nonlinear theory of electroelastic and magnetoelastic interactions

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Nonlinear Theory Of Electroelastic And Magnetoelastic Interactions

Author : Luis Dorfmann
ISBN : 9781461495963
Genre : Technology & Engineering
File Size : 54. 96 MB
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This book provides a unified theory on nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classic theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize relevant theories of continuum mechanics, required to account for the deformability of material and present a constitutive framework for the nonlinear magneto-and electroelastic interactions in a highly deformable material. The equations contained in the book formulate and solve a variety of representative boundary-value problems for both nonlinear magnetoelasticity and electroelasticity.

Generalized Models And Non Classical Approaches In Complex Materials 1

Author : Holm Altenbach
ISBN : 9783319724409
Genre : Technology & Engineering
File Size : 52. 7 MB
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This book is the first of 2 special volumes dedicated to the memory of Gérard Maugin. Including 40 papers that reflect his vast field of scientific activity, the contributions discuss non-standard methods (generalized model) to demonstrate the wide range of subjects that were covered by this exceptional scientific leader. The topics range from micromechanical basics to engineering applications, focusing on new models and applications of well-known models to new problems. They include micro–macro aspects, computational endeavors, options for identifying constitutive equations, and old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.

The Role Of Mechanics In The Study Of Lipid Bilayers

Author : David Steigmann
ISBN : 9783319563480
Genre : Technology & Engineering
File Size : 20. 6 MB
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This book is the first collection of lipid-membrane research conducted by leading mechanicians and experts in continuum mechanics. It brings the overall intellectual framework afforded by modern continuum mechanics to bear on a host of challenging problems in lipid membrane physics. These include unique and authoritative treatments of differential geometry, shape elasticity, surface flow and diffusion, interleaf membrane friction, phase transitions, electroelasticity and flexoelectricity, and computational modelling.

Constitutive Models For Rubber X

Author : Alexander Lion
ISBN : 9781351840392
Genre : Technology & Engineering
File Size : 81. 28 MB
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In order to develop innovative products, to reduce development costs and the number of prototypes and to accelerate development processes, numerical simulations become more and more attractive. As such, numerical simulations are instrumental in understanding complicated material properties like chemical ageing, crack propagation or the strain- and temperature-induced crystallisation of rubber. Therefore, experimentally validated and physically meaningful constitutive models are indispensable. Elastomers are used for products like tyres, engine and suspension mounts or seals, to name a few. The interest in modelling the quasi-static stress-strain behaviour was dominant in the past decades, but nowadays the interests also include influences of environmental conditions. The latest developments on the material behaviour of elastomers are collected in the present volume. Constitutive Models for Rubber X is a comprehensive compilation of nearly all oral and poster contributions to the European Conference on Constitutive Models for Rubber (Munich, 28-31 August 2017). The 95 highly topical contributions reflect the state of-the-art in material modelling and testing of elastomers. They cover the fields of material testing and processing, filler reinforcement, electromagnetic sensitive elastomers, dynamic properties, constitutive modelling, micromechanics, finite element implementation, stress softening, chemical ageing, fatigue and durability. In the area of rubbery materials and structures, applied research will play an important role also in the coming decades. Constitutive Models for Rubber X is of interest to developers and researchers involved in the rubber processing and CAE software industries, as well as for academics in nearly all disciplines of engineering and material sciences.

