A Geometric Approach To Thermomechanics Of Dissipating Continua

Author : Lalao Rakotomanana
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 45,5 Mb
Release : 2012-09-08
Category : Mathematics
ISBN : 9780817681326

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A Geometric Approach to Thermomechanics of Dissipating Continua by Lalao Rakotomanana Pdf

Across the centuries, the development and growth of mathematical concepts have been strongly stimulated by the needs of mechanics. Vector algebra was developed to describe the equilibrium of force systems and originated from Stevin's experiments (1548-1620). Vector analysis was then introduced to study velocity fields and force fields. Classical dynamics required the differential calculus developed by Newton (1687). Nevertheless, the concept of particle acceleration was the starting point for introducing a structured spacetime. Instantaneous velocity involved the set of particle positions in space. Vector algebra theory was not sufficient to compare the different velocities of a particle in the course of time. There was a need to (parallel) transport these velocities at a single point before any vector algebraic operation. The appropriate mathematical structure for this transport was the connection. I The Euclidean connection derived from the metric tensor of the referential body was the only connection used in mechanics for over two centuries. Then, major steps in the evolution of spacetime concepts were made by Einstein in 1905 (special relativity) and 1915 (general relativity) by using Riemannian connection. Slightly later, nonrelativistic spacetime which includes the main features of general relativity I It took about one and a half centuries for connection theory to be accepted as an independent theory in mathematics. Major steps for the connection concept are attributed to a series of findings: Riemann 1854, Christoffel 1869, Ricci 1888, Levi-Civita 1917, WeyJ 1918, Cartan 1923, Eshermann 1950.

Author : John D Clayton
Publisher : World Scientific
Page : 192 pages
File Size : 50,5 Mb
Release : 2014-07-31
Category : Mathematics
ISBN : 9789814616058

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Differential Geometry and Kinematics of Continua by John D Clayton Pdf

This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry. Of particular interest are anholonomic aspects arising from a multiplicative decomposition of the deformation gradient into two terms, neither of which in isolation necessarily obeys the integrability conditions satisfied by the gradient of a smooth vector field. The concise format emphasizes clarity and ease of reference, and detailed step-by-step derivations of most analytical results are provided. Contents: IntroductionGeometric FundamentalsKinematics of Integrable DeformationGeometry of Anholonomic DeformationKinematics of Anholonomic DeformationList of SymbolsBibliographyIndex Readership: Researchers in mathematical physics and engineering mechanics. Key Features:Presentation of mathematical operations and examples in anholonomic space associated with a multiplicative decomposition (e.g., of the gradient of motion) is more general and comprehensive than any given elsewhere and contains original ideas and new resultsLine-by-line derivations are frequent and exhaustive, to facilitate practice and enable verification of final resultsGeneral analysis is given in generic curvilinear coordinates; particular sections deal with applications and examples in Cartesian, cylindrical, spherical, and convected coordinates. Indicial and direct notations of tensor calculus enable connections with historic and modern literature, respectivelyKeywords:Differential Geometry;Tensor Analysis;Continuum Mechanics;Kinematics;Deformation;Anholonomic Coordinates

Author : Holm Altenbach,Gérard A. Maugin,Vladimir Erofeev
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 55,9 Mb
Release : 2011-04-02
Category : Technology & Engineering
ISBN : 9783642192197

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Mechanics of Generalized Continua by Holm Altenbach,Gérard A. Maugin,Vladimir Erofeev Pdf

This collection on „Mechanics of Generalized Continua - from Micromechanical Basics to Engineering Applications“ brings together leading scientists in this field from France, Russian Federation, and Germany. The attention in this publication is be focussed on the most recent research items, i.e., - new models, - application of well-known models to new problems, - micro-macro aspects, - computational effort, - possibilities to identify the constitutive equations, and - old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.

Author : Lalaonirina R. Rakotomanana
Publisher : Springer
Page : 325 pages
File Size : 51,6 Mb
Release : 2018-07-04
Category : Science
ISBN : 9783319917825

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Covariance and Gauge Invariance in Continuum Physics by Lalaonirina R. Rakotomanana Pdf

This book presents a Lagrangian approach model to formulate various fields of continuum physics, ranging from gradient continuum elasticity to relativistic gravito-electromagnetism. It extends the classical theories based on Riemann geometry to Riemann-Cartan geometry, and then describes non-homogeneous continuum and spacetime with torsion in Einstein-Cartan relativistic gravitation. It investigates two aspects of invariance of the Lagrangian: covariance of formulation following the method of Lovelock and Rund, and gauge invariance where the active diffeomorphism invariance is considered by using local Poincaré gauge theory according to the Utiyama method. Further, it develops various extensions of strain gradient continuum elasticity, relativistic gravitation and electromagnetism when the torsion field of the Riemann-Cartan continuum is not equal to zero. Lastly, it derives heterogeneous wave propagation equations within twisted and curved manifolds and proposes a relation between electromagnetic potential and torsion tensor.

