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Waves in Nonlinear Pre-Stressed Materials

Waves in Nonlinear Pre-Stressed Materials
Author: M. Destrade
Publisher: Springer Science & Business Media
Total Pages: 287
Release: 2007-11-08
Genre: Technology & Engineering
ISBN: 3211735720
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Papers in this book provide a state-of-the-art examination of waves in pre-stressed materials. You’ll gain new perspectives via a multi-disciplinary approach that interweaves key topics. These topics include the mathematical modeling of incremental material response (elastic and inelastic), an analysis of the governing differential equations, and boundary-value problems. Detailed illustrations help you visualize key concepts and processes.

Waves in Nonlinear Elastic Media with Inhomogeneous Pre-stress

Waves in Nonlinear Elastic Media with Inhomogeneous Pre-stress
Author: Tom Shearer
Publisher:
Total Pages:
Release: 2013
Genre:
ISBN:
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In this thesis, the effect of inhomogeneous pre-stress on elastic wave propagation and scattering in nonlinear elastic materials is investigated. Four main problems are considered: 1. torsional wave propagation in a pre-stressed annular cylinder, 2. the scattering of horizontally polarised shear waves from a cylindrical cavity in a pre-stressed, infinite, nonlinear elastic material, 3. the use of pre-stress to cloak cylindrical cavities from incoming horizontally polarised shear waves, and 4. the scattering of shear waves from a spherical cavity in a pre-stressed, infinite, nonlinear elastic material. It is observed that waves in a hyperelastic material are significantly affected by pre-stress, and different results are obtained from those which would be obtained if the underlying stress was neglected and only geometrical changes were considered. In Chapter 3 we show that the dispersion curves for torsional waves propagating in an annular cylinder are strongly dependent on the pre-stress applied. A greater pressure on the inner surface than the outer causes the roots of the dispersion curves to be spaced further apart, whereas a greater pressure on the outer surface than the inner causes them to be spaced closer together. We also show that a longitudinal stretch causes the cut-on frequencies to move closer together and decreases the gradient of the dispersion curves, whilst a longitudinal compression causes the cut-on frequencies to move further apart and increases the gradient of the dispersion curves. In Chapter 4 we observe that pre-stress affects the scattering coefficients for shear waves scattered from a cylindrical cavity. It is shown that, for certain parameter values, the scattering coefficients obtained in a pre-stressed medium are closer to those that would be obtained in the undeformed configuration than those that would be obtained in the deformed configuration if the pre-stress were neglected. This result is utilised in Chapter 5 where the cloaking of a cylindrical cavity from horizontally polarised shear waves is examined. It is shown that neo-Hookean materials are optimal for this type of cloaking. A stonger dependence of the strain energy function on the second strain invariant leads to a less efficient cloak. We observe that, for a Mooney-Rivlin material, as S1 tends from 1 towards 0 (in other words, as a material becomes less dependent on the first strain invariant, and more dependent on the second strain invariant), there is more scattering from the cloaking region. For materials which are strongly dependent on the second strain invariant the pre-stress actually increases the scattering cross-section relative to the scattering cross-section for an unstressed material, hence these materials are unsuitable for pre-stress cloaking. Finally, in Chapter 6 we study the effect of pressure applied to the inner surface of a spherical cavity and at infinity on the propagation and scattering of shear waves in an unbounded medium. It is shown that the scattering coefficients and cross-sections for this problem are strongly dependent on the pre-stress considered. We observe that a region of inhomogeneous pre-stress can lead to some counterintuitive relationships between cavity size and scattering cross-sections and coefficients.

Nonlinear Mechanics of Soft Fibrous Materials

Nonlinear Mechanics of Soft Fibrous Materials
Author: Luis Dorfmann
Publisher: Springer
Total Pages: 311
Release: 2014-12-02
Genre: Science
ISBN: 3709118387
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The book presents a state-of-the-art overview of the fundamental theories, established models and ongoing research related to the modeling of these materials. Two approaches are conventionally used to develop constitutive relations for highly deformable fibrous materials. According to the phenomenological approach, a strain energy density function can be defined in terms of strain invariants. The other approach is based on kinetic theories, which treats a fibrous material as a randomly oriented inter-tangled network of long molecular chains bridged by permanent and temporary junctions. At the micro-level, these are associated with chemical crosslinks and active entanglements, respectively. The papers include carefully crafted overviews of the fundamental formulation of the three-dimensional theory from several points of view, and address their equivalences and differences. Also included are solutions to boundary-value problems which are amenable to experimental verification. A further aspect is the elasticity of filaments, stability of equilibrium and thermodynamics of the molecular network theory.

