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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
Phonon, surface      231
Photon      20 38
Photon, pseudomomentum      205
Physical force      1 65
Physical momentum      9 65 179 205
Physical momentum, balance      73
Physical momentum, equation      116
Physical velocity      44
Piezoelectric ceramics      200
Piezoelectricity      195
Piezomagnetism      195
Piola — Kirchhoff balance laws      63
Piola — Kirchhoff balance laws, first stress      16 64 236
Piola — Kirchhoff balance laws, nominal stress      15
Piola — Kirchhoff balance laws, second stress      16
Piola’s finite strain tensor      46
Piola’s finite strain tensor, transformation      64 74
placement      40
Plastic flow surface      240
Plastic rate of deformation      244
Point, material      40
Polar decomposition theorem      48
Polarization, electric      73 171
Polarization, surface      191
Ponderomotive couple      176
Ponderomotive force      174 179
potential energy      7 21
Power      1
Power, virtual, principle of      6 62
Poynting’s vector      206
Pressure      11
Principle, d’Alembert’s      5
Principle, natural, Hamiltonian      105
Principle, statics      4
Principle, stationary complementary energy      120
Principle, variational      182 189 226
Principle, variational, complementary-energy      118
Principle, virtual power      6 11 62
Projection      76
Projection, canonical      69
Pseudomomentum      20 34
Pseudomomentum, balance of      240
Pseudomomentum, balance of, total      114
Pseudomomentum, conservation of total      191
Pseudomomentum, electromagnetic      183 208 210
Pseudomomentum, global, conservation of      89 194
Pseudomomentum, interpretation      82
Pseudomomentum, material inhomogeneity      78
Pseudomomentum, phonons      205
Pseudomomentum, photons      205
Pseudomomentum, total, Eshelby      183
Pseudomomentum, unbalance      117 180 183
Pull back      76
Quasi-electrostatics      105
Quasi-linear hyperbolic operator      75
Quasi-magnetostatics      195
Quasi-particles      216
Rate, energy-release      32 203
Rate, plastic, deformation      244
Rate, strain      12 50
Rate, strain, Eulerlan      52
Rayleigh surface mode      230
Rayleigh — Bettl theorem      21
Reaction      3
Reductive perturbation method      213
Reference, configuration      15 41
Reference, frame      41
Relativity, general      69 133
Representation, theorem      71
Representation, theorem, Cauchy      72
Retardation, crack growth      203
Rice’s J-integral      32
Riemann — Christoffel curvature tensor      55
Riemannian curvature      128
Riemannian metric      134
Rigid body      12
Rigid body, motion      41 53
Rigid change of frame      53
Rigid displacement      47
Rotation, infinitesimal four-dimensional      110
Rotation, material frame      110
Scalar-valued isotropic function      71
Scale change      86 95 108
Scattering, inverse      224
Schrodinger, nonlinear equation      215
Schrodinger, nonlinear equation, nonlinear system      228
Second gradient theory      99 116 139
Second law of thermodynamics      235
Second Piola — Kirchhoff stress      16 68
Secularity condition      213
Separating duality      13
SH mode      230
Shape-memory alloy      222
Simple material      62
Sine-Gordon equation      213
Sine-Gordon equation, double      215
Sine-Gordon systems      217
Sine-Gordon — d’Alembert systems      223
Singularity, distortion      19
Singularity, force on a      24
Singularity, stress      33
Small-strain      57
Small-strain, approximation      93 245
Small-strain, theory      49
Solids, elastic electromagnetic      170
Solitary wave      214 221
Soliton, envelope      229
Soliton, solution, bright      229
Soliton, solutions, particle-like behavior of      232
Soliton, theory      81 115 215
Soliton, theory, conservation laws in      212
Soliton, topological      217
Soliton-soliton collision      232
Solution soliton, bright      229
Space-time, Newtonian      40
Spin, effects      144
Spin, gravitation, theory      146
Spin, intrinsic      60
Spin, tensor      112
Spin-angular, canonical momentum tensor      145
Standard material      34
State, natural      66
Statics, principle of      4
