Download or read book Material Inhomogeneities and their Evolution written by Marcelo Epstein and published by Springer Science & Business Media. This book was released on 2007-09-05 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Material Inhomogeneities and their Evolution written by Marcelo Epstein and published by Springer Science & Business Media. This book was released on 2007-08-03 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Material Inhomogeneities in Elasticity written by G.A. Maugin and published by CRC Press. This book was released on 2020-09-11 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Biomechanics written by Manuel Doblare and published by EOLSS Publications. This book was released on 2015-12-30 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biomechanics is a component of Encyclopedia of Physical Sciences, Engineering and Technology Resources in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The enormous progress in the field of health sciences that has been achieved in the 19th and 20th centuries would have not been possible without the enabling interaction and support of sophisticated technologies that progressively gave rise to a new interdisciplinary field named alternatively as bioengineering or biomedical engineering. Although both terms are synonymous, the latter is less general since it limits the field of application to medicine and clinical practice, while the former covers semantically the whole field of interaction between life sciences and engineering, thus including also applications in biology, biochemistry or the many '-omics'. We use in this book the second, with more general meaning, recalling the very important relation between fundamental science and engineering. And this also recognizes the tremendous economic and social impacts of direct application of engineering in medicine that maintains the health industry as one with the fastest growth in the world economy. Biomechanics, in particular, aims to explain and predict the mechanics of the different components of living beings, from molecules to organisms as well as to design, manufacture and use of any artificial device that interacts with the mechanics of living beings. It helps, therefore, to understand how living systems move, to characterize the interaction between forces and deformation along all spatial scales, to analyze the interaction between structural behavior and microstructure, with the very important particularity of dealing with adaptive systems, able to adapt their internal structure, size and geometry to the particular mechanical environment in which they develop their activity, to understand and predict alterations in the mechanical function due to injuries, diseases or pathologies and, finally, to propose methods of artificial intervention for functional diagnosis or recovery. Biomechanics is today a very highly interdisciplinary subject that attracts the attention of engineers, mathematicians, physicists, chemists, material specialists, biologists, medical doctors, etc. They work in many different topics from a purely scientific objective to industrial applications and with an increasing arsenal of sophisticated modeling and experimental tools but always with the final objectives of better understanding the fundamentals of life and improve the quality of life of human beings. One purpose in this volume has been to present an overview of some of these many possible subjects in a self-contained way for a general audience. This volume is aimed at the following major target audiences: University and College Students, Educators, Professional Practitioners, and Research Personnel.

Download or read book Mechanics of Functionally Graded Material Structures written by Isaac E. T. Al ELISHAKOFF and published by World Scientific. This book was released on 2015-10-29 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanics of Functionally Graded Material Structures is an authoritative and fresh look at various functionally graded materials, customizing them with various structures. The book is devoted to tailoring material properties to the needed structural performance. The authors pair materials with the appropriate structures based upon their purpose and use.Material grading of structures depending upon thickness, axial and polar directions are discussed. Three dimensional analysis of rectangular plates made of functional graded materials and vibrational tailoring of inhomogeneous beams and circular plates are both covered in great detail. The authors derive novel closed form solutions that can serve as benchmarks that numerical solutions can be compared to. These are published for the first time in the literature. This is a unique book that gives the first exposition of the effects of various grading mechanisms on the structural behavior as well as taking into account vibrations and buckling.

Download or read book Material Geometry Groupoids In Continuum Mechanics written by Manuel De Leon and published by World Scientific. This book was released on 2021-04-23 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first in which the theory of groupoids and algebroids is applied to the study of the properties of uniformity and homogeneity of continuous media. It is a further step in the application of differential geometry to the mechanics of continua, initiated years ago with the introduction of the theory of G-structures, in which the group G denotes the group of material symmetries, to study smoothly uniform materials.The new approach presented in this book goes much further by being much more general. It is not a generalization per se, but rather a natural way of considering the algebraic-geometric structure induced by the so-called material isomorphisms. This approach has allowed us to encompass non-uniform materials and discover new properties of uniformity and homogeneity that certain material bodies can possess, thus opening a new area in the discipline.

Download or read book The Geometrical Language of Continuum Mechanics written by Marcelo Epstein and published by Cambridge University Press. This book was released on 2010-07-26 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Epstein presents the fundamental concepts of modern differential geometry within the framework of continuum mechanics. Divided into three parts of roughly equal length, the book opens with a motivational chapter to impress upon the reader that differential geometry is indeed the natural language of continuum mechanics or, better still, that the latter is a prime example of the application and materialisation of the former. In the second part, the fundamental notions of differential geometry are presented with rigor using a writing style that is as informal as possible. Differentiable manifolds, tangent bundles, exterior derivatives, Lie derivatives, and Lie groups are illustrated in terms of their mechanical interpretations. The third part includes the theory of fiber bundles, G-structures, and groupoids, which are applicable to bodies with internal structure and to the description of material inhomogeneity. The abstract notions of differential geometry are thus illuminated by practical and intuitively meaningful engineering applications.

