Notes on progressive deformation and deformation paths

Abstract

The concepts of incremental deformation and invariant directions of deformation are precisely defined. Then, rotational and irrotational deformation are characterized comparing the principal directions of the deformed configuration (or directions of the strain ellipsoid axes) with the corresponding principal directions in the initial configuration. Coaxial and non-coaxial deformations are subsequently defined as the result of comparing the directions of the finite strain ellipsoid with those of the incremental strain ellipsoid. Both pairs of concepts can be considered at any stage of the deformation, but their variation along the progressive deformation can also be considered, allowing deformation paths to be established. The convenience of complementing the graphs that show deformation paths as a variation of the shape of the strain ellipsoid (ellipse in plane deformation), with graphs that illustrate the rotationality and non-coaxiality of the progressive deformation, is suggested. Finally, geologically relevant types of deformation paths are described, relating them to mechanisms involved in the development of structures generated by rock deformation.