Gurtin M.E. The mechanics and thermodynamics of continua. - Cambridge: Cambridge University Press, 2010. - xxi, 694 p.: ill. - Ref.: p.671-681. - Ind.: 683-694. - ISBN 978-0-521-40598-0  Место хранения:   019 | Институт теплофизики им. С.С.Кутателадзе CO РАН | Новосибирск | Библиотека

Оглавление / Contents

Preface ....................................................... xix PART I VECTOR AND TENSOR ALGEBRA ....................................... 1 1 Vector Algebra .............................................. 3 2 Tensor Algebra .............................................. 9 PART II VECTOR AND TENSOR ANALYSIS ..................................... 39 3 Differentiation ............................................ 41 4 Integral Theorems .......................................... 52 PART III KINEMATICS ..................................................... 59 5 Motion of a Body ........................................... 61 6 The Deformation Gradient ................................... 64 7 Stretch, Strain, and Rotation .............................. 69 8 Deformation of Volume and Area ............................. 75 9 Material and Spatial Descriptions of Fields ................ 80 10 Special Motions ............................................ 86 11 Stretching and Spin in an Arbitrary Motion ................. 89 12 Material and Spatial Tensor Fields. Fullback and Pushforward ................................................ 95 13 Modes of Evolution for Vector and Tensor Fields ............ 98 14 Motions with Constant Velocity Gradient ................... 107 15 Material and Spatial Integration .......................... 109 16 Reynolds' Transport Relation. Isochoric Motions ........... 113 17 More Kinematics ........................................... 115 PART IV BASIC MECHANICAL PRINCIPLES ................................... 125 18 Balance of Mass ........................................... 127 19 Forces and Moments. Balance Laws for Linear and Angular Momentum .................................................. 131 20 Frames of Reference ....................................... 146 21 Frame-Indifference Principle .............................. 157 22 Alternative Formulations of the Force and Moment Balances .................................................. 161 23 Mechanical Laws for a Spatial Control Volume .............. 168 24 Referential Forms for the Mechanical Laws ................. 173 25 Further Discussion of Stress .............................. 177 PART V BASIC THERMODYNAMICAL PRINCIPLES .............................. 181 26 The First Law: Balance of Energy .......................... 183 27 The Second Law: Nonnegative Production of Entropy ......... 186 28 General Theorems .......................................... 190 29 A Free-Energy Imbalance for Mechanical Theories ........... 194 30 The First Two Laws for a Spatial Control Volume ........... 197 31 The First Two Laws Expressed Referentially ................ 199 PART VI MECHANICAL AND THERMODYNAMICAL LAWS AT A SHOCK WAVE ........... 207 32 Shock Wave Kinematics ..................................... 209 33 Basic Laws at a Shock Wave: Jump Conditions ............... 216 PART VII INTERLUDE: BASIC HYPOTHESES FOR DEVELOPING PHYSICALLY MEANINGFUL CONSTITUTIVE THEORIES .............................. 221 34 General Considerations .................................... 223 35 Constitutive Response Functions ........................... 224 36 Frame-Indifference and Compatibility with Thermodynamics ............................................ 225 PART VIII RIGID HEAT CONDUCTORS ......................................... 227 37 Basic Laws ................................................ 229 38 General Constitutive Equations ............................ 230 39 Thermodynamics and Constitutive Restrictions: The Coleman-Noll Procedure .................................... 232 40 Consequences of the State Restrictions .................... 234 41 Consequences of the Heat-Conduction Inequality ............ 236 42 Fourier's Law ............................................. 237 PART IX THE MECHANICAL THEORY OF COMPRESSIBLE AND INCOMPRESSIBLE FLUIDS ........................................................ 239 43 Brief Review .............................................. 241 44 Elastic Fluids ............................................ 244 45 Compressible, Viscous Fluids .............................. 250 46 Incompressible Fluids ..................................... 259 PART X MECHANICAL THEORY OF ELASTIC SOLIDS ........................... 271 47 Brief Review .............................................. 273 48 Constitutive Theory ....................................... 276 49 Summary of Basic Equations. Initial/Boundary-Value Problems .................................................. 282 50 Material Symmetry ......................................... 284 51 Simple Shear of a Homogeneous, Isotropic Elastic Body ..... 294 52 The Linear Theory of Elasticity ........................... 297 53 Digression: Incompressibility ............................. 316 54 Incompressible Elastic Materials .......................... 319 55 Approximately Incompressible Elastic Materials ............ 326 PART XI THERMOELASTICITY .............................................. 331 56 Brief Review .............................................. 