A SURVEY OF THE MATHEMATICS AVAILABLE FOR DESCRIBING FRACTURE

Abstract

An attempt is made to extend the mathematical finite strain theory of general rheological bodies to the inclusion of discontinuous displacements, i.e. to the description of fractures and related phenomena. A general analytical representation of discontinuities is given. A particularly simple type of discontinuity has been singled out for special investigation, i.e. "dislocations". The notion of "dislocation" is investigated from the standpoint of finite strain theory and several theorems are proved. Finally, the requirements for the establishment of a dynamic theory of fractures are outlined. It is shown that the mathematical theory cannot be carried further without additional physical investigations. The direction in which these have to be sought is indicated.