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Volume 114
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Rheology and nonlocal flow behaviors of granular materials under annular shear with normal stress and shear velocity control
Tao Wang a, Xuejie Zhang b, Wei Wang a, Kun Liu a, Xiaojun Liu a, Jian Zhou a *
a Institute of Tribology, School of Mechanical Engineering, Hefei University of Technology, Hefei, 230009, China
b School of Mechanical and Electrical Engineering, Anhui Jianzhu University, Hefei, 230601, China
10.1016/j.partic.2026.05.001
Volume 114, July 2026, Pages 446-460
Received 5 March 2026, Revised 20 April 2026, Accepted 1 May 2026, Available online 13 May 2026, Version of Record 19 May 2026.
E-mail: jianzhou@hfut.edu.cn
Highlights

• Rheology and nonlocal effect of annular shear were analyzed using PFC3D–FLAC3D.

• Normal stress and shear velocity govern shear localization and stress transmission.

• Nonlocal length of radial velocity is stress-insensitive but decreases with shear velocity.

• Inner dense-flow rings show a μ(I)-type trend and outer low-I rings remain nonlocal.


Abstract

To study the rheological and nonlocal flow behaviors of annular shear granular materials under stress control and shear velocity control conditions, a three-dimensional annular shear numerical model was constructed using the PFC3D–FLAC3D platform, and the flow responses and microstructural evolution were analyzed under different control paths. The results show that increasing normal stress enhances the steady flow while suppressing velocity fluctuations, whereas increasing shear velocity leads to a nonlinear enhancement of flow intensity accompanied by stronger fluctuations. In the outer creep region, the normalized radial velocity profiles obtained under different conditions are well described by the same exponential form, and the characteristic length is insensitive to normal stress, exhibiting only a slight variation within 1.90–2.27 times the mean particle diameter. In contrast, increasing shear velocity decreases this characteristic decay length from 3.08 to 1.91 times the mean particle diameter.This indicates a contracted outer decay scale, reduced radial influence range, and enhanced localization; shear velocity has a stronger impact onthe nonlocal decay length than normal stress. Ring-wise inertial-number analysis indicates that the dense-flow region under both control paths exhibits a comparable frictional rheological trend, whereas the outer low-inertia region is governed by quasi-static creep and nonlocal effects. Together with the calibrated nonlocal characteristic length, these results provide constitutive guidance for continuum modeling of dense-flow and creeping regions in annular shear.

Graphical abstract
Keywords
Granular rheology; Annular shear flow; Inertial number; Contact network; Nonlocal effect
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