333 57 Constitutive Theory ....................................... 335 58 Natural Reference Configuration for a Given Temperature ... 348 59 Linear Thermoelasticity ................................... 354 PART XII SPECIES DIFFUSION COUPLED TO ELASTICITY ....................... 361 60 Balance Laws for Forces, Moments, and the Conventional External Power ............................................ 363 61 Mass Balance for a Single Diffusing Species ............... 364 62 Free-Energy Imbalance Revisited. Chemical Potential ....... 366 63 Multiple Species .......................................... 369 64 Digression: The Thermodynamic Laws in the Presence of Species Transport ......................................... 371 65 Referential Laws .......................................... 374 66 Constitutive Theory for a Single Species .................. 377 67 Material Symmetry ......................................... 385 68 Natural Reference Configuration ........................... 388 69 Summary of Basic Equations for a Single Species ........... 390 70 Constitutive Theory for Multiple Species .................. 391 71 Summary of Basic Equations for N Independent Species ...... 396 72 Substitutional Alloys ..................................... 398 73 Linearization ............................................. 408 PART XIII THEORY OF ISOTROPIC PLASTIC SOLIDS UNDERGOING SMALL DEFORMATIONS .................................................. 415 74 Some Phenomenological Aspects of the Elastic-Plastic Stress-Strain Response of Polycrystalline Metals .......... 417 75 Formulation of the Conventional Theory. Preliminaries ..... 422 76 Formulation of the Mises Theory of Plastic Flow ........... 426 77 Inversion of the Mises Flow Rule: Ėp in Terms of Ė and T ..................................................... 445 78 Rate-Dependent Plastic Materials .......................... 449 79 Maximum Dissipation ....................................... 454 80 Hardening Characterized by a Defect Energy ................ 465 81 The Thermodynamics of Mises-Hill Plasticity ............... 469 82 Formulation of Initial/Boundary-Value Problems for the Mises Flow Equations as Variational Inequalities .......... 479 PART XIV SMALL DEFORMATION, ISOTROPIC PLASTICITY BASED ON THE PRINCIPLE OF VIRTUAL POWER ................................ 485 83 Introduction .............................................. 487 84 Conventional Theory Based on the Principle of Virtual Power ..................................................... 489 85 Basic Constitutive Theory ................................. 499 86 Material Stability and Its Relation to Maximum Dissipation ............................................... 501 PART XV STRAIN GRADIENT PLASTICITY BASED ON THE PRINCIPLE OF VIRTUAL POWER .............................................. 505 87 Introduction .............................................. 507 88 Kinematics ................................................ 509 89 The Gradient Theory of Aifantis ........................... 512 90 The Gradient Theory of Gurtin and Anand ................... 524 PART XVI LARGE-DEFORMATION THEORY OF ISOTROPIC PLASTIC SOLIDS .......... 539 91 Kinematics ................................................ 541 92 Virtual-Power Formulation of the Standard and Microscopic Force Balances ................................ 548 93 Free-Energy Imbalance ..................................... 553 94 Two New Stresses .......................................... 555 95 Constitutive Theory ....................................... 557 96 Summary of the Basic Equations. Remarks ................... 566 97 Plastic Irrotationality: The Condition Wp ≡ 0 ............. 567 98 Yield Surface. Yield Function. Consistency Condition ...... 569 99 |Dp| in Terms of Ė and Me .................................. 571 100 Evolution Equation for the Second Piola Stress ............ 576 101 Rate-Dependent Plastic Materials .......................... 579 PART XVII THEORY OF SINGLE CRYSTALS UNDERGOING SMALL DEFORMATIONS ....... 583 102 Basic Single-Crystal Kinematics ........................... 586 103 The Burgers Vector and the Flow of Screw and Edge Dislocations .............................................. 588 104 Conventional Theory of Single-Crystals .................... 593 105 Single-Crystal Plasticity at Small Length-Scales: A Small-Deformation Gradient Theory ....................... 604 PART XVIII SINGLE CRYSTALS UNDERGOING LARGE DEFORMATIONS ................. 621 106 Basic Single-Crystal Kinematics ........................... 623 107 The Burgers Vector and the Flow of Screw and Edge Dislocations .............................................. 626 108 Virtual-Power Formulation of the Standard and Microscopic Force Balances ................................ 634 109 Free-Energy Imbalance ..................................... 639 110 Conventional Theory ....................................... 641 111 Taylor's Model of Polycrystal ............................. 646 112 Single-Crystal Plasticity at Small Length Scales: A Large-Deformation Gradient Theory ....................... 653 113 Isotropic Functions ....................................... 665 114 The Exponential of a Tensor ............................... 669 References .................................................... 671 Index ......................................................... 683