平面应变状态下砂土剪切带分析

Analysis of shear band in sand under plane strain state

提出一种砂土剪切带的两相平衡模型,此模型可看作一种新颖的分岔解。把剪切带考虑作高应变相,剪切带外部其它区域考虑作低应变相。在跨越两相界面处,考虑了变形梯度和应力的不连续性,以及拖曳力和位移的连续性,并且强加了Maxwell关系。推导出砂土在平面应变载荷下的控制方程,并且此分析归结为寻找使控制方程得到唯一一组物理上可以接受的实数解的载荷的最小值。Maxwell应力、剪切带内部和外部的应力应变、剪切带倾角等均可确定,并与实验所观察到的结果相一致。

A model of two-phase equilibrium for shear bands in sand is suggested in this paper, which may be viewed as a novel bifurcation solution. The shear bands are considered as a high-strain phase and the other regions outside shear bands as a low-strain phase. Across interfaces between two phases, discontinuity of deformation gradient and stress is considered, and continuity of traction and displacements and the Maxwell relation are imposed. Governing equations for sand under plane strain loading are deduced, and the analysis is reduced to finding the minimum value of the loading at which the governing equations have a unique, real, physically acceptable solution. The Maxwell stress, the stresses and strains inside and outside the shear band, and the shear band orientation angle are determined, which are in good agreement with the experimental observations.