Author : Arnold F. Nikiforov,Vladimir G. Novikov,Vasili B. Uvarov
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 50,7 Mb
Release : 2005-02-17
Category : Law
ISBN : 3764321830

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Quantum-Statistical Models of Hot Dense Matter by Arnold F. Nikiforov,Vladimir G. Novikov,Vasili B. Uvarov Pdf

This book studies the widely used theoretical models for calculating properties of hot dense matter. Calculations are illustrated by plots and tables, and they are compared with experimental results. The purpose is to help understanding of atomic physics in hot plasma and to aid in developing efficient and robust computer codes for calculating opacity and equations of state for arbitrary material in a wide range of temperatures and densities.

Author : Piotr T. Chruściel,Helmut Felix Friedrich
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 47,7 Mb
Release : 2004
Category : Science
ISBN : 3764371307

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The Einstein Equations and the Large Scale Behavior of Gravitational Fields by Piotr T. Chruściel,Helmut Felix Friedrich Pdf

Accompanying DVD-ROM contains the electronic proceedings of the summer school on mathematical general relativity and global properties of solutions of Einstein's equations held at Cargèse, Corsica, France, July 20-Aug. 10, 2002.

Author : Paul Steinmann,Gérard A. Maugin
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 45,5 Mb
Release : 2006-01-20
Category : Technology & Engineering
ISBN : 9780387262611

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Mechanics of Material Forces by Paul Steinmann,Gérard A. Maugin Pdf

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.

Author : M. Cerrolaza
Publisher : World Scientific
Page : 254 pages
File Size : 55,8 Mb
Release : 2004
Category : Technology & Engineering
ISBN : 9781860944659

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Computational Bioengineering by M. Cerrolaza Pdf

This book is a significant contribution to the state of the art in the field of computational bioengineering ? from the need for a living human database to meshless methods in biomechanics, from computational mechanobiology to the evaluation of stresses in hip prosthesis replacement, from lattice Boltzmann methods for analyzing blood flow to the analysis of fluid movement in long bones, among other interesting topics treated herein. Well-known international experts in bioengineering have contributed to the book, giving it a unique style and cutting-edge material for graduate students, academic researchers and design bioengineers, as well as those interested in getting a better understanding of such complex and fascinating human and living processes.

Author : Francesco dell'Isola,Mircea Sofonea,David Steigmann
Publisher : Springer
Page : 327 pages
File Size : 41,6 Mb
Release : 2017-03-10
Category : Science
ISBN : 9789811037641

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Mathematical Modelling in Solid Mechanics by Francesco dell'Isola,Mircea Sofonea,David Steigmann Pdf

This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling analysis of elasto-plastic structures engineering optimization and design, global optimization and related algorithms The book presents selected papers presented at ETAMM 2016. It includes new and original results written by internationally recognized specialists.

Author : Gerard A Maugin
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 53,6 Mb
Release : 2013-04-08
Category : Science
ISBN : 9789400763531

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Continuum Mechanics Through the Twentieth Century by Gerard A Maugin Pdf

This overview of the development of continuum mechanics throughout the twentieth century is unique and ambitious. Utilizing a historical perspective, it combines an exposition on the technical progress made in the field and a marked interest in the role played by remarkable individuals and scientific schools and institutions on a rapidly evolving social background. It underlines the newly raised technical questions and their answers, and the ongoing reflections on the bases of continuum mechanics associated, or in competition, with other branches of the physical sciences, including thermodynamics. The emphasis is placed on the development of a more realistic modeling of deformable solids and the exploitation of new mathematical tools. The book presents a balanced appraisal of advances made in various parts of the world. The author contributes his technical expertise, personal recollections, and international experience to this general overview, which is very informative albeit concise.

Author : Gérard A. Maugin,Andrei V. Metrikine
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 42,5 Mb
Release : 2010-03-24
Category : Mathematics
ISBN : 9781441956958

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Mechanics of Generalized Continua by Gérard A. Maugin,Andrei V. Metrikine Pdf

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 : Vladimir A. Marchenko,Evgueni Ya. Khruslov
Publisher : Springer Science & Business Media
Page : 407 pages
File Size : 55,6 Mb
Release : 2008-12-22
Category : Mathematics
ISBN : 9780817644680

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Homogenization of Partial Differential Equations by Vladimir A. Marchenko,Evgueni Ya. Khruslov Pdf

A comprehensive study of homogenized problems, focusing on the construction of nonstandard models Details a method for modeling processes in microinhomogeneous media (radiophysics, filtration theory, rheology, elasticity theory, and other domains) Complete proofs of all main results, numerous examples Classroom text or comprehensive reference for graduate students, applied mathematicians, physicists, and engineers

Author : Anonim
Publisher : Unknown
Page : 676 pages
File Size : 48,5 Mb
Release : 2003
Category : American literature
ISBN : UOM:39015066043152

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American Book Publishing Record by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 1156 pages
File Size : 46,6 Mb
Release : 2005
Category : Mathematics
ISBN : UOM:39015062317212

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Mathematical Reviews by Anonim Pdf

Author : Frédéric Barbaresco,Frank Nielsen
Publisher : Springer Nature
Page : 466 pages
File Size : 49,8 Mb
Release : 2021-06-27
Category : Mathematics
ISBN : 9783030779573

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Geometric Structures of Statistical Physics, Information Geometry, and Learning by Frédéric Barbaresco,Frank Nielsen Pdf

Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces. This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing.