Литература
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The Perfect Crystal. The Brave's lattice. Real crystal. Defects in crystal structure. Point and linear defects. Dislocations. What is meant by dislocation density? The dimensionality of dislocation density. Influence of dislocations on material properties. The dependence of strength of metals on dislocation density. Macroscopic modeling of dislocations using a tubular sample as an example. Example of helical dislocations. Stress-strain state and displacements at tube points from helical dislocation. Bürgers vector and dislocation line in the case of helical dislocation. Solutions of equations of elasticity theory with singularities. The Kelvin problem. The force factor in the Kelvin's problem. Tensor of Kelvin. Determination of displacements in a homogeneous, isotropic medium in the case of a given distributed load on a line, surface and volume. Solutions with higher order singularities. Sources as force factors leading to solutions with features of higher order. A matrix of sources. Double force without and with torque. Center of dilatation. Center of rotation. Determination of displacements in a medium from a source distributed with a given density in a finite area. Volterra dislocations. Dislocation line and Buergers vector. Displacements in a medium from a Wol- terre dislocation. Buergers formula. Application of Buergers formula to the case of helical dislocation. Application of Buergers formula to the case of edge dislocation. Cohesion conditions for external deformations. Second order differential operator Ink (incompatibility). The Ga-Miltonian operator and rules for dealing with it. The Helmholtz representation for a vector. The Kroehner representation for a tensor. Statement of the problem of internal stresses in an infinite medium. Tensor of Kröner stress functions. Expression for the Kröner function tensor through the components of the incoherence tensor. The dislocation density tensor. Meaning and dimensionality of its components. Representation of incoherence tensor through dislocation density tensor. Expression of Kröhner stress tensor through dislocation parameters. Peach-Kehler formula for dislocation stresses.