GEOMETRICAL CONDITIONS FOR DEFORMATION AND FRACTURE RELATED TO THE EARTHQUAKES (1)

Abstract

The problem of the creation of the fractures system in the continua is discussed by the method of geometry. The concept of manifolds plays an important role for formulating the problems of general deformations including fractures. The stochastic nature of the fracturing is equivalent to the variety of the coordinate systems. The conditions for the field equation are searched from two viewpoints, i.e., the St. Venant's compatibility conditions and the dislocation density. We find that these are concerned with conditions for integrability according to Poincare's lemma of differential forms.