
At a Glance
314 Pages
24.77 x 16.51 x 1.91
Hardcover
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Industry Reviews
From the reviews:
"The strength of the book lies in the presentation of a very general and rational framework for constitutive formulations and the role thermodynamics plays in these formulations. [...] Continuum Mechanics is recommended more as a reference book for students and researchers in applied mechanics and structural mechanics [...] The text is also recommended as a textbook for students in the fields of theoretical physics and applied mathematics for which a more rational framework of continuum mechanics is required." (Applied Mechanics Review, 56/3, 2003)
"It is probably a pleasure for all scientists working in the field of continuum mechanics to have a new book by hand which gives a compact and modern introduction into continuum mechanics and thermodynamics and which is enhanced with numerous examples and exercises. ... the book can be recommended to senior undergraduates and graduate students at the master and PhD level as well as to research scientists and teachers." (Technische Mechanik, Vol. 25 (2), 2005)
"This book contains a modern presentation of the basic principles of continuum mechanics ... together with an introduction to the basic ideas of rational extended thermodynamics. ... The book is self-contained, since the appendix contains all relevant material and notation of tensor analysis which is needed in the book. ... the unified treatment of both rational continuum mechanics and extended thermodynamics is a novelty and renders the book a useful didactic tool." (Paolo Cermelli, Mathematical Reviews, 2005 c)
"The book under review has been written and used in conjunction with an introductory course on continuum mechanics ... . Each chapter has examples and exercises to supplement the basic material. ... this is a compact well-written textbook on continuum mechanics, with a strong emphasis on thermodynamics." (Cornelius O. Horgan, SIAM Reviews, Vol. 45 (2), 2003)
"This book is intended primarily asa textbook for graduate students and advanced undergraduate students in theoretical physics, applied mathematics, and engineering sciences. The text can also serve as a reference book for students and researchers in the fields of applied and structural mechanics. ... The strength of the book lies in the presentation of a very general and rational framework for constitutive formulations and the role thermodynamics plays in these formulations. ... In summary, Continuum Mechanics is recommended ... ." (E. DeSantiago, Applied Mechanics Reviews, Vol. 56 (3), 2003)
| Kinematics | p. 1 |
| Configuration and Deformation | p. 1 |
| Change of Reference Configuration | p. 4 |
| Strain and Rotation | p. 4 |
| Linear Strain Tensors | p. 8 |
| Motion | p. 13 |
| Material and Spatial Descriptions | p. 14 |
| Relative Deformation | p. 17 |
| Rate of Deformation | p. 20 |
| Change of Frame and Objective Tensors | p. 22 |
| Transformation Property of Motion | p. 25 |
| Property of Some Kinematic Quantities | p. 26 |
| Balance Laws | p. 31 |
| General Balance Equation | p. 31 |
| Field Equation and Jump Condition | p. 35 |
| Balance Equations in Material Coordinates | p. 36 |
| Conservation of Mass | p. 38 |
| Laws of Dynamics | p. 41 |
| Forces and Moments | p. 42 |
| Stress Tensor | p. 43 |
| Conservation of Linear and Angular Momenta | p. 50 |
| Conservation of Energy | p. 51 |
| Summary of Basic Equations | p. 54 |
| Basic Equations in Material Coordinates | p. 56 |
| Boundary Conditions of a Material Body | p. 57 |
| Field Equations in Arbitrary Frames | p. 58 |
| Basic Principles of Constitutive Theories | p. 63 |
| Constitutive Relation | p. 63 |
| Principle of Material Objectivity | p. 65 |
| In Referential Description | p. 68 |
| An Example: a Particular Class of Materials | p. 70 |
| Simple Material Bodies | p. 72 |
| Reduced Constitutive Relations | p. 75 |
| Material Symmetry | p. 77 |
| Constitutive Equation for a Simple Solid Body | p. 81 |
| Constitutive Equation for a Simple Fluid | p. 82 |
| Fluid Crystal with an Intrinsic Direction | p. 84 |
