PLANAR DEFORMATION OF COHESIONLESS GRANULAR MEDIA

A theory for planar deformation of cohesionless granular media is presented. Although this study follows closely the methodology used by Mandel (1947), Spencer (1964) and Mehrabadi and Cowin (1978) it differs in many respects from the contents of these papers. Both the angle of dilatancy and the orientation of the family of the velocity characteristics (slip lines) with respect to the direction of the principal axes of stress are assumed variant and dependent on the loading history of the element. The velocity and stress characteristics are assumed not to be coincidental (necessarliy) and it is reasoned that deformation may proceed along one family of the slip lines only. A hypothesis regarding the symmetry of orientation of slip lines with respect to the principal stress directions and a second one regarding the minimal value for a so called 'energy correction factor' involving the ratio of the first invariant of the strain rate tensor to the second invariant strain rate deviation tensor is stated. It is shown that the adaptation of these hypotheses leads directly to St. Venant's principle: the coaxiality of the stress and the strain rate tensors. It should be stressed that coaxiality conclusion reached in this paper is in variance with the conclusions reached by the above authors (see also Spencer. 1981) and the conclusions of Christoffersen et al. (1981) who approached the problem more fundamentally using micromechanical modeling.