## Theory of ElasticityLev Davidovich Landau, Evgeniĭ Mikhaĭlovich Lifshit︠s︡, Arnolʹd Markovich Kosevich, Lev Petrovich Pitaevskiĭ A 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 |

2 The stress tensor | 3 |

3 The thermodynamics of deformation | 7 |

4 Hookes law | 9 |

5 Homogeneous deformations | 11 |

6 Deformations with change of temperature | 14 |

7 The equations of equilibrium for isotropic bodies | 16 |

8 Equilibrium of an elastic medium bounded by a plane | 22 |

26 Anharmonic vibrations | 104 |

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 |

30 Distribution of interacting dislocations | 124 |

31 Equilibrium of a crack in an elastic medium | 127 |

32 The equation of thermal conduction in solids | 133 |

33 Thermal conduction in crystals | 134 |

9 Solid bodies in contact | 26 |

10 The elastic properties of crystals | 32 |

THE EQUILIBRIUM OF RODS AND PLATES 11 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 |

15 Deformations of shells 34 | 54 |

16 Torsion of rods | 59 |

17 Bending of rods | 64 |

18 The energy of a deformed rod | 67 |

19 The equations of equilibrium of rods | 70 |

20 Small deflections of rods | 76 |

21 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 |

25 Vibration of rods ahd plates | 99 |

34 Viscosity of solids | 135 |

35 The absorption of sound in solids | 137 |

36 Highly viscous fluids | 142 |

37 Static deformations of nematics | 144 |

38 Straight disclinations in nematics | 147 |

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

40 Topological properties of disclinations | 156 |

41 Equations of motion of nematics | 158 |

42 Dissipative coefficients of nematics | 163 |

43 Propagation of small oscillations in nematics | 165 |

44 Mechanics of cholesterics | 170 |

45 Elastic properties of smectics | 172 |

46 Dislocations in smectics | 177 |

47 Equations of motion of smectics | 179 |

48 Sound in smectics | 182 |

185 | |

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### Common terms and phrases

angle arbitrary axes axis bending biharmonic equation body forces boundary conditions Burgers vector centre clamped coefficient components constant contour corresponding cross-section crystal crystallites curl deflection denote density derivatives Determine the deformation differential direction disclination dislocation line dispersion relation displacement vector edge elastic energy element equations of equilibrium equations of motion expression external forces force F forces applied formula free energy function given gives glide plane grad Hence integral internal stresses isotropic isotropic body lattice Let us consider linear longitudinal longitudinal waves moduli nematic non-zero obtain oscillations parallel perpendicular plate polar coordinates propagation quadratic quantities radius respect result rotation shear shell small compared smectics Solution strain tensor stress tensor stretching Substituting suffixes surface symmetry temperature tensor uik thermal conduction thermodynamic torsion transformation transverse transverse waves two-dimensional undeformed unit length unit volume values velocity vibrations wave vector xy-plane z-axis zero