A micromechanics-based Cosserat-type model for dense particulate solids |
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Authors: | Xi Zhang Robert G Jeffrey and Yiu-Wing Mai |
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Institution: | (1) Gdansk University of Technology, Gdansk, Poland;(2) Graz University of Technology, Graz, Austria |
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Abstract: | A two-dimensional continuum theory is presented for cohesionless granular media consisting of identical rigid disks. While
the normal deformation of contacting particles is constrained, the tangential frictional contact is modelled by a line spring
with a constant stiffness. To describe the static frictional system transmitting couples at contacts, a Cosserat-type continuum
including rotational degrees of freedom is appropriate. Contrary to the classical elastic medium, movement of particles within
a granular system in response to applied loads can give rise to localisations of force chains and large voids. In addition
to relative displacement and rotation, a director governing the direction of interparticle forces and a phase field delineating
density variation, are therefore introduced. Total work done involving these two order parameters for a particle is attained
on an orientation average. Based on the formulation of free energy, a concentration- and anisotropy-dependent formulation
for static quantities (stress and couple stress) in the rate form is derived in light of the principles of thermodynamics.
It is consistent with the requirement of observer independence and material symmetry. The governing equations for two order
parameters are derived, in which void concentration and stress anisotropy are related to relative displacement and rotation.
As an example, the proposed model is applied to the hardening regime of deformation of a dense particle assembly with initial
perfect lattice under simple shear. It is demonstrated that in the presence of dilatancy and director variation, there exists
a linear relation between the shear stress and strain, in coincidence with experimental observations. |
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