A constitutive theory is developed in this present steady, homogeneous
, granular shear flows of identical, smooth and highly inelastic spher
es. The important mean fields in these flows are the solid fraction, m
ean velocity and full second moment of fluctuation velocity. The const
itutive theory, which consists of the pressure tensor and the collisio
nal source of second moment, is based upon an anisotropic Maxwellian v
elocity distribution function. The constitutive relation for the press
ure tensor contains contribution coming from both kinetic transport be
tween collisions and collisional transport between particles. Conseque
ntly, it applies toward the full range of the solid fractions. The con
stitutive theory is combined in this study with the balance equation f
or full second moment so as to determine each component of the second
moment and the pressure tensor. Most strikingly, normal pressure discr
epancies, which increase with particle inelasticity, are observed here
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