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Maugin G.A. — Material inhomogeneities in elasticity
Maugin G.A. — Material inhomogeneities in elasticity

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Название: Material inhomogeneities in elasticity

Автор: Maugin G.A.

Аннотация:

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.


Язык: en

Рубрика: Физика/Классическая физика/Упругие среды/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 276

Добавлена в каталог: 17.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abraham’s electromagnetic momentum      206
Absolute parallelism      128
Acoustic tensor, Christoffel      76
action      3
Action, Hamiltonian      97 182
Adiaba tic-perturbation approximation      219
Admissibility, thermodynamical      236
Alloy, shape-memory      222
Alternator      56
Analytical continuum mechanics      96
Analytical mechanics      6
Anelastic behavior, J-integrals in      246
Anelastic deformation      237
Anelastic materials, material forces in      234
Angular momentum, current      112
Angular momentum, material      110
Anisotropic elasticity, linear      81
Approximation, adiabatic-perturbation      219
Approximation, Galilean      174
Approximation, nonrelativistic      171
Approximation, small-strain      93 245
Area change      50
Asymmetric connection      145
At-a-distance force      8 17
Balance law(s), Euler — Cauchy      59
Balance law(s), material      73 86
Balance law(s), momentum, covariant material      131
Balance law(s), Piola — Kirchhoff      63
Balance law(s), pseudomomentum      240
Balance law(s), total pseudomomentum      114
Balance, linear momentum, formulations      84
Balance, physical momentum      75
Body, dielectric      182
Body, elastic oriented      223
Body, elastic, definition      65
Body, ferroelastic      222
Body, rigid      12
Boundary condition, natural      9 62
Boundary condition, natural, Eulerian      120-1
Boussinesq, crystal equation      220
Boussinesq, equation      212
Bracket, Lie-Poisson      115
Bright soliton solution      229
Burgers vector      18 58 198
Canonical energy-momentum      144
Canonical formulation      192
Canonical formulation, Hamiltonian      113
Canonical momentum      219
Canonical projection      69
Canonical spin-angular momentum tensor      145
Cauchy      61 71
Cauchy, lemma      61
Cauchy, nonsymmetric stress tensor      176
Cauchy, representation theroem      72
Cauchy, stress      244
Cauchy, stress, tensor      8 62
Ceramic, piezoelectric      200
Change, area      50
Change, frame, rigid      53
Change, scale      85 95 108
Christoffel, acoustic tensor      76
Christoffel, symbols      55
Classes, equivalent      140
Clausius — Duhem inequality      236
Collision, soliton-soliton      232
Compatibility, condition      56
Compatibility, kinematical      51
Compatibility, strains      54
Complementary energy      118
Complementary energy, stationary principle      121
Complementary energy, variational principle      118
Computational methods      6
Condition, compatibility      56
Condition, impenetrability      43
Condition, natural boundary      62
Condition, secularity      213
Configuration, global reference      43
Configuration, gradient      43
Configuration, intermediate (elastically released)      243
Configuration, local reference      42
Configuration, reference      15 41
Configuration, virtual      42
Configurational force(s)      24 120
Conjugate pairs      69
Connection      131
Connection, asymmetric      145
Connection, symbols      132
Conservation law(s)      58 132
Conservation law(s), energy      5 105 117
Conservation law(s), soliton theory      212
Conservation law(s), wave theory      211
Conservation, global pseudomomentum      80
Conservation, mass, equation of      9
Conservation, total pseudomomentum      191 194
Constitutive equations      14 65
Contact force      8 12 17
Continuous distribution(s)      134 143
Continuum material      40
Continuum mechanics      10
Continuum mechanics, analytical      96
Convected time derivative      174
Convection      65 73
Convex analysis      34
Coordinates, holonomic system      54
Coordinates, Lagrangian      14
Coordinates, material      14
Couple, ponderomotive      176
Couple-stresses      143
Covariant derivative      131 145
Covariant differentiation      56
Covariant material balance law of momentum      131
Covector      131
Crack      32
Crack-growth criterion      33
Crack-growth enhancement      200
Crack-growth retardation in      203
Crystal      17
Crystal, elastic      39
Crystal, equalion, Boussinesq      220
Crystal, ferroelectric      199
Crystal, momentum      20 64 205
Crystalline elastic materials      66
Crystallographic frame      132
Current angular momentum      112
Current dislocation      123
Current momentum      103
Curvature, Riemannian      55 128
De Broglie, equation      35
De Broglie, relation      205
Dead loading      122
Decomposition, polar, theorem of      48
Defect, microscopic      18
Deformable dielectric, breakdown of      203
Deformation, anelastic      237
Deformation, gradient      44
Deformation, plastic rate of      244
Deformed metric      46 82 105
Density, dislocation      58
Density, field-momentum      83 205 210 216
Density, tensor, dislocation      134
