Nonlinear theory of dislocations and disclinations in elastic bodies

by Leonid M. Zubov

The author applies methods of nonlinear elasticity to the investigation of the defects in the crystal structure of solids such as dislocations and disclinations. These defects characterize mainly the plastic and strength properties of many constructional materials. Contrary to the well-developed nonlinear continual theory of dislocations continuously distributed in the body, which is based on geometrical ideas, the nonlinear analysis of isolated dislocations and disclinations is less developed; it is given for the first time in this book. This analysis is essential since the deformation near the axes of an isolated defect is rather big, so the linear theory is not applicable here. The general theory of Volterra's dislocations in elastic media under large deformations is developed. A number of exact solutions of the problems are found. The nonlinear approach to investigating the isolated defects produces the results that often differ qualitatively from those of the linear theory. The bo