great interest in the scientific community as of late for their potential to revolutionize several multidisciplinary applications. Metamaterials are defined as synthetic/man-made materials which have been engineered to possess a number of desired unusual, and often counterintuitive properties which do not occur naturally. The inception of metamaterials into engineering science was in the field of optics when a material exhibiting an apparent negative index of refraction was designed. Following this, so-called "optical metamaterials" were researched and implemented in the field of electromagnetic cloaking, as well as utilized to design superlenses with sub-wavelength resolution. Recently a subclass of metamaterials known as elastic metamaterials has become of great interest to engineering scientists. This is a large class of materials which exhibits one or more unusual elastic properties such as negative Poisson's ratio, negative effective stiffness, negative shear modulus, and many more. Elastic metamaterials have potential for application in the fields of impact mitigation, shock absorption, wave attenuation, energy shielding, and wave guiding, to name a few.\\ In order to facilitate the use of this new class of materials, it is of paramount importance to possess the ability to predict the behaviour of these materials under specific, as well as sufficiently general loading conditions. There are two main ways to do this; the first of which is experimentally, through trial and error, and the second is analytically by creating a mathematical model capable of predicting both material behaviour and effective properties under specific loading conditions. This thesis will focus on the latter method.\\ There exists a myriad of mathematical techniques for material characterization, some of these techniques include homogenization methods, unit cell design, discrete modelling, and continuum modelling. This thesis will focus on the continuum modelling of a class of elastic metamaterials with local rotational effects. Typically, when local effects need to be considered in the framework of a continuum, the micropolar continuum model is the first avenue people explore. In this thesis it will be shown that this model is incapable of capturing all of the salient features present in both one, and two dimensional elastic metamaterials belonging to this class.\\ In this thesis a series of continuum models are developed with increasing generality. First, in the third chapter, a micropolar-type continuum model is derived for a specific one-dimensional double negative metamaterial capable of exhibiting negative mass and/or negative modulus under certain loading frequencies when subject to harmonic loads. This is done by analyzing a discrete structure, obtaining the equations of motion, and then making a continuous approximation to bring the discrete model to the continuum framework. This model is used to evaluate the transient response of a specific one-dimensional semi-infinite elastic metamaterial when subject to an axial impact. In the fourth chapter, a higher order continuum model is developed in a manner very similar to the methodology presented in the third chapter, but with a higher order derivative of the rotational variable $\theta$. This model is then generalized to an entire class of materials, even though it is developed using a representative discrete structure. Harmonic wave propagation is then studied in the same one-dimensional elastic metamaterial that was modelled in the third chapter using this new model, leading to the determination of the stop and passing bands, as well as the determination of the dispersion relation governing the wave propagation. This new model is then compared to both the model in the third chapter, as well as the discrete model to determine the range of suitability. In the fifth chapter a model for a two-dimensional class of elastic metamaterials with local rotation is developed in a slightly different way than in the previous two chapters. In this chapter a set of constitutive laws for the relevant class of materials is proposed, and then a representative discrete metamaterial is modelled, and approximated as a continuum to prove suitability of the model. This model is then used to study harmonic longitudinal (P) and transverse (S) wave propagation in the material, which covers all cases of general two-dimensional wave propagation. The stop and passing bands, as well as the dispersion relations were determined for both wave propagation schemes and the effect of local rotation was analyzed. The sixth chapter uses the model developed in the fifth chapter to study surface wave propagation in a new continuum with local rotation. The dispersion relation of the surface wave is obtained, as well as expressions for the decay parameters, $b1$ and $b2$. The behaviour of the general dispersion relation, as well as some simplified cases are investigated. It is found that surface waves propagating through a continuum with local rotation are dispersive even when the local rotational effects are small compared to the translational ones. Two parameters governing general wave propagation, $f$ and $g$ are identified. The parameter $f$ controls the height of frequency peaks in the dispersion relation, and the parameter $g$ controls the location of the second peak. Furthermore, for values of $f \approx 1$ or greater, surface waves are found to propagate with wavespeeds significantly lower than $c_R$, a phenomenon unique to this continuum. Finally, the motion of the particles residing on the surface of this continuum is determined to be elliptical when subject to surface wave propagation, similar to classical Rayleigh wave propagation.

Author: Francesco dell'Isola
Publisher: Springer Nature
ISBN: 3030805506
Category : Science
Languages : en
Pages : 377

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Book Description
This book evaluates the importance of various historical sources and discusses their role in the creation and transmission of scientific knowledge. It presents an annotated translation of the introductory words given by Johan Ludvig Heiberg to his translation of the works of Archimedes. Further, it offers English translations of and commentaries on selected fundamental works by Ernst Hellinger and Gabrio Piola, which lay the groundwork for the modern theory of advanced materials, and also examines the criteria used to evaluate scientific works.

Author: Konstantin Z Markov
Publisher: World Scientific
ISBN: 9814548154
Category :
Languages : en
Pages : 682

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Book Description
The purpose of this symposium is to bring together scientists working on continuum theories of discrete mechanical and thermodynamical systems in the realm of mathematics, theoretical and applied mechanics, physics, material science and engineering. It aims to join together the divergent languages, questions and methods developed in the respective disciplines and to stimulate broad interdisciplinary exchange of ideas and results. The main topics, discussed in the lectures, concern thermodynamics, transport theory, statistical mechanics; continuum mechanics of complex fluids and deformable solids with microstructure; continuum theory of living structures; defect dynamics, synergetics, solitons, coherent structures; dislocations and plasticity; fundamentals of fracture mechanics.

Author: Francesco Marmo
Publisher: Springer Nature
ISBN: 3030427072
Category : Technology & Engineering
Languages : en
Pages : 275

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Book Description
This book presents a range of research projects focusing on innovative numerical and modeling strategies for the nonlinear analysis of structures and metamaterials. The topics covered concern various analysis approaches based on classical finite element solutions, structural optimization, and analytical solutions in order to present a comprehensive overview of the latest scientific advances. Although based on pioneering research, the contributions are focused on immediate and direct application in practice, providing valuable tools for researchers and practicing professionals alike.

Author: Holm Altenbach
Publisher: Springer Nature
ISBN: 3031261860
Category : Science
Languages : en
Pages : 781

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Book Description
In this book, well-known scientists discuss modern aspects of generalized continua, in order to better understand modern materials and advanced structures. They possess complicated internal structure, and it requires the development of new approaches to model such structures and new effects caused by it. This book combines fundamental contributions in honor of Victor Eremeyev and his 60th birthday.

Author: Ivan Giorgio
Publisher: Springer Nature
ISBN: 3031045483
Category : Science
Languages : en
Pages : 739

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Book Description
This book is devoted to the 60th birthday of the Prof. Francesco dell’Isola, who is known for his long-term contribution in the field of multiscale materials. It contains several contributions from researchers in the field, covering theoretical analyses, computational aspects and experiments.