作者机构：
[谢方平; 邓平; 吴明亮; 唐伦; 刘勇; 王慧敏] College of Engineering, Hunan Agricultural University, Changsha 410128, China;[余应弘] Hunan Academy of Agricultural Sciences, Changsha 410125, China
通讯机构：
College of Engineering, Hunan Agricultural University, China
作者机构：
[吴明亮; 裴毅; 施祖强; 黄维; 徐波] College of Engineering, Hunan Agricultural University, Changsha 410128, China;[陈飞勇] East Star Technology Ltd., Tokyo 111-0041, Japan
通讯机构：
College of Engineering, Hunan Agricultural University, China
作者机构：
[谢方平; 孙松林; 胡文武; 蒋蘋; 罗亚辉] College of Engineering, Hunan Agricultural University, Changsha 410128, China;[蒋蘋] College of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China
通讯机构：
College of Engineering, Hunan Agricultural University, China
作者机构：
[谢方平; 任述光; 汤楚宙] College of Engineering, Hunan Agricultural University, Changsha 410128, China;[卢向阳; 孙松林] College of Bioscience and Technology, Hunan Agricultural University, Changsha 410128, China;[罗锡文] College of Engineering, South China Agricultural University, Guangzhou 510642, China
通讯机构：
College of Engineering, South China Agricultural University, China
作者机构：
[汤楚宙; 罗海峰; 谢方平; 吴明亮] College of Engineering, Hunan Agricultural University, Changsha 410128, China;[官春云; 陈社员] Institute of Oil, Hunan Agricultural University, Changsha 410128, China
通讯机构：
College of Engineering, Hunan Agricultural University, China
作者机构：
[张义同; 齐德碹] School of Mechanical Engineering, Tianjin University, Tianjin 300072, China;[任述光] College of Engineering and Technology, Hunan Agricultural University, Changsha, Hunan 410128, China
通讯机构：
School of Mechanical Engineering, Tianjin University, China
作者机构：
[王志军] Hu'nan Agricultural Engineering Research Institute, Changsha 410004, China;[谢方平; 孙松林] College of Engineering, Hu'nan Agricultural University, Changsha 410128, China
通讯机构：
Hu'nan Agricultural Engineering Research Institute, China
作者机构：
[梁建国] School of Civil Engineering and Architecture, Changsha University of Science and Technology, Changsha 410076, China;[汤峰] College of Engineering, Hunan Agricultural University, Changsha 410128, China;[Zeng, Xiaojun] China Machinery International Engineering Design and Research Institute, Changsha 410076, China
通讯机构：
School of Civil Engineering and Architecture, Changsha University of Science and Technology, China
关键词：
strain localization;locally-deformed bands;shear bands;two-phase equilibrium;granular model of sand
摘要：
In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics, shear bands in sand are considered as high-strain phase (plastic phase) of sand and the materials outside the bands are still in low-strain phase (elastic phase), namely, the two phases of sand can coexist under certain condition. As a one-dimensional example, the results show that, for materials with strain-softening behavior, the two-phase solution is a stable branch of solutions, but the method to find two-phase solutions is very different from the one for bifurcation analysis. The theory of multi-phase equilibrium and the slow plastic flow model are applied to predict the formation and patterns of shear bands in sand specimens, discontinuity of deformation gradient and stress across interfaces between shear bands and other regions is considered, the continuity of displacements and traction across interfaces is imposed, and the Maxwell relation is satisfied. The governing equations are deduced. The critical stress for the formation of a shear band, both the stresses and strains inside the band and outside the band, and the inclination angle of the band can all be predicted. The predicted results are consistent with experimental measurements.
作者机构：
[徐家福; 张义同; 谢宇新; 任述光] School of Mechanical Engineering, Tianjin University, Tianjin 300072, China;[任述光] College of Engineering and Technology, Hunan Agricultural University, Changsha 410128, China
通讯机构：
School of Mechanical Engineering, Tianjin University, China