Derivative, covariant      131 145
Derivative, material      9 15
Derivative, time, convected      174
Derivative, time, total      193
Derivative, variational      146
Description, completely material      138
Description, direct motion      103
Description, inverse motion      85 105
Dielectric, body      182
Dielectric, deformable, breakdown of      203
Dielectric, elastic      203
Dielectric, medium      184
Dielectric, nonmagnetizable      189
Differentiation, covariant      56
Dirac’s distribution      58 123
Direct-motion description      46 68 103
Disclination      143
Discrete structure      17
Dislocation      18 134 214
Dislocation, current      123
Dislocation, density      58
Dislocation, density, tensor      134
Dislocation, velocity      123
dispersion      75
Displacement      49
Displacement, electric      73
Displacement, rigid      47
Dissipation      33
Dissipation, force, material      242
Dissipation, inequality      238 244
Dissipation, pseudo-potential      239
Distant parallelism      128
Distortion, singularities of      19
Distribution, continuous      134 143
Distribution, continuous, Dirac’s      58 123
Distribution, continuous, theory      6
Divergence, material      130
Divergence, transformations      94
Double sine-Gordon equation      215
Driving force      219
Duality      11
Duality, separating      13
Ductile materials      247
Dynamical elasticity      212
Dynamics, lattice      18
D’Alembert, equation      211
D’Alembert, principle      5
D’Alembert, viewpoint      5
effective mass      24
Effective stress, Eshelby      142
Einstein tensor      57
Einstein — Cartan gravitation theory      144
Einstein — Cartan spaces      144
Elastic body, definition      65
Elastic crystals      39
Elastic dielectrics      203
Elastic ferroelectrics      223
Elastic ferromagnets      223
Elastic incompatibility      57
Elastic material, crystalline      66
Elastic material, crystalline, homogeneity      70
Elastic oriented bodies      223
Elastic solids, electromagnetic      170
Elasticity as a field theory      96
Elasticity, dynamical      212
Elasticity, nonlinear, theory      220
Elasticity, theory, geometrical aspects      125
Elasto-viscoplasticity      239
Elastoplasticity      239 244
Electric charge, force on an      30
Electric displacement      73
electric field      83
Electric force, Peach — Koehler      198
Electric polarization      73 171
Electroacoustics, nonlinear      187
Electroelasticity      191
Electroelasticity, fracture in      194
Electroelastostatics      196
Electromagnetic elastic solids      170
Electromagnetic momentum      175
Electromagnetic momentum, Abraham’s      206
Electromagnetic momentum, Minkowski’s      206
Electromagnetic pseudomomentum      183 208 210
Electromagnetic stress      207
Electromechanical J-integral      202
Electrostatics      30
Electrostatics, quasi-      195
Electrostriction      195
Element, finite      13
Ellipticity      75
Energy      1
Energy, complementary      118
Energy, conservation      105 116
Energy, equation      88
Energy, flux      88
Energy, free, Helmholtz      230
Energy, interaction      20
Energy, internal      13
Energy, local, equation      62
Energy, potential      7 21
Energy, release rate      32 203
Energy, stationary complementary principle      121
Energy, surface      33
Energy, theorem of      12
Energy-momentum, canonical      144
Energy-momentum, tensor      30 103 107
Envelope soliton      229
Equation of motion, Euler — Cauchy      176
Equation, Boussinesq      212
Equation, Boussinesq, crystal      220
Equation, conservation of mass      9
Equation, constitutive      14 65
Equation, de Broglie’s      35
Equation, double sine-Gordon      215
Equation, d’Alembert’s      211
Equation, energy      88
Equation, evolution      192 228 232
Equation, global evolution      115
Equation, Korteweg — de Vries (KdV)      213
Equation, local energy      62
Equation, material formulation, Maxwell’s      177
Equation, Maxwell’s      30 172 177
Equation, Maxwell’s in matter      177
Equation, nonlinear, Schrodinger      215
Equation, physical-momentum      116
Equation, sine-Gordon      214
Equivalent classes      140
Ericksen’s remark      76
Eshelbian mechanics      38
Eshelby, concept of material force      17
Eshelby, effective stress      142
Eshelby, hyperstress      142
Eshelby, stress      142
Eshelby, stress, tensor      27 79 129 130 181 242
Eshelby, total      183
Euler — Cauchy balance laws      59
Euler — Cauchy equations of motion      17f
Eulerian natural boundary condition      120
Eulerian rate of strain      52
Eulerian strain tensor      47
Eulerian variations      98
Eulerian wave      36
Evolution equation      192 228 232
Evolution global, equation      115
Expansion, uniform      86
Experiment, Jones — Richards      209
Extensive quantity      8 60
Ferroelastic body      222
Ferroelectric crystals      199
Ferroelectrics, elastic      223
Ferromagnets, elastic      223
Field(s), electric      73
Field(s), momentum      37
Field(s), momentum, density      83 205 210 216
Field(s), theory of      7
Field(s), theory, elasticity as a      96
Finger’s finite strain      47
Finite element      13
Finite material strain, relative      48
Finite strain, Finger      47
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