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Material Inhomogeneities In Elasticity

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Material Inhomogeneities In Elasticity

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Author : G.A. Maugin
language : en
Publisher: CRC Press
Release Date : 2020-09-11

Material Inhomogeneities In Elasticity written by G.A. Maugin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-11 with Mathematics categories.

Self contained, this book presents a thorough introduction to the complementary notions of physical forces and material (or configurational) forces. All the required elements of continuum mechanics, deformation theory and differential geometry are also covered. This book will be a great help to many, whilst revealing to others a rather new facet of continuum mechanics in general, and elasticity in particular. An organized exposition of continuum mechanics on the material manifold is given which allows for the consideration of material inhomogeneities in their most appropriate framework. In such a frame the nonlinear elasticity of anisotropic inhomogenous materials appears to be a true field theory. Extensions to the cases of electroelasticity and magnetelasticity are then straightforward. In addition, this original approach provides systematic computational means for the evaluation of characteristic parameters which are useful in various branches of applied mechanics and mathematical physics. This is the case for path-independent integrals and energy-release rates in brittle fracture, the influence of electromagnetic fields on fracture criteria (such as in ceramics), the notion of momentum of electromagnetic fields in matter in optics, and the perturbation of solitons propagating in elastic dispersive systems.

Material Inhomogeneities And Their Evolution

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Author : Marcelo Epstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-03

Material Inhomogeneities And Their Evolution written by Marcelo Epstein 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 2007-08-03 with Science categories.

With its origins in the theories of continuous distributions of dislocations and ofmetalplasticity,inhomogeneitytheoryisarichandvibrant?eldofresearch. The recognition of the important role played by con?gurational or material forces in phenomena such as growth and remodelling is perhaps its greatest present-day impetus. While some excellent comprehensive works approa- ing the subject from di?erent angles have been published, the objective of this monograph is to present a point of view that emphasizes the di?erenti- geometric aspects of inhomogeneity theory. In so doing, we follow the general lines of thought that we have propounded in many publications and presen- tions over the last two decades. Although based on these sources, this book is a stand-alone entity and contains some new results and perspectives. At the same time, it does not intend to present either a historical account of the - velopment of the subject or a comprehensive picture of the various schools of thought that can be encountered by perusing scholarly journals and attending specialized symposia. The book is divided into three parts, the ?rst of which is entirely devoted to the formulation of the theory in the absence of evolution. In other words, time is conspicuously absent from Part I. It opens with the geometric ch- acterization of material inhomogeneity within the context of simple bodies in Chapter 1, followed by extensions to second-grade and Cosserat media in Chapters 2 and 3.

Anisotropy And Inhomogeneity In Elasticity And Plasticity

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Author : Yves Christian Angel
language : en
Publisher:
Release Date : 1993

Anisotropy And Inhomogeneity In Elasticity And Plasticity written by Yves Christian Angel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.

Material Inhomogeneities In Elasticity

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Author : G.A. Maugin
language : en
Publisher: CRC Press
Release Date : 2020-09-10

Configurational Forces

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Author : Gerard A. Maugin
language : en
Publisher: CRC Press
Release Date : 2016-04-19

Configurational Forces written by Gerard A. Maugin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.

Exploring recent developments in continuum mechanics, Configurational Forces: Thermomechanics, Physics, Mathematics, and Numerics presents the general framework for configurational forces. It also covers a range of applications in engineering and condensed matter physics. The author presents the fundamentals of accepted standard continuum mechanics, before introducing Eshelby material stress, field theory, variational formulations, Noether’s theorem, and the resulting conservation laws. In the chapter on complex continua, he compares the classical perspective of B.D. Coleman and W. Noll with the viewpoint linked to abstract field theory. He then describes the important notion of local structural rearrangement and its relationship to Eshelby stress. After looking at the relevance of Eshelby stress in the thermodynamic description of singular interfaces, the text focuses on fracture problems, microstructured media, systems with mass exchanges, and electromagnetic deformable media. The concluding chapters discuss the exploitation of the canonical conservation law of momentum in nonlinear wave propagation, the application of canonical-momentum conservation law and material force in numerical schemes, and similarities of fluid mechanics and aerodynamics. Written by a long-time researcher in mechanical engineering, this book provides a detailed treatment of the theory of configurational forces—one of the latest and most fruitful advances in macroscopic field theories. Through many applications, it shows the depth and efficiency of this theory.