Stationary complementary energy principle      121
Strain, compatibility      54
Strain, finite Finger’s      47
Strain, infinitesimal      49
Strain, material, relative finite      48
Strain, measures of      46
Strain, rate      12 50
Strain, rate, Eulerian      52
Strain, small      57
Strain, small, approximation      93 245
Strain, small, theory of      49
Strain, tensor Cauchy — Green      46
Strain, tensor Cauchy — Green, Eulerian      47
Strain, tensor Cauchy — Green, finite Piola’s      46
Strain, tensor Cauchy — Green, Lagrangian      47
Strain, theory      46
Stress      8
Stress, Cauchy      244
Stress, couple      143
Stress, effective, Eshelby      142
Stress, electromagnetic      207
Stress, Eshelby      27 79 129 139 181 242
Stress, first      16 236
Stress, intensity coefficients      203
Stress, Maxwell      31
Stress, Maxwell, mixed      86
Stress, Maxwell, second Piola — Kirchhoff      68
Stress, nominal Piola — Kirchhoff      15
Stress, Piola — Kirchhoff      64
Stress, second Piola — Kirchhoff      16
Stress, singularity      33
Stress, tensor, Cauchy      62
Stress, tensor, Cauchy, nonsymmetric      176
Stress, thermodynamic      67
Stress, thermodynamical      16
Stress, total, Eshelby      183
Structure, discrete      17
Surface, energy      33
Surface, force      17
Surface, mode, Rayleigh      230
Surface, phonons      231
Surface, plastic-flow      240
Surface, polarization      191
Symbol(s), Christoffel      55
Symbol(s), connection      132
Symmetric, free-field, Maxwell      175
Symmetrization procedure      112
Symmetry, generalized      94
Symmetry, material, group      127
System of holonomic coordinates      54
System, integrable      215
System, integrable, exactly      230
System, sine-Gordon      217
System, sine-Gordon — d’Alembert      223
System, Zakharov’s      229
Tensor, Cauchy      8
Tensor, density, dislocation      134
Tensor, energy momentum      103 207
Tensor, interaction      175
Tensor, momentum, spin-angular, canonical      145
Tensor, nonsymmetric Cauchy      176
Tensor, spin      122
Tensor, stress, Eshelby      129 139 240
Test functions      6
Tetrahedron argument      8
Theorem, energy      12
Theorem, Noether’s      100 105 183
Theory, distribution      6
Theory, elasticity, geometrical aspects      125
Theory, field      7—96
Theory, first-order gradient      97 125
Theory, gravitation Einstein — Cartan      144
Theory, gravitation-spin      146
Theory, nonlinear elasticity      220
Theory, second-gradient      99 110 139
Theory, soliton      115 215
Theory, soliton, conservation laws in      212
Theory, wave, conservation laws in      211
Thermodynamical admissibility      236
Thermodynamical stress      16
Thermodynamics, first law of      234
Thermodynamics, second law of      235
Time derivative, convected      174
Time derivative, total      193
Time translations      189
Topological invariant      218
Topological solitons      217
Torsion      128 143
Transformation, Galilean      177
Transformation, Legendre — Fenchel      118 188 240
Translations, time      189
Unbalance, form      78
Unbalance, law      74
Unbalance, pseudomomentum      117 180 183
Uniform expansion      86
Variable, internal (thermodynamic)      234
Variation, Eulerian      98
Variation, Lagrangian      98
Variational derivative      146
Variational formulation      6 103 105 136
Variational Principle      182 189 226
Variational principle, complementary-energy      118
Vector, Burgers      58 198
Vector, Poynting’s      206
Velocity, dislocation      123
Velocity, generalized      192
Velocity, gradient, tensor      51
Velocity, material      45 178
Velocity, physical      44
Virtual configuration      42
Virtual power principle      6 11 62
Virtual work      6
Vis viva      5
Viscoplasticity, elasto-      239
viscosity      239
Wave, Eulerian      36
Wave, ion-acoustic      229
Wave, Lagrangian      36
Wave, monochromatic      35
Wave, solitary      214 221
Wave, theory, conservation laws in      211
Weak formulation      94
Weak formulation, Newton’s law      4
Work, virtual      6
Zakharov, generalized system      230
Zakharov, nonlinear system      228
Zakharov, system      229
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