General theory of defects in continuous media

Abstract

A new general theory of defects in continuous media is introduced. The general mechanisms of generation and healing of defects are established. The kinematic description of continuum media with defects is presented. The definition of defects of different levels is given, and the classification of continuous media with defects is introduced. The hierarchic structure of the theory of defects is established and discussed. It is shown that all the known types of defects are naturally included in the presented classification of defects. A new broad class of defects of new types is established and interpreted. It is shown that the existence of new classes of defects is directly connected with some known theoretical and experimental data on the possibility of generation of such defects as dislocations and disclinations. In particular, it is shown that the generation of dislocations is necessarily connected with the existence of disclinations. The formal class of defects being a source of disclinations is specified. A formal generalization of classification of defects is developed to include the defects of arbitrary finite level. The development of consistent theory of defects is very important from both, fundamental and applied viewpoints. The potential applications include, in particular, the modeling of dispersed composite materials, porous media, dynamics of surface effects, crackling, cavitation and turbulence.