Strona 2_redak - Instytut Agrofizyki im. Bohdana Dobrzańskiego ...

37
granule as a natural consequence of the principle of conservation of momentum. The
introduction in the material model of the grain size, i.e. a value with the dimension of
length, permits the obtaining of a non-zero thickness of the shear band. For granule
rotations to contribute to the deformation of the material, the change of average stress
on a distance equal to the size of a granule should be large enough for a moment of
force to appear, greater than the rolling friction [119].
a) b)
u s
u s
n
s
d
Fig. 3.16. Shear band: a) classical theory of plasticity approach, b) microstructural approach
Similar conclusions are arrived at through considerations conducted on the grounds of
the microstructural approach, and from realized on their basis simulations of the
behaviour of granular material in successive stages of deformation, made according to
the MDEM method mentioned earlier. Iwashita and Oda [72] proved that in the
course of density hardening there gradually forms a certain structure of granule
contact points combining into chains along which a larger part of the main shear
stress is transmitted (fig. 3.17a). In the course of the process, granule contacts
formed earlier disappear to be replaced by new contacts. Due to this, the axis of
the chain follows the direction of the major principal stress. Between the chains,
elongated pores parallel to the chains are formed, which makes the material to
become anisotropic (fig. 3.17b). Such a structure gradually becomes less and less
stable, as there appears a shortage of points of support along the direction of the
minor principal stress. The process leads to the exhaustion of the strength of the
material. From that moment the microstructure undergoes a gradual restructuring
through buckling of the long load bearing columns formed before. Limitations of
the chain buckling leads to the localization of strain. As a result of the process, the
well known shear band is formed. Due to the buckling of the force bearing
columns, pores between the columns expand, resulting in a sudden increase in
porosity. Column buckling leads to considerable rotation of the granules. A strong
gradient of rotation appears, localized within the narrow space of the shear band.