Continuum Mechanics Volume Iii

Author : José Merodio
ISBN : 9781848263741
Genre :
File Size : 51. 17 MB
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The main objective of continuum mechanics is to predict the response of a body that is under the action of external and/or internal influences, i.e. to capture and describe different mechanisms associated with the motion of a body that is under the action of loading. A body in continuum mechanics is considered to be matter continuously distributed in space. Hence, no attention is given to the microscopic (atomic) structure of real materials although non-classical generalized theories of continuum mechanics are able to deal with the mesoscopic structure of matter (i.e. defects, cracks, dispersive lengths, ...). Matter occupies space in time and the response of a body in continuum mechanics is restricted to the Newtonian space-time of classical mechanics in this volume. Einstein’s theory of relativity is not considered. In the classical sense, loading is considered as any action that changes the motion of the body. This includes, for instance, a change in temperature or a force applied. By introducing the concept of configurational forces a load may also be considered as a force that drives a change in the material space, for example the opening of a crack. Continuum mechanics refers to field descriptions of phenomena that are usually modeled by partial differential equations and, from a mathematical point of view, require non-standard knowledge of non-simple technicalities. One purpose in this volume has been to present the different subjects in a self-contained way for a general audience. The organization of the volume is as follows. Mathematically, to predict the response of a body it is necessary to formulate boundary value problems governed by balance laws. The theme of the volume, that is an overview of the subject, has been written with this idea in mind for beginners in the topic. Chapter 1 is an introduction to continuum mechanics based on a one-dimensional framework in which, simultaneously, a more detailed organization of the chapters of this volume is given. A one-dimensional approach to continuum mechanics in some aspects maybe misleading since the analysis is oversimplified. Nevertheless, it allows us to introduce the subject through the early basic steps of the continuum analysis for a general audience. Chapters 3, 4 and 5 are devoted to the mathematical setting of continuum analysis: kinematics, balance laws and thermodynamics, respectively. Chapters 6 and 7 are devoted to constitutive equations. Chapters 8 and 9 deal with different issues in the context of linear elastostatics and linear elastodynamics and waves, respectively, for solids. Linear Elasticity is a classical and central theory of continuum mechanics. Chapter 10 deals with fluids while chapter 11 analyzes the coupled theory of thermoelasticity. Chapter 12 deals with nonlinear elasticity and its role in the continuum framework. Chapters 13 and 14 are dedicated to different applications of solid and fluid mechanics, respectively. The rest of the chapters involve some advanced topics. Chapter 15 is dedicated to turbulence, one of the main challenges in fluid mechanics. Chapter 16 deals with electro-magneto active materials (a coupled theory). Chapter 17 deals with specific ideas of soft matter and chapter 18 deals with configurational forces. In chapter 19, constitutive equations are introduced in a general (implicit) form. Well-posedness (existence, time of existence, uniqueness, continuity) of the equations of the mechanics of continua is an important topic which involves sophisticated mathematical machinery. Chapter 20 presents different analyses related to these topics. Continuum Mechanics is an interdisciplinary subject that attracts the attention of engineers, mathematicians, physicists, etc., working in many different disciplines from a purely scientific environment to industrial applications including biology, materials science, engineering, and many other subjects.

Mechanics And Electrodynamics Of Magneto And Electro Elastic Materials

Author : Raymond Ogden
ISBN : 3709107016
Genre : Technology & Engineering
File Size : 74. 41 MB
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This volume presents a state-of-the-art overview of the continuum theory of both electro- and magneto-sensitive elastomers and polymers, which includes mathematical and computational aspects of the modelling of these materials from the point of view of material properties and, in particular, the "smart-material" control of their mechanical properties.

Nonlinear Waves In Elastic Crystals

Author : Gérard A. Maugin
ISBN : 0198534841
Genre : Mathematics
File Size : 65. 19 MB
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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 aselastic 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 thecrystal structure and these are analysed using the equations of rational mechanics. In this way the student is 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. Alarge 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.

Applied Mechanics Reviews

Author :
ISBN : OSU:32435065742082
Genre : Mechanics, Applied
File Size : 22. 46 MB
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Electromagnetic Field Matter Interactions In Thermoelasic Solids And Viscous Fluids

Author : Kolumban Hutter
ISBN : UVA:X030116003
Genre : Mathematics
File Size : 66. 28 MB
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This book delivers a thorough derivation of nonrelativistic interaction models of electromagnetic field theories with thermoelastic solids and viscous fluids, the intention being to derive unique representations for the observable field quantities. This volume is intended for and will be useful to students and researchers working on all aspects of electromagneto-mechanical interactions in the materials sciences of complex solids and fluids.

International Aerospace Abstracts

Author :
ISBN : UOM:39015057251939
Genre : Aeronautics
File Size : 83. 53 MB
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