Nonlinear Mechanics Of Crystals
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Nonlinear Mechanics Of Crystals
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Author : John D. Clayton
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-01
Nonlinear Mechanics Of Crystals written by John D. Clayton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-01 with Science categories.
This book describes behavior of crystalline solids primarily via methods of modern continuum mechanics. Emphasis is given to geometrically nonlinear descriptions, i.e., finite deformations. Primary topics include anisotropic crystal elasticity, plasticity, and methods for representing effects of defects in the solid on the material's mechanical response. Defects include crystal dislocations, point defects, twins, voids or pores, and micro-cracks. Thermoelastic, dielectric, and piezoelectric behaviors are addressed. Traditional and higher-order gradient theories of mechanical behavior of crystalline solids are discussed. Differential-geometric representations of kinematics of finite deformations and lattice defect distributions are presented. Multi-scale modeling concepts are described in the context of elastic and plastic material behavior. Representative substances towards which modeling techniques may be applied are single- and poly- crystalline metals and alloys, ceramics, and minerals. This book is intended for use by scientists and engineers involved in advanced constitutive modeling of nonlinear mechanical behavior of solid crystalline materials. Knowledge of fundamentals of continuum mechanics and tensor calculus is a prerequisite for accessing much of the text. This book could be used as supplemental material for graduate courses on continuum mechanics, elasticity, plasticity, micromechanics, or dislocation mechanics, for students in various disciplines of engineering, materials science, applied mathematics, and condensed matter physics.
Nonlinear Waves In Elastic Crystals
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Author : Gérard A. Maugin
language : en
Publisher:
Release Date : 1999
Nonlinear Waves In Elastic Crystals written by Gérard A. Maugin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
The mathematical modelling of changing structures in materials is of increasing importance to industry where applications of the theory are found in subjects as diverse as aerospace and medicine. This book deals with aspects of the nonlinear dynamics of deformable ordered solids (known as elastic crystals) where the nonlinear effects combine or compete with each other. Physical and mathematical models are discused and computational aspects are also included. Different models are considered - on discrete as well as continuum scales - applying heat, electricity, or magnetism to the crystal structure and these are analysed using the equations of rational mechanics. Students are introduced to the important equations of nonlinear science that describe shock waves, solitons and chaos and also the non-exactly integrable systems or partial differential equations. A large number of problems and examples are included, many taken from recent research and involving both one-dimensional and two-dimensional problems as well as some coupled degress of freedom.
Mechanics And Mathematics Of Crystals
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Author : Jerald L. Ericksen
language : en
Publisher: World Scientific
Release Date : 2005
Mechanics And Mathematics Of Crystals written by Jerald L. Ericksen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
This book is a unique and comprehensive collection of pioneering contributions to the mechanics of crystals by J L Ericksen, a prominent and leading contributor to the study of the mechanics and mathematics of crystalline solids over the past 35 years.It presents a splendid corpus of research papers that cover areas on crystal symmetry, constitutive equations, defects and phase transitions — all topics of current importance to a broad group of workers in the field.The volume thus provides in one place material that is frequently referenced by numerous researchers on crystals across a spectrum of activities in areas of continuum mechanics, applied mathematics, engineering and materials science.Each group of papers or chapters in the book is preceded by a summary introduction that describes how the papers on that topic fit together, and in which Ericksen sketches the context of each paper and shares with the reader his thinking and insightfulness in writing it. The volume, edited by internationally renowned scholars whose works in finite elasticity and continuum mechanics have appeared in a variety of books and prestigious journals published over the past four decades, also includes a very interesting brief autobiography by Ericksen. In it he describes his early life in Oregon, his wartime experiences, his student days and postgraduate study, his introduction to scientific work, and what motivated him in his research. An English translation and revision of the first paper in this volume, originally published in Russian, appears here for the first time.
Introduction To Geometrically Nonlinear Continuum Dislocation Theory
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Author : Christian B. Silbermann
language : en
Publisher: Springer Nature
Release Date : 2021-03-02
Introduction To Geometrically Nonlinear Continuum Dislocation Theory written by Christian B. Silbermann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-02 with Technology & Engineering categories.
This book provides an introduction to geometrically non-linear single crystal plasticity with continuously distributed dislocations. A symbolic tensor notation is used to focus on the physics. The book also shows the implementation of the theory into the finite element method. Moreover, a simple simulation example demonstrates the capability of the theory to describe the emergence of planar lattice defects (subgrain boundaries) and introduces characteristics of pattern forming systems. Numerical challenges involved in the localization phenomena are discussed in detail.
Constitutive Equations Of Nonlinear Electromagnetic Elastic Crystals
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Author : E. Kiral
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Constitutive Equations Of Nonlinear Electromagnetic Elastic Crystals written by E. Kiral and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Continuum physics is concemed with the predictions of deformations, stress, temperature, and electromagnetic fields in deformable and fluent bodies. To that extent, mathematical formulation requires the establishment of basic balance laws and constitutive equations. Balance laws are the union of those of continuum thermomechanics and MaxweIl's equations, as coIlected in Chapter 1. To dose the theory it is necessary to formulate equations for the material response to extemal stimuli. These equations bring into play the material properties of the media under consideration. In their simplest forms these are the constitutive laws, such as Hooke's law of dassical elasticity, Stokes' law of viscosity of viscous fluids, Fourier's law of heat conduction, Ohm's law of electric conduction, etc. For large deformations and fields in material media, the constitutive laws become very complicated, in vol ving all physical effects and material symmetry. The present work is concemed with the material symmetry regulations arising from the crystaIlographic symmetry of magnetic crystals. While there exist some works on the thirty-two conventional crystal dasses, exduding the linear case, there exists no study on the nonlinear constitutive equations for the ninty magnetic crystal dasses. Yet the interaction of strong electromagnetic fields with deformable solids cannot be explained without the material sym metry regulations relevant to magnetic crystals. In this monograph, we present a thorough discussion of magnetic symmetry by means of group theory. We consider onlyone scalar function which depends on one symmetric second-order tensor (e. g."
