Incompatible deformation in rock mechanics

Compatibility, i.e., continuous displacement field, is often taken for granted but experience teaches that rock deformation is in most cases discontinuous. The relation between incompatible deformation and continuous distribution of dislocations is established since long and is recalled in this paper. Contrary to several applications of Cosserat theory to already laminated (jointed) rock, the main goal of this paper is to give an explanation for the formation of discontinuities (joints) in rock as a result of a particular type of buckling which leads the body outside of the Euclidean space of its original configuration.