World Scientific Handbook Of Metamaterials And Plasmonics (In 4 Volumes)

World Scientific Handbook Of Metamaterials And Plasmonics (In 4 Volumes)
Author: Maier Stefan A
Publisher: World Scientific
Total Pages: 1992
Release: 2011-06-14
Genre: Technology & Engineering
ISBN: 9813228741
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Metamaterials represent a new emerging innovative field of research which has shown rapid acceleration over the last couple of years. In this handbook, we present the richness of the field of metamaterials in its widest sense, describing artificial media with sub-wavelength structure for control over wave propagation in four volumes. Volume 1 focuses on the fundamentals of electromagnetic metamaterials in all their richness, including metasurfaces and hyperbolic metamaterials. Volume 2 widens the picture to include elastic, acoustic, and seismic systems, whereas Volume 3 presents nonlinear and active photonic metamaterials. Finally, Volume 4 includes recent progress in the field of nanoplasmonics, used extensively for the tailoring of the unit cell response of photonic metamaterials. In its totality, we hope that this handbook will be useful for a wide spectrum of readers, from students to active researchers in industry, as well as teachers of advanced courses on wave propagation. Contents: Volume 1: Electromagnetic Metamaterials (Ekaterina Shamonina): PrefaceElectromagnetic Metamaterials: Homogenization and Effective Properties of Mixtures (Ari Sihvola)Effective Medium Theory of Electromagnetic and Quantum Metamaterials (Mário G Silveirinha)Hyperbolic Metamaterials (Igor I Smolyaninov)Circuit and Analytical Modelling of Extraordinary Transmission Metamaterials (Francisco Medina, Francisco Mesa, Raul Rodríguez-Berral and Carlos Molero)Electromagnetic Metasurfaces: Synthesis, Realizations and Discussions (Karim Achouri and Christophe Caloz)Metasurfaces for General Control of Reflection and Transmission (Sergei Tretyakov, Viktar Asadchy and Ana Díaz-Rubio)Scattering at the Extreme with Metamaterials and Plasmonics (Francesco Monticone and Andrea Alù)All-Dielectric Nanophotonics: Fundamentals, Fabrication, and Applications (Alexander Krasnok, Roman Savelev, Denis Baranov and Pavel Belov)Tunable Metamaterials (Ilya V Shadrivov and Dragomir N Neshev)Spatial Solitonic and Nonlinear Plasmonic Aspects of Metamaterials (Allan D Boardman, Alesandro Alberucci, Gaetano Assanto, Yu G Rapoport, Vladimir V Grimalsky, Vasyl M Ivchenko and Eugen N Tkachenko)Metamaterial Catheter Receivers for Internal Magnetic Resonance Imaging (Richard R A Syms, Ian R Young and Laszlo Solymar)Microwave Sensors Based on Symmetry Properties and Metamaterial Concepts (Jordi Naqui, Ali K Horestani, Christophe Fumeaux and Ferran Martín)Volume 2: Elastic, Acoustic, and Seismic Metamaterials (Richard Craster and Sébastien Guenneau): PrefaceDynamic Homogenization of Acoustic and Elastic Metamaterials and Phononic Crystals (Richard Craster, Tryfon Antonakakis and Sébastien Guenneau)Acoustic Metamaterial (Nicholas Fang, Jun Xu, Navid Nemati, Nicolas Viard and Denis Lafarge)Flat Lens Focusing of Flexural Waves in Thin Plates (Patrick Sebbah and Marc Dubois)Space–Time Cloaking (Martin W McCall and Paul Kinsler)Soda Cans Metamaterial: Homogenization and Beyond (Fabrice Lemoult, Geoffroy Lerosey, Nadège Kaïna and Mathias Fink)New Trends Toward Locally-Resonant Metamaterials at the Mesoscopic Scale (Philippe Roux, Matthieu Rupin, Fabrice Lemoult, Geoffroy Lerosey, Andrea Colombi, Richard Craster, Sébastien Guenneau, William A Kuperman and Earl G Williams)Seismic Metamaterials: Controlling Surface Rayleigh Waves Using Analogies with Electromagnetic Metamaterials (Stéphane Brûlé, Stefan Enoch, Sébastien Guenneau and

Selected Topics in Nonlinear Wave Mechanics

Selected Topics in Nonlinear Wave Mechanics
Author: C.I. Christov
Publisher: Springer Science & Business Media
Total Pages: 274
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461200954
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This book gives an overview ofthe current state of nonlinear wave mechanics with emphasis on strong discontinuities (shock waves) and localized self preserving shapes (solitons) in both elastic and fluid media. The exposition is intentionallyat a detailed mathematical and physical level, our expectation being that the reader will enjoy coming to grips in a concrete manner with advances in this fascinating subject. Historically, modern research in nonlinear wave mechanics began with the famous 1858 piston problem paper of Riemann on shock waves and con tinued into the early part of the last century with the work of Hadamard, Rankine, and Hugoniot. After WWII, research into nonlinear propagation of dispersive waves rapidly accelerated with the advent of computers. Works of particular importance in the immediate post-war years include those of von Neumann, Fermi, and Lax. Later, additional contributions were made by Lighthill, Glimm, Strauss, Wendroff, and Bishop. Dispersion alone leads to shock fronts of the propagating waves. That the nonlinearity can com pensate for the dispersion, leading to propagation with a stable wave having constant velocity and shape (solitons) came as a surprise. A solitary wave was first discussed by J. Scott Russell in 1845 in "Report of British Asso ciations for the Advancement of Science. " He had, while horseback riding, observed a solitary wave travelling along a water channel and followed its unbroken progress for over a mile.