Download or read book Non commuting Variations in Mathematics and Physics written by Serge Preston and published by Springer. This book was released on 2016-03-02 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations. Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equations with dissipation and corresponding s balance laws is presented.

Download or read book Mechanics of Material Forces written by Paul Steinmann and published by Springer Science & Business Media. This book was released on 2006-01-20 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Finite Elasticity Theory written by David J. Steigmann and published by Oxford University Press. This book was released on 2017-08-25 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing case studies and examples, the book aims to cover extensive research particularly on surface stress and topics related to the variational approach to the subject, and non-standard topics such as the rigorous treatment of constraints and a full discussion of algebraic inequalities associated with realistic material behaviour, and their implications. Serving as an introduction to the basic elements of Finite Elasticity, this textbook is the cornerstone for any graduate-level on the topic, while also providing a template for a host of theories in Solid Mechanics.

Download or read book Continuum Thermomechanics written by Gérard A. Maugin and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributed by world-renowned specialists on the occasion of Paul Germain's 80th birthday, this unique book reflects the foundational works and the intellectual influence of this author. It presents the realm of modern thermomechanics with its extraordinary wealth of applications to the behaviour of materials, whether solid or fluid. The thirty-one contributions follow an easygoing autobiographical sketch by Paul Germain, and highlight the power and richness of a methodological approach to the phenomenology of many materials. This approach combines harmoniously thermodynamics and continuum theory in order to provide exploitable, thermodynamically admissible models of a large variety of behaviours and phenomena, including those of diffusion, thermoelasticity, viscoplasticity, relaxation, hysteresis, wetting, shape-memory effects, growth, phase transitions, stability, fracture, shocks, machining of materials, microstructured solids, complex fluids, etc. Especially aimed at graduate students, researchers, and engineers in mechanical engineering and materials science, this book also presents the state of the art in an active field of research and opens new horizons in other scientific fields, such as applied mathematics and applied physics, because of the intellectual satisfaction and remarkable efficiency provided by the advocated approach.

Download or read book Geometry of Incompatible Deformations written by and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-03-04 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Differential Geometry and Continuum Mechanics written by Gui-Qiang G. Chen and published by Springer. This book was released on 2015-08-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the exciting interface between differential geometry and continuum mechanics, now recognised as being of increasing technological significance. Topics discussed include isometric embeddings in differential geometry and the relation with microstructure in nonlinear elasticity, the use of manifolds in the description of microstructure in continuum mechanics, experimental measurement of microstructure, defects, dislocations, surface energies, and nematic liquid crystals. Compensated compactness in partial differential equations is also treated. The volume is intended for specialists and non-specialists in pure and applied geometry, continuum mechanics, theoretical physics, materials and engineering sciences, and partial differential equations. It will also be of interest to postdoctoral scientists and advanced postgraduate research students. These proceedings include revised written versions of the majority of papers presented by leading experts at the ICMS Edinburgh Workshop on Differential Geometry and Continuum Mechanics held in June 2013. All papers have been peer reviewed.

Download or read book Field Theory of Multiscale Plasticity written by Tadashi Hasebe and published by Cambridge University Press. This book was released on 2023-12-31 with total page 861 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers foundations of dislocations and metallurgy, with up-to-date discussion of multiscale modeling, including the field theory of multiscale plasticity.

Download or read book Waves And Rays In Elastic Continua written by Michael A Slawinski and published by World Scientific Publishing Company. This book was released on 2010-09-09 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book — which is the second, and significantly extended, edition of the textbook originally published by Elsevier Science — emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves.The book is divided into three main sections: Elastic Continua, Waves and Rays and Variational Formulation of Rays. There is also a fourth part, which consists of appendices.In Elastic Continua, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Waves and Rays, we use these equations to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, we invoke the concept of a ray. In Variational Formulation of Rays, we show that, in elastic continua, a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In the Appendices, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols.

Download or read book Configurational Forces written by Gerard A. Maugin and published by CRC Press. This book was released on 2016-04-19 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book IUTAM Symposium on Anisotropy Inhomogeneity and Nonlinearity in Solid Mechanics written by David Parker and published by Springer Science & Business Media. This book was released on 1995-08-31 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the IUTAM-ISIMM Symposium, held in Nottingham, U.K., 30 August--3 September 1994