Elastic Media with Microstructure II: Three-Dimensional Models

Crystals and polycrystals, composites and polymers, grids and multibar systems can be considered as examples of media with microstructure. A characteristic feature of all such models is the existence of scale parameters which are con- nected with microgeometry or long-range interacting forces. As a result the cor- responding theory must essentially be a nonlocal one. This treatment provides a systematic investigation of the effects of micro- structure, inner degrees of freedom and non locality in elastic media. The prop- agation of linear and nonlinear waves in dispersive media, static, deterministic and stochastic problems, and the theory of local defects and dislocations are considered in detail. Especial attention is paid to approximate models and lim- iting transitions to classical elasticity. The book forms the second part of a revised and updated edition of the author's monograph published under the same title in Russian in 1975. The first part (Vol. 26 of Springer Series in Solid-State Sciences) presents a self- contained theory of one-dimensional models. The theory of three-dimensional models is considered in this volume. I would like to thank E. Kroner and A. Seeger for supporting the idea of an English edition of my original Russian book. I am also grateful to E. Borie, H. Lotsch and H. Zorski who read the manuscript and offered many sugges- tions. Houston, Texas Isaak A. Kunin January, 1983 Contents 1. Introduction ............................................ .