Continuum Mechanics Turbulence Nonlinear Electro And Magnetoelastic Interactions Liquid Crystals Configurational Forces Implicit Constitutive Relations Introductory Topics In The Mathematical Theory Of Continuum Mechanics
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Author :
language : en
Publisher:
Release Date : 2011
Continuum Mechanics Turbulence Nonlinear Electro And Magnetoelastic Interactions Liquid Crystals Configurational Forces Implicit Constitutive Relations Introductory Topics In The Mathematical Theory Of Continuum Mechanics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Continuum mechanics categories.
Nonlinear Optical Crystals A Complete Survey
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Author : David N. Nikogosyan
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-21
Nonlinear Optical Crystals A Complete Survey written by David N. Nikogosyan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-21 with Science categories.
Nonlinear Optical Crystals contains the most complete and up-to-date reference material on properties of nonlinear optical crystals including: Traditional and specific applications The mathematical formulas necessary for the calculation of the frequency conversion process A survey of 63 nonlinear optical crystals containing more than 1500 different references with full titles Recent applications of common and novel nonlinear materials, including quasi-phase matching Special consideration for periodically-poled and self-frequency-doubling materials Significant amount of crystallophysical, thermophysical, spectroscopic, electro-optic and magneto-optic information
Continuum Models For Phase Transitions And Twinning In Crystals
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Author : Mario Pitteri
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2002-06-27
Continuum Models For Phase Transitions And Twinning In Crystals written by Mario Pitteri and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-06-27 with Mathematics categories.
Continuum Models for Phase Transitions and Twinning in Crystals presents the fundamentals of a remarkably successful approach to crystal thermomechanics. Developed over the last two decades, it is based on the mathematical theory of nonlinear thermoelasticity, in which a new viewpoint on material symmetry, motivated by molecular theories, plays a central role. This is the first organized presentation of a nonlinear elastic approach to twinning and displacive phase transition in crystalline solids. The authors develop geometry, kinematics, and energy invariance in crystals in strong connection and with the purpose of investigating the actual mechanical aspects of the phenomena, particularly in an elastostatics framework based on the minimization of a thermodynamic potential. Interesting for both mechanics and mathematical analysis, the new theory offers the possibility of investigating the formation of microstructures in materials undergoing martensitic phase transitions, such as shape-memory alloys. Although phenomena such as twinning and phase transitions were once thought to fall outside the range of elastic models, research efforts in these areas have proved quite fruitful. Relevant to a variety of disciplines, including mathematical physics, continuum mechanics, and materials science, Continuum Models for Phase Transitions and Twinning in Crystals is your opportunity to explore these current research methods and topics.
Nonlinear Electromechanical Effects And Applications
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Author : G A Maugin
language : en
Publisher: World Scientific Publishing Company
Release Date : 1986-01-01
Nonlinear Electromechanical Effects And Applications written by G A Maugin and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-01-01 with categories.
The book develops a cross-disciplinary approach to the phenomenon of linear and nonlinear wave propagation in piezoelectric crystals. Based on the rigorous presentation of nonlinear continuum mechanics and electromechanical interactions in anisotropic bodies, the work starts from primary principles, is progressive and develops the subject matter by means of worked out examples up to the most recent applications in signal processing, introducing the most efficient methods of applied mathematics. The attention is especially focused on phenomena such as the formation of shocks, the generation harmonics, the anisochronism of resonators, nonlinear surface waves, the convolution of signals by means of surface-wave guides, the nonlinear couling between the crystal and deformations, the compensation between dispersion and nonlinearity. The work should be of pedagogical and practical interest to graduate students and research workers in various fields of applied science and engineering. Request Inspection Copy
Coherent Structures In Granular Crystals
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Author : Christopher Chong
language : en
Publisher: Springer
Release Date : 2018-03-29
Coherent Structures In Granular Crystals written by Christopher Chong and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-29 with Science categories.
This book summarizes a number of fundamental developments at the interface of granular crystals and the mathematical and computational analysis of some of their key localized nonlinear wave solutions. The subject presents a blend of the appeal of granular crystals as a prototypical engineering tested for a variety of diverse applications, the novelty in the nonlinear physics of its coherent structures, and the tractability of a series of mathematical and computational techniques to analyse them. While the focus is on principal one-dimensional solutions such as shock waves, traveling waves, and discrete breathers, numerous extensions of the discussed patterns, e.g., in two dimensions, chains with defects, heterogeneous settings, and other recent developments are discussed. The emphasis on the subject was motivated by models in condensed matter physics, ferroelectrics, high energy physics, and statistical mechanics, leading to developments in mathematical analysis, numerical computation and insights on the physical aspects of the model. The book appeals to researchers in the field, as well as for graduate and advanced undergraduate students. It will be of interest to mathematicians, physicists and engineers alike.