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Ericksen J.L. — Introduction to the Thermodynamics of Solids
Ericksen J.L. — Introduction to the Thermodynamics of Solids

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Название: Introduction to the Thermodynamics of Solids

Автор: Ericksen J.L.

Аннотация:

There is a large and growing gap between what is covered in most elementary thermodynamics courses and what is used in current research on nonlinear phenomena encountered in solids. In an attempt to fill that gap, Professor Ericksen has drawn on his experience in research on solids, to devise a series of lectures for graduate students from various departments at the University of Minnesota. The aim is to introduce and illustrate uses of various important ideas with analysis which can be done, using elementary mathematics. Often, important applications involve using the thermodynamic theory of equilibrium. In part, this involves a strategy for designing experiments to determine equations of state. Simple strategies are discussed for thermoelastic bars and an ideal gas-solid mixture. A simple strategy can fail when instabilities are encountered. Illustrative examples of thermodynamic stability theory include rudimentary analysis of cold-drawing in polymers, martensitic transformations in plates, instabilities in rubber ballons and sheets, peeling tapes, breaking bars, buckling of beams and instabilities produced by electromagnetic fields in liquid crystals. Non-equilibrium theory is illustrated by head conduction in rigid and deformable bars, including a fairly common way of using the Clausius- Duhem inequality to get thermodynamic restrictions on constitutive equations. Also covered is some elementary one-dimensional theory of shock waves and slower-moving phase boundaries. Drawing on all these experiences, the final chapter treats general ideas in a more abstract way. Included here are discussions of some of the real difficulties.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 189

Добавлена в каталог: 03.03.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Accumulation function      176
Austenite      57
Ballistic free energy      7—8 14 38 40 112
Biaxial stretch      79—83 see
Bifurcation, diagrams      62—65
Bifurcation, pitchfork      63 87—89 134—135
Bifurcation, sub-critical      64
Black-body radiation      144
Body couples, electric      129
Body couples, magnetic      129
Breaking bars      see "Discontinuities"
Brownian motion      7 150
Buckling bar      137—141 see
Caratheorodory's second law      173—174
Chemical potentials      111 114
Clausius — Clapeyron equation      49 66
Clausius — Duhem inequality, one-dimensional form      12 14 17 25 93 154
Clausius — Duhem inequality, three-dimensional form      174—175
Clausius — Planck Inequality      4 13—14 155
Clausius' inequality      172
Clausius' second law      169—171
Concentrations      115
Conical boundary conditions      129—130
Convex functions      16 60 82
Cycles      156—157 166—167 168 170 176
Difficulties in applying thermodynamics      7 26 34 143—146 161—166
Discontinuities      see also "Clausius — Clapeyron equation" "Mixtures" "Waves"
Discontinuities in bars in equilibria      50 52—54
Discontinuities in bars, breaking      99
Discontinuities in bars, shock waves      93—99
Discontinuities in plates      61—62
Discontinuities, peeling      100—106
Dissipation      154—155 see
Efficiency of engines      157—158 168
Endpoint minima      53 69 140
Energy      see also "Ballistic free energy" "Field "Helmholtz "Internal "Laws "Strain "Surface
Energy, general concepts      1—3 11 151 166 168
Energy, mathematical representations      11—12 23 109—110
entropy      see also "Clausius — Duhem inequality" "Clausius "Dissipation" "Ideal "Law
Entropy, experimental determination      16
Entropy, general concepts      3—6 11 149 152—153 154 165 166 170
Entropy, mathematical representations      11 99 111—112 124—125 127—128
Equal area rules      45 55 72 75
Equilibrium concepts      6—9 149
Euler's elastica      138—141 142
Field energies, electromagnetic      127—128 143
Field energies, gravitational      69 139—140
Flexural rigidity      139
Fourier's law      17
Freedericsz transition      137
Gibbs' definitions of equilibrium      see "Equilibrium concepts"
Gibbs' function      116
Heat flux      12 23 153 174 see "Heat
Heat transfer      see also "Ideal heat bath"
Heat transfer, conduction      12 17—21 24—27 153
Heat transfer, general concepts      1—4 12 23 153 154 169—179
Heat transfer, radiation      12—14 153
Helmholtz free energy      see also "Thermodynamic experiments"
Helmholtz free energy, balloons      68
Helmholtz free energy, bars      18 24 40 50 96 145
Helmholtz free energy, liquid crystals      124—125
Helmholtz free energy, mixtures      113—115
Helmholtz free energy, plates      30 58—59
Helmholtz free energy, rubber sheets      81
Hypothesis of local thermodynamic equilibrium      26 160 165
Hysteresis      47—48
Ideal heat baths      3—4 13—14 172 see
Kelvin — Planck's second law      172
Latent heat      49 158
Laws of Thermodynamics, First      1—3 168
Laws of Thermodynamics, Second      see "Caratheodory's second law" "Clausius' "Kelvin "Serrin's
Laws of Thermodynamics, Third      179
Laws of thermodynamics, zero'th      179
Loading devices, conservative      2 38 69 127 128 140
Loading devices, dead loads      37—48 59—62
Loading devices, dissipative      2
Loading devices, fluid pressures      69—77 111—122
Loading devices, hard      50—55
Loading devices, passive      2
Martensite      57
Martensitic transformations      57—62 84
Material symmetry      30 79—80 124—125
Maxwell line      53 55 72
Metastable configurations      46—48 54—55 60—62 75—76
Mixtures, phase mixtures      61 145
Mixtures, theory of fluid-solid mixtures      109—122
Newton's law of cooling      13
Nonequilibrium constitutive theory, heat transfer in rigid bars      17—20
Nonequilibrium constitutive theory, thermoelastic bars      24—26
Objectivity      25 124
Orientation of liquid crystals      123—130
Poincare's inequality      133
Point of convexity      16
Power      1—2 23 38 144 151
Principle of local states      26 160 see
Processes, cyclic      156 166—167
Processes, general      1 147—148
Processes, irreversible      152 154
Processes, quasi-static      5
Processes, reversible      4 5 20—21 26 149—155
Processes, static      149
Processes, superprocesses      151 156
Rankine — Hugoniot curve      97
Rankine — Hugoniot equation      97
Rayleigh curve      97
Rayleigh quotient      133
Reference configurations      21 29 67 79 138
Rubber plateau      162 164
Second derivative tests      15 40 52 60 70—71 73 85—89 105—106 117 134
Serrin's second law      176
Specific heat      31—33 120 154—155
Spinoidal regimes      47 143
States      1 158—166
Stefan — Boltzmann radiation law      13
Strain and stretch      22 30 67—68 79 139
Strain energy      32 79 100 120 125 139
Stress      23 30 80
Stress relaxation      163
Strong anchoring      129
Surface energies      96 99 100 101
Temperature      3 19 27 146—147 169 179—180
Thermal expansion      31—32 34 58 120
Thermodynamic experiments      31-34 118-122
Thermodynamic systems      1 144
Time reversals      150—154
Treloar instability      83—84
Twins and twinning      57 61
Variations      6—9 14—15 38—40 51—53 112—114 132—134 147
Viscoelastic effects      26 161—167
Waves, acoustic wave speed      97
Waves, fast shock waves      97
Waves, jump conditions      94—98
Waves, referential wave speed      93
Waves, slow shock waves      96
Waves, stress waves      98
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