中文摘要：

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。

英文摘要：

The bifurcation analysis was derived in three-dimensional stress states by using a critical state constitutive model by Yao et al.（2004）,which based on the nonassociated flow rule.Theoretical analysis shows that,bifurcation is dependent closely on the stress path.Bifurcation occurs in the hardening regime under the Lode angle changing between minus twenty-five degree and fifteen degree,and the stress ratio,principal strain at bifurcation and inclination angle of shear bands first increase and then decrease with increasing of the Lode angle.But there is no bifurcation occurring in other stress path under constant mean stress.Finally,the return mapping algorithm is adopted in order to implement the model into a nonlinear finite element analysis software ABAQUS through the user material subroutine（UMAT） interface.Numerical simulation results show that the bifurcation also exists in the numerical analysis.The comparison between the numerical results and theoretical solutions indicates that both are in good agreement.