| Isotropic Materials | p. 86 |
| p. 88 | |
| Fading Memory | p. 89 |
| Linear Viscoelasticity | p. 90 |
| Boltzmann-Volterra Theory of Viscoelasticity | p. 92 |
| Linear Viscoelasticity of Rate Type | p. 93 |
| Remark on Objectivity of Linear Elasticity | p. 94 |
| Representation of Constitutive Functions | p. 97 |
| Materials of Grade n | p. 97 |
| Isotropic Functions | p. 98 |
| Isotropic Elastic Materials and Linear Elasticity | p. 107 |
| Reiner-Rivlin Fluids and Navier-Stokes Fluids | p. 109 |
| Elastic Fluids | p. 111 |
| Representation of Isotropic Functions | p. 112 |
| Isotropic Thermoelastic Solids and Viscous Heat-Conducting Fluids | p. 118 |
| Hemitropic Invariants | p. 119 |
| Anisotropic Invariants | p. 122 |
| Transverse Isotropy and Orthotropy | p. 124 |
| On Irreducibility of Invariant Sets | p. 126 |
| Entropy Principle | p. 129 |
| Entropy Inequality | p. 129 |
| Entropy Principle | p. 131 |
| Thermodynamics of Elastic Materials | p. 132 |
| Linear Thermoelasticity | p. 135 |
| Elastic Materials with Internal Constraints | p. 139 |
| Stability of Equilibrium | p. 144 |
| Thermodynamic Stability Criteria | p. 148 |
| Phase Equilibrium | p. 149 |
| Isotropic Elastic Solids | p. 153 |
| Constitutive Equations | p. 153 |
| Boundary Value Problems in Elasticity | p. 155 |
| Homogeneous Stretch | p. 157 |
| Uniaxial Stretch | p. 158 |
| Biaxial Stretch | p. 159 |
| Symmetric Loading of a Square Sheet | p. 160 |
| Stability of a Square Sheet | p. 162 |
| Simple Shear | p. 166 |
| Pure Shear of a Square Block | p. 169 |
| Finite Deformation of Spherical Shells | p. 173 |
| Eversion of a Spherical Shell | p. 175 |
| Inflation of a Spherical Shell | p. 176 |
| Stability of Spherical Shells | p. 179 |
| Stability under Constant Pressures | p. 180 |
| Stability for an Enclosed Spherical Shell | p. 181 |
| Thermodynamics with Lagrange Multipliers | p. 183 |
| Supply-Free Bodies | p. 183 |
| Viscous Heat-Conducting Fluid | p. 184 |
| General Results | p. 186 |
| Navier-Stokes-Fourier Fluids | p. 188 |
| Method of Lagrange Multipliers | p. 189 |
| An Algebraic Problem | p. 190 |
| Local Solvability | p. 191 |
| Relation Between Entropy Flux and Heat Flux | p. 194 |
| Theorem of Parallel Isotropic Vector Functions | p. 194 |
| Rational Extended Thermodynamics | p. 199 |
| Introduction | p. 199 |
| Formal Structure of System of Balance Equations | p. 200 |
| Symmetric Hyperbolic System | p. 201 |
| Galilean Invariance | p. 204 |
| System of Moment Equations | p. 207 |
| Closure Problem | p. 213 |
| Entropy Principle | p. 214 |
| Formal Procedures | p. 216 |
| Thirteen-Moment Theory of Viscous Heat-Conducting Fluid | p. 217 |
| Field Equations | p. 223 |
| Entropy and Entropy Flux | p. 225 |
| Monatomic Ideal Gases | p. 226 |
| Thirteen-Moment Theory | p. 227 |
| Constitutive Equations | p. 228 |
| Stationary Heat Conduction in Ideal Gases | p. 228 |
| Fourier's Law and Heat Conduction | p. 229 |
| Heat Conduction in Thirteen-Moment Theory | p. 229 |
| Remark on Boundary Value Problems | p. 232 |
| Elementary Tensor Analysis | p. 233 |
| Linear Algebra | p. 233 |
| Inner Product | p. 234 |
| Dual Bases | p. 235 |
| Tensor Product | p. 238 |
| Transformation Rules for Components | p. 243 |
| Determinant and Trace | p. 245 |
| Exterior Product and Vector Product | p. 251 |
| Second-Order Tensors | p. 254 |
| Some Theorems of Linear Algebra | p. 256 |
| Tensor Calculus | p. 262 |
| Euclidean Point Space | p. 262 |
| Differentiation | p. 263 |
| Coordinate System | p. 272 |
| Covariant Derivatives | p. 275 |
| Other Differential Operators | p. 277 |
| Physical Components | p. 281 |
| Orthogonal Coordinate Systems | p. 282 |
| References | p. 289 |
| Index | p. 293 |
| Table of Contents provided by Publisher. All Rights Reserved. |
ISBN: 9783540430193
ISBN-10: 3540430199
Series: Advanced Texts in Physics
Published: 28th May 2002
Format: Hardcover
Language: English
Number of Pages: 314
Audience: College, Tertiary and University
Publisher: Springer Nature B.V.
Country of Publication: DE
Dimensions (cm): 24.77 x 16.51 x 1.91
Weight (kg): 0.6
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