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

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Ќазвание: Introduction to the Thermodynamics of Solids

јвтор: Ericksen J.L.


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

–убрика: ‘изика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1998

 оличество страниц: 189

ƒобавлена в каталог: 03.03.2014

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
Accumulation function      176
Austenite      57
Ballistic free energy      7Ч8 14 38 40 112
Biaxial stretch      79Ч83 see
Bifurcation, diagrams      62Ч65
Bifurcation, pitchfork      63 87Ч89 134Ч135
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      137Ч141 see
Caratheorodory's second law      173Ч174
Chemical potentials      111 114
Clausius Ч Clapeyron equation      49 66
Clausius Ч Duhem inequality, one-dimensional form      12 14 17 25 93 154
Clausius Ч Duhem inequality, three-dimensional form      174Ч175
Clausius Ч Planck Inequality      4 13Ч14 155
Clausius' inequality      172
Clausius' second law      169Ч171
Concentrations      115
Conical boundary conditions      129Ч130
Convex functions      16 60 82
Cycles      156Ч157 166Ч167 168 170 176
Difficulties in applying thermodynamics      7 26 34 143Ч146 161Ч166
Discontinuities      see also "Clausius Ч Clapeyron equation" "Mixtures" "Waves"
Discontinuities in bars in equilibria      50 52Ч54
Discontinuities in bars, breaking      99
Discontinuities in bars, shock waves      93Ч99
Discontinuities in plates      61Ч62
Discontinuities, peeling      100Ч106
Dissipation      154Ч155 see
Efficiency of engines      157Ч158 168
Endpoint minima      53 69 140
Energy      see also "Ballistic free energy" "Field "Helmholtz "Internal "Laws "Strain "Surface
Energy, general concepts      1Ч3 11 151 166 168
Energy, mathematical representations      11Ч12 23 109Ч110
entropy      see also "Clausius Ч Duhem inequality" "Clausius "Dissipation" "Ideal "Law
Entropy, experimental determination      16
Entropy, general concepts      3Ч6 11 149 152Ч153 154 165 166 170
Entropy, mathematical representations      11 99 111Ч112 124Ч125 127Ч128
Equal area rules      45 55 72 75
Equilibrium concepts      6Ч9 149
Euler's elastica      138Ч141 142
Field energies, electromagnetic      127Ч128 143
Field energies, gravitational      69 139Ч140
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 17Ч21 24Ч27 153
Heat transfer, general concepts      1Ч4 12 23 153 154 169Ч179
Heat transfer, radiation      12Ч14 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      124Ч125
Helmholtz free energy, mixtures      113Ч115
Helmholtz free energy, plates      30 58Ч59
Helmholtz free energy, rubber sheets      81
Hypothesis of local thermodynamic equilibrium      26 160 165
Hysteresis      47Ч48
Ideal heat baths      3Ч4 13Ч14 172 see
Kelvin Ч Planck's second law      172
Latent heat      49 158
Laws of Thermodynamics, First      1Ч3 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      37Ч48 59Ч62
Loading devices, dissipative      2
Loading devices, fluid pressures      69Ч77 111Ч122
Loading devices, hard      50Ч55
Loading devices, passive      2
Martensite      57
Martensitic transformations      57Ч62 84
Material symmetry      30 79Ч80 124Ч125
Maxwell line      53 55 72
Metastable configurations      46Ч48 54Ч55 60Ч62 75Ч76
Mixtures, phase mixtures      61 145
Mixtures, theory of fluid-solid mixtures      109Ч122
Newton's law of cooling      13
Nonequilibrium constitutive theory, heat transfer in rigid bars      17Ч20
Nonequilibrium constitutive theory, thermoelastic bars      24Ч26
Objectivity      25 124
Orientation of liquid crystals      123Ч130
Poincare's inequality      133
Point of convexity      16
Power      1Ч2 23 38 144 151
Principle of local states      26 160 see
Processes, cyclic      156 166Ч167
Processes, general      1 147Ч148
Processes, irreversible      152 154
Processes, quasi-static      5
Processes, reversible      4 5 20Ч21 26 149Ч155
Processes, static      149
Processes, superprocesses      151 156
Rankine Ч Hugoniot curve      97
Rankine Ч 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 70Ч71 73 85Ч89 105Ч106 117 134
Serrin's second law      176
Specific heat      31Ч33 120 154Ч155
Spinoidal regimes      47 143
States      1 158Ч166
Stefan Ч Boltzmann radiation law      13
Strain and stretch      22 30 67Ч68 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 146Ч147 169 179Ч180
Thermal expansion      31Ч32 34 58 120
Thermodynamic experiments      31-34 118-122
Thermodynamic systems      1 144
Time reversals      150Ч154
Treloar instability      83Ч84
Twins and twinning      57 61
Variations      6Ч9 14Ч15 38Ч40 51Ч53 112Ч114 132Ч134 147
Viscoelastic effects      26 161Ч167
Waves, acoustic wave speed      97
Waves, fast shock waves      97
Waves, jump conditions      94Ч98
Waves, referential wave speed      93
Waves, slow shock waves      96
Waves, stress waves      98
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