## Theory of Elasticity: Volume 7A comprehensive textbook covering not only the ordinary theory of the deformation of solids, but also some topics not usually found in textbooks on the subject, such as thermal conduction and viscosity in solids. |

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### Contents

FUNDAMENTAL EQUATIONS 1 The strain tensor | 1 |

The stress tensor | 3 |

The thermodynamics of deformation | 7 |

Hookes law | 9 |

Homogeneous deformations | 11 |

Deformations with change of temperature | 14 |

The equations of equilibrium for isotropic bodies | 16 |

Equilibrium of an elastic medium bounded by a plane | 23 |

DISLOCATIONS 27 Elastic deformations in the presence of a dislocation | 108 |

28 The action of a stress field on a dislocation | 116 |

29 A continuous distribution of dislocations | 119 |

As well as some minor corrections and additions a chapter on the macroscopic theory | 122 |

30 Distribution of interacting dislocations | 124 |

Equilibrium of a crack in an elastic medium | 127 |

THERMAL CONDUCTION AND VISCOSITY IN SOLIDS 32 The equation of thermal conduction in solids | 133 |

Thermal conduction in crystals | 134 |

Solid bodies in contact | 26 |

longitudinal velocity of sound | 31 |

The elastic properties of crystals | 32 |

THE EQUILIBRIUM OF RODS AND PLATES gil The energy of a bent plate | 38 |

12 The equation of equilibrium for a plate | 40 |

13 Longitudinal deformations of plates | 46 |

14 Large deflections of plates | 50 |

Deformations of shells | 54 |

Torsion of rods | 59 |

Bending of rods | 64 |

g18 The energy of a deformed rod | 67 |

19 The equations of equilibrium of rods | 70 |

20 Small deflections of rods | 76 |

The stability of elastic systems | 83 |

ELASTIC WAVES 22 Elastic waves in an isotropic medium | 87 |

23 Elastic waves in crystals | 92 |

24 Surface waves | 94 |

Vibration of rods and plates | 99 |

Anharmonic vibrations | 104 |

Viscosity of solids | 135 |

The absorption of sound in solids | 137 |

Highly viscous fluids | 142 |

MECHANICS OF LIQUID CRYSTALS 837 Static deformations of nematics | 144 |

Straight disclinations in nematics | 147 |

Nonsingular axially symmetrical solution of the equilibrium equations for a nematic | 152 |

Topological properties of disclinations | 156 |

Equations of motion of nematics | 158 |

42 Dissipative coefficients of nematics | 163 |

43 Propagation of small oscillations in nematics | 165 |

Mechanics of cholesterics | 170 |

Elastic properties of smectics | 172 |

Dislocations in smectics | 177 |

Equations of motion of smectics | 179 |

Sound in smectics | 182 |

185 | |

186 | |

### Other editions - View all

Theory of Elasticity, Volume 7 L D Landau,L. P. Pitaevskii,A. M. Kosevich,E.M. Lifshitz Limited preview - 2012 |

Theory of Elasticity Lev Davidovich Landau,Evgenij Michajlovič Lifšic (physicien.) Snippet view - 1959 |

### Common terms and phrases

According acting angle applied axes axis becomes bending body boundary conditions calculate called coefficients compared components compression consider constant contour coordinates corresponding cross-section crystal defined deflection deformation density depends derivatives Determine differential direction dislocation displacement dissipative distance distribution edge elastic element equal equations of equilibrium equations of motion expression external field fluid force formula free energy frequency function given gives Hence independent integral internal isotropic length liquid longitudinal means medium nematic normal obtain occurs origin oscillations parallel plane plate polar positive PROBLEM propagation properties quantities regarded relation relative remain respect result rotation satisfies sides SOLUTION strain tensor stress tensor stretching Substituting surface symmetry temperature thermal torsion transformation transverse unit values vector volume wave written z-axis zero дх