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Fabric diagrams, which stand for the distribution of contact
vectors between particles in a granular packing, affect the
response of granular materials. This study first uses the
Discrete Element Method (DEM) to investigate the correlation
between the two-dimensional fabric diagram and the stress
tensor. Then the concept of micromechanics incorporating the
numerical approach is used to exam the influences of fabric
tensor, which is evolved from the fabric diagram, on the
isotropic, orthotropic and anisotropic material properties
under the assumption of plane stress state. It is found that
the constitutive equations for the aforementioned three kinds
of material properties by the micro-continuum mechanics under
the plane stress state can be characterized by two parameters
in the fabric tensor. The valid bounds of those two parameters
are also discussed in this study. Accordingly, the analytical
equations correlating the parameters in fabric tensor, the
contact stiffness between particles and the elements in the
tensor of elastic constants of material are derived. The
mutual influences among those variables are also addressed in
detail in this study.
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