Several internal parameters are studied for a 3D simple shear flow of soft polydispersed granular materials consisting of viscoelastic spheres. These internal parameters include the contact time, the multiple collision group size, and the coordination number. It is found that the contour plots of the contact time and the coordination number in the plane defined by the concentration (solid fraction) and dimensionless stiffness are similar. These contours are qualitatively the same as the regime chart/flowmap proposed in earlier studies. The resulting constitutive relation shows different rate dependency at different concentrations and shear rates. Based on a simple dimensional analysis and a power law formulation, the rate dependency may be expressed by an index. The two extreme values of this index, 0 and 1, correspond to solidlike and gaslike granular materials, respectively. The contour map of this rate index (the power of the dimensionless shear rate in the constitutive relation) resembles those of the lambda-shaped curve typical of a phase diagram for ordinary materials. (C) 2008 The Society of Rheology.