Advances in Mechanism Design III

Advances in Mechanism Design III
Author: Jaroslav Beran
Publisher: Springer Nature
Total Pages: 338
Release: 2021-08-03
Genre: Technology & Engineering
ISBN: 3030835944
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This book presents the latest research advances relating to machines and mechanisms. Featuring papers from the XIII International Conference on the Theory of Machines and Mechanisms (TMM 2020), held in Liberec, Czech Republic, on September 7-9, 2021, it includes a selection of the most important new results and developments. The book is divided into five parts, representing a well-balanced overview, and spanning the general theory of machines and mechanisms, through analysis and synthesis of planar and spatial mechanisms, linkages and cams, robots and manipulators, dynamics of machines and mechanisms, rotor dynamics, computational mechanics, vibration and noise in machines, optimization of mechanisms and machines, mechanisms of textile machines, mechatronics and control and monitoring systems of machines. This conference is traditionally held every four years under the auspices of the international organisation IFToMM and the Czech Society for Mechanics.

Shell Structures: Theory and Applications Volume 4

Shell Structures: Theory and Applications Volume 4
Author: Wojciech Pietraszkiewicz
Publisher: CRC Press
Total Pages: 574
Release: 2017-10-30
Genre: Technology & Engineering
ISBN: 135168048X
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Shells are basic structural elements of modern technology and everyday life. Examples of shell structures in technology include automobile bodies, water and oil tanks, pipelines, silos, wind turbine towers, and nanotubes. Nature is full of living shells such as leaves of trees, blooming flowers, seashells, cell membranes or wings of insects. In the human body arteries, the eye shell, the diaphragm, the skin and the pericardium are all shells as well. Shell Structures: Theory and Applications, Volume 4 contains 132 contributions presented at the 11th Conference on Shell Structures: Theory and Applications (Gdansk, Poland, 11-13 October 2017). The papers reflect a wide spectrum of scientific and engineering problems from theoretical modelling through strength, stability and dynamic behaviour, numerical analyses, biomechanic applications up to engineering design of shell structures. Shell Structures: Theory and Applications, Volume 4 will be of interest to academics, researchers, designers and engineers dealing with modelling and analyses of shell structures. It may also provide supplementary reading to graduate students in Civil, Mechanical, Naval and Aerospace Engineering.

Universality of Nonclassical Nonlinearity

Universality of Nonclassical Nonlinearity
Author: Pier Paolo Delsanto
Publisher: Springer Science & Business Media
Total Pages: 535
Release: 2006-12-13
Genre: Science
ISBN: 038735851X
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This book presents the results of two major international research projects on phenomenology, theory and applications of Nonclassical Nonlinearity. It conveys concepts, experimental techniques and applications which were previously found in specialized journals. It also allows for an interdisciplinary audience to better understand the range of practical applications, and is timely and interesting to both researchers and professionals.

Nonlinear Wave Dynamics of Materials and Structures

Nonlinear Wave Dynamics of Materials and Structures
Author: Holm Altenbach
Publisher: Springer Nature
Total Pages: 473
Release: 2020-04-22
Genre: Technology & Engineering
ISBN: 3030387089
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This book marks the 60th birthday of Prof. Vladimir Erofeev – a well-known specialist in the field of wave processes in solids, fluids, and structures. Featuring a collection of papers related to Prof. Erofeev’s contributions in the field, it presents articles on the current problems concerning the theory of nonlinear wave processes in generalized continua and structures. It also discusses a number of applications as well as various discrete and continuous dynamic models of structures and media and problems of nonlinear acoustic diagnostics.

Mechanics of Soft Materials

Mechanics of Soft Materials
Author: Konstantin Volokh
Publisher: Springer
Total Pages: 158
Release: 2016-06-17
Genre: Science
ISBN: 9811015996
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This book provides a concise introduction to soft matter modelling. It offers an up-to-date review of continuum mechanical description of soft and biological materials from the basics to the latest scientific materials. It includes multi-physics descriptions, such as chemo-, thermo-, electro- mechanical coupling. It derives from a graduate course at Technion that has been established in recent years. It presents original explanations for some standard materials and features elaborated examples on all topics throughout the text. PowerPoint lecture notes can be provided to instructors.