超固结土模型平面应变分叉理论解与数值模拟

Analytical Solution and Numerical Simulation for Plane Strain Bifurcation in Constitutive Model for Over-Consolidated Clays

应变局部化理论最基本的问题在于局部化分叉产生的条件.针对基于伏斯列夫面超固结黏土三维弹塑性本构模型,推导平面应变条件下局部化分叉理论解及因局部化分叉而产生的剪切带倾角的表达式,并分析不同超固结比对局部化分叉理论解和剪切带倾角的影响.理论分析表明,在平面应变条件下,土体局部化分叉出现在应力应变硬化阶段,剪切带倾角在分叉前随着应变局部化的扩张发生显著变化,在分叉后趋于稳定.最后,利用非线性有限元软件ABAQUS,在平面应变应力路径下对均匀各向同性多单元立方体局部化分叉现象进行数值分析,得出的局部化分叉数值解与理论解较为一致,验证了理论解的可靠性.

A fundamental problem concerning the theory of strain localization is the condition of the occurrence of localization bifurcation.Based on the Hvorslev envelope-based three-dimensional elastoplastic constitutive model for over-consolidated clay,an analytical solution of bifurcation and the expression of inclination angle for shear band caused by localization bifurcation are derived for strain localization in plane strain stress states.Meanwhile,influences of over-consolidation ratio（OCR） on the analytical solution and the inclination angle are analyzed.The theoretical analysis shows that onset of localization bifurcation occurs in the hardening regime under the plane strain conditions and,with strain localization expanding,the change in inclination angle of shear band is striking before bifurcation and steady thereafter.On the other hand,numerical simulation of plane strain tests on the isotropically homogenous cubic specimen for the bifurcation is carried out by using a finite element analysis software ABAQUS with the model implemented.Numerical solutions exhibit a good overall agreement with analytical solutions for the bifurcation onset,indicating that the analytical solutions are reasonable.