Configurational Mechanics Of Materials

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Author : Reinhold Kienzler
language : en
Publisher: Springer
Release Date : 2014-05-04

Configurational Mechanics Of Materials written by Reinhold Kienzler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Technology & Engineering categories.

In several applications it is well recognized that all materials, on some scale, cannot be regarded as perfect continua. They rather contain a variety of numerous defects, such as micro-cracks, inclusions, vacancies, voids, dislocations, etc. To characterize such defects, the notion of "force” acting on a "defect” in the material needs to be introduced which leads to a whole engineering science of "Configurational Mechanics of Materials”. The lecture notes cover the numerous elements of configurational mechanics, including mathematical foundations, linear and nonlinear elasticity and continuum mechanics, coupled fields, fracture mechanics, as well as strength-of-materials.

Continuum Mechanics Volume Iii

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Author : José Merodio
language : en
Publisher: EOLSS Publications
Release Date : 2011-11-30

Continuum Mechanics Volume Iii written by José Merodio and has been published by EOLSS Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with categories.

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.

Multiscale Lattices And Composite Materials Optimal Design Modeling And Characterization

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Author : Fernando Fraternali
language : en
Publisher: Frontiers Media SA
Release Date : 2019-11-26

Multiscale Lattices And Composite Materials Optimal Design Modeling And Characterization written by Fernando Fraternali and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-26 with categories.

Mechanics Of Material Forces

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Author : Paul Steinmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-20

Mechanics Of Material Forces written by Paul Steinmann 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 2006-01-20 with Technology & Engineering categories.

The notion dealt with in this volume of proceedings is often traced back to the late 19th-century writings of a rather obscure scientist, C. V. Burton. A probable reason for this is that the painstaking de ciphering of this author's paper in the Philosophical Magazine (Vol. 33, pp. 191-204, 1891) seems to reveal a notion that was introduced in math ematical form much later, that of local structural rearrangement. This notion obviously takes place on the material manifold of modern con tinuum mechanics. It is more or less clear that seemingly different phe nomena - phase transition, local destruction of matter in the form of the loss of local ordering (such as in the appearance of structural defects or of the loss of cohesion by the appearance of damage or the exten sion of cracks), plasticity, material growth in the bulk or at the surface by accretion, wear, and the production of debris - should enter a com mon framework where, by pure logic, the material manifold has to play a prominent role. Finding the mathematical formulation for this was one of the great achievements of J. D. Eshelby. He was led to consider the apparent but true motion or displacement of embedded material inhomogeneities, and thus he began to investigate the "driving force" causing this motion or displacement, something any good mechanician would naturally introduce through the duahty inherent in mechanics since J. L. d'Alembert.

Configurational Mechanics

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Author : V.K. Kalpakides
language : en
Publisher: CRC Press
Release Date : 2004-11-23

Configurational Mechanics written by V.K. Kalpakides and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-23 with Technology & Engineering categories.

This book comprises papers that were presented at the Symposium on Configurational Mechanics, during the 5th EUROMECH Soil Mechanics Conference in Thessaloniki in August 2003. Configurational (or material) mechanics -in contrast to Newtonian mechanics in Euclidean space- concerns any sort of change or "motion" in the material configuration. This framework provides a novel and unifying view on otherwise diverse disciplines like fracture mechanics, phase transitions, plasticity and dislocation theory. In addition, configurational mechanics can be used in computations because it provides a fruitful interpretation of the field equations in the discretized space. This volume contains eleven contributions from specialists from around Europe Articles concern both theoretical and computational mechanics, electroplasticity, magnetoelasticity, elastoplasticity as well as granular, multiphase and micropolar media.

Material Inhomogeneities In Elasticity

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