就服从非关联流动法则软化型砂的临界状态本构模型,在不同应力路径下的分叉进行了理论和数值分析。理论分析表明:分叉现象强烈依赖于应力路径,即当平均应力p一定时,应力路径在洛德角在-25o～15o之间时,均会在应力-应变关系硬化阶段出现分叉现象,而其他应力路径下不会产生分叉。并且分叉时对应的应力比、主应变及剪切带倾角都随洛德角的增加而变化,其值是先增加而后减小。采用回映应力更新算法,编写了该本构模型材料子程序,借助有限元软件ABAQUS及材料子程序,通过数值计算方法预测到了分叉点所对应的应力状态,表明了分叉现象在数值计算中的存在性,并通过数值预测值和理论解的对比,两者结果基本一致。 Based on the non-associated flow laws of the critical state constitutive model of softened sand, the bifurcation under different stress paths is theoretically and numerically analyzed. Theoretical analysis shows that the bifurcation strongly depends on the stress path. When the average stress p is constant, the bifurcation occurs in the stress-strain relationship during the stress-strain relationship when the stress path is between -25o and 15o. The other stress path will not produce bifurcation. And the corresponding stress ratio, main strain and shear band inclination at bifurcation all change with the increase of Lode angle, and its value increases first and then decreases. The backscattering stress update algorithm was used to write the material subroutine of this constitutive model. With the aid of finite element software ABAQUS and material subroutine, the stress state corresponding to the bifurcation point was predicted by the numerical calculation method. The bifurcation phenomenon in the numerical calculation The results of the two are basically the same through the comparison between the predicted value and the theoretical solution.