Deformation Modes of a Packing of
Rigid Grains: Rotation, Counter-rotation, dislocation field
Abstract:
The properties of the processes
of deformation of a packing of rigid grains are analysed when the exact
distribution of the normal forces at contacts is known. Importance of grain
rotation and of counter-rotation of adjacent grains is stressed. It is shown
that all deformation modes form an incomplete vectorial space D. This allows the statistics of
fluctuation to be determined. Parallel with anti-ferromagnetism is then drawn
and frustration of rotation is shown to be the leading dissipating mechanism.
However this does not allow to make the parallel with spinglass due to the
structure of the space of deformation modes which is vectorial, which ensures
response linearity. In order to demonstrate experimentally the validity of the
approach and the existence of the incomplete vectorial space of deformation,
experimental examples are studied using regular arrays. They do demonstrate the
mechanism of counter-rotation and the existence of the vectorial space of
deformation. This theory is applied to compare different experiment and
simulation results on the deformation of square and triangular lattices of
rods, which can only be done through a statistical approach based on existence
of different modes of deformation. Non linear behaviour of the modes is
demonstrated experimentally; link with the continuous theory of dislocation is
made.
Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn
poudres & grains 11, 19-41 ( March 2 000)