Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies

ISBN-13: 9783642082986 / Angielski / Miękka / 2011 / 208 str.

Leonid M. Zubov

Opis

The author applies methods of nonlinear elasticity to investigate the defects in the crystal structure of solids such as dislocations and disclinations that characterize the plastic and strength properties of many materials. Contrary to the geometrically motivated nonlinear theory of dislocations continuously distributed over the body, nonlinear analysis of isolated dislocations and disclinations is less developed; it is given for the first time in this book, and in a form accessible to both students and researchers. The general theory of Volterra's dislocations in elastic media under large deformations is developed. A number of exact solutions are found. The nonlinear approach to investigating the isolated defects produces results that often differ qualitatively from those of the linear theory.

Spis treści

Volterra’s Dislocations in Elastic Body. Large Deformation.- Stressed State of Nonlinearly Elastic Bodies with Dislocations and Disclinations.- Exact Solutions Stressed to the Problems on Volterra Dislocations in Nonlinearly Elastic Bodies.- Isolated Defects in Nonlinearly Elastic Bodies with Couple Stresses.- Nonlinear Theory of Dislocations and Disclinations in Elastic Shells.- Stability of Equilibrium and Wave Propagation in Bodies with Inherent Stresses.

Blurb

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 book addresses students and researchers.