Material Geometry Groupoids In Continuum Mechanics PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Material Geometry Groupoids In Continuum Mechanics PDF full book. Access full book title Material Geometry Groupoids In Continuum Mechanics.
Author | : Manuel De Leon |
Publisher | : World Scientific |
Total Pages | : 226 |
Release | : 2021-04-23 |
Genre | : Mathematics |
ISBN | : 9811232563 |
Download Material Geometry: Groupoids In Continuum Mechanics Book in PDF, ePub and Kindle
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.
Author | : Marcelo Epstein |
Publisher | : Cambridge University Press |
Total Pages | : 325 |
Release | : 2010-07-26 |
Genre | : Science |
ISBN | : 113949046X |
Download The Geometrical Language of Continuum Mechanics Book in PDF, ePub and Kindle
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.
Author | : Marcelo Epstein |
Publisher | : Springer |
Total Pages | : 147 |
Release | : 2014-07-02 |
Genre | : Mathematics |
ISBN | : 3319069209 |
Download Differential Geometry Book in PDF, ePub and Kindle
Differential Geometry offers a concise introduction to some basic notions of modern differential geometry and their applications to solid mechanics and physics. Concepts such as manifolds, groups, fibre bundles and groupoids are first introduced within a purely topological framework. They are shown to be relevant to the description of space-time, configuration spaces of mechanical systems, symmetries in general, microstructure and local and distant symmetries of the constitutive response of continuous media. Once these ideas have been grasped at the topological level, the differential structure needed for the description of physical fields is introduced in terms of differentiable manifolds and principal frame bundles. These mathematical concepts are then illustrated with examples from continuum kinematics, Lagrangian and Hamiltonian mechanics, Cauchy fluxes and dislocation theory. This book will be useful for researchers and graduate students in science and engineering.
Author | : Reuven Segev |
Publisher | : Springer Nature |
Total Pages | : 416 |
Release | : 2020-05-13 |
Genre | : Mathematics |
ISBN | : 3030426831 |
Download Geometric Continuum Mechanics Book in PDF, ePub and Kindle
This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include: Global stress and hyper-stress theories Applications of de Rham currents to singular dislocations Manifolds of mappings for continuum mechanics Kinematics of defects in solid crystals Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.
Author | : Marcelo Epstein |
Publisher | : Springer Science & Business Media |
Total Pages | : 278 |
Release | : 2007-08-03 |
Genre | : Science |
ISBN | : 3540723730 |
Download Material Inhomogeneities and their Evolution Book in PDF, ePub and Kindle
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.
Author | : Giovanni Romano |
Publisher | : CreateSpace |
Total Pages | : 102 |
Release | : 2014-11-01 |
Genre | : |
ISBN | : 9781503172197 |
Download Geometry and Continuum Mechanics Book in PDF, ePub and Kindle
Continuum Mechanics (CM) is a natural field of application of concepts and methods of Differential Geometry (DG). The very foundations of both disciplines are intertwined in a deep manner. A presentation of basic issues in CM adopting the powerful tools of modern DG is still substantially lacking. This booklet is intended to contribute to fill this gap, with specific reference to Elasticity theory. The classical subject is thoroughly revisited and revised in its basic aspects and in the general context of finite deformations. A case study of rubber-like materials enlightens the new concepts introduced by the geometric theory and opens the way for applications to soft materials such as the ones of interest in biomechanics.
Author | : Donald E. Carlson |
Publisher | : Springer Science & Business Media |
Total Pages | : 431 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9401007284 |
Download Advances in Continuum Mechanics and Thermodynamics of Material Behavior Book in PDF, ePub and Kindle
The papers included in this volume were presented at the Symposium on Advances in the Continuum Mechanics and Thermodynamics of Material Behavior, held as part of the 1999 Joint ASME Applied Mechanics and Materials Summer Conference at Virginia Tech on June 27-30, 1999. The Symposium was held in honor of Professor Roger L. Fosdick on his 60th birthday. The papers are written by prominent researchers in the fields of mechanics, thermodynamics, materials modeling, and applied mathematics. They address open questions and present the latest development in these and related areas. This volume is a valuable reference for researchers and graduate students in universities and research laboratories.
Author | : Gérard A. Maugin |
Publisher | : Springer Science & Business Media |
Total Pages | : 337 |
Release | : 2010-03-24 |
Genre | : Mathematics |
ISBN | : 1441956956 |
Download Mechanics of Generalized Continua Book in PDF, ePub and Kindle
In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers. The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics and can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.
Author | : Simon R. Eugster |
Publisher | : Springer |
Total Pages | : 146 |
Release | : 2015-03-19 |
Genre | : Science |
ISBN | : 3319164953 |
Download Geometric Continuum Mechanics and Induced Beam Theories Book in PDF, ePub and Kindle
This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.
Author | : Reuven Segev |
Publisher | : Birkhäuser |
Total Pages | : 0 |
Release | : 2023-10-02 |
Genre | : Mathematics |
ISBN | : 9783031356544 |
Download Foundations of Geometric Continuum Mechanics Book in PDF, ePub and Kindle
This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the author’s extension of the theory will enable researchers to better describe the mechanics of modern materials and biological tissues. The global approach to continuum mechanics also enables the formulation and solutions of practical optimization problems. Foundations of Geometric Continuum Mechanics will be an invaluable resource for researchers in the area, particularly mathematicians, physicists, and engineers interested in the foundational notions of continuum mechanics.