## Theory of Elasticity, Volume 7 |

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Page 38

A similar

which contains both symmetry elements (C2 and an). In the argument given,

however, the direction of only one co-ordinate axis (that of z) is fixed ; those of x

and y ...

A similar

**expression**is obtained for the class C%, and also for the class Cm,which contains both symmetry elements (C2 and an). In the argument given,

however, the direction of only one co-ordinate axis (that of z) is fixed ; those of x

and y ...

Page 80

By using the vector SI to characterise the deformation and ascertaining its

properties, we can derive an

The elastic energy per unit length of the rod is a quadratic function of the

deformation, ...

By using the vector SI to characterise the deformation and ascertaining its

properties, we can derive an

**expression**for the elastic free energy of a bent rod.The elastic energy per unit length of the rod is a quadratic function of the

deformation, ...

Page 155

It has the following evident symmetry properties : Viklm = Vimik = ^kUm = Vikml- (

34.4) The

free energy of a crystal : the elastic modulus tensor is replaced by the tensor ...

It has the following evident symmetry properties : Viklm = Vimik = ^kUm = Vikml- (

34.4) The

**expression**(34.3) is exactly analogous to the**expression**(10.1) for thefree energy of a crystal : the elastic modulus tensor is replaced by the tensor ...

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### Contents

FUNDAMENTAL EQUATIONS 1 The strain tensor | 1 |

2 The stress tensor | 4 |

3 The thermodynamics of deformation | 8 |

Copyright | |

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### Other editions - View all

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

### Common terms and phrases

angle arbitrary axis bending biharmonic equation boundary conditions Burgers vector centre clamped coefficient components constant contour corresponding cross-section crystal crystallites curvature deflection denote derivatives Determine the deformation direction dislocation line displacement vector dxdy edge elastic wave element equations of equilibrium equations of motion expression external forces fluid force F forces acting forces applied formula free energy frequency function given gives Hence Hooke's law integral internal stresses isotropic isotropic body lattice Let us consider longitudinal longitudinal waves medium moduli non-zero parallel perpendicular plate Poisson's ratio quadratic quantities radius region of contact relation respect result rotation shear shell small compared Solution strain tensor stress tensor stretching Substituting suffixes symmetry temperature thermal conduction thin torsion transverse transverse waves two-dimensional undeformed unit length unit volume values velocity of propagation vibrations wave vector z-axis zero