超固结土本构模型分叉三维理论分析及数值模拟

应变局部化分叉的产生强烈依赖于本构模型的弹塑性矩阵。以基于伏斯列夫面超固结黏土三维本构模型为研究对象，推导了三维应力下产生分叉的应力条件，求出了该模型在常平均应力时不同应力路径下分叉三维解析结果。解析结果表明：该模型在应力洛德角为-26.5°～7.5°时，有分叉现象产生，分叉产生于土体应力应变的硬化阶段，且分叉后剪切带倾角变化趋于稳定；而应力洛德角在-30°～-26.5°及7.5°～30°时无分叉现象出现。最后，利用有限元软件ABAQUS的材料子程序接口，采用回映应力更新算法，编写了材料特性子程序，实现了该模型在有限元数值分析中的应用，对均匀各向同性多单元立方体进行常平均应力时真三轴试验数值模拟，并比较数值计算结果与解析结果，验证了解析解与数值模拟结果的一致性。

Theoretical analysis and numerical simulation of three-dimensional bifurcation by constitutive model for over-consolidated clays

Bifurcation depends much on the elastoplastic matrix of constitutive model. An analytical solution of bifurcation is derived in three-dimensional stress states by taking the elastoplastic constitutive model proposed by Yao et al. for over consolidated clay based on the revised Hvorslev envelope. The bifurcation solution to the model along different stress paths under constant mean stress is obtained. The theoretical analysis shows that the onset of bifurcation occurs in the hardening regime at the Lode's angle in the range of -26.5°～7.5°, and that the change in the inclination angle of shear band after bifurcation is steady. There is no bifurcation occurring at the Lode's angle in the ranges of -30°～-26.5° and 7.5°～30°. On the other hand, 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. The numerical simulation of true triaxial tests on isotropically homogenous cubic specimens along different stress paths under constant mean stress is carried out. A comparison indicates that the numerical results agree with the theoretical solutions.