## Theory of Elasticity, Volume 7 |

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Page 6

The moment of the forces on a portion of the body can then be written simply as

Ma ~j(F,xt-Ftxi)dV = j( °uxk — ak&i) dfi. (2.4) It is easy to find the

body undergoing uniform compression from all sides {hydrostatic compression).

The moment of the forces on a portion of the body can then be written simply as

Ma ~j(F,xt-Ftxi)dV = j( °uxk — ak&i) dfi. (2.4) It is easy to find the

**stress tensor**for abody undergoing uniform compression from all sides {hydrostatic compression).

Page 12

Equation (4.7) shows that the relative change in volume (u«) in any deformation

of an isotropic body depends only on the sum an of the diagonal components of

the

Equation (4.7) shows that the relative change in volume (u«) in any deformation

of an isotropic body depends only on the sum an of the diagonal components of

the

**stress tensor**, and the relation between uu and an is determined only by the ...Page 155

In particular, the tensor rjium in an isotropic body has only two independent

components, and Y can be written in a form analogous to ... We have /, = da'ujdxi,

(34.6) where the dissipative

Vikimuim.

In particular, the tensor rjium in an isotropic body has only two independent

components, and Y can be written in a form analogous to ... We have /, = da'ujdxi,

(34.6) where the dissipative

**stress tensor**a'ik is defined by a'ik = dYjdtiik =Vikimuim.

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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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### 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