广义塑性梯度模型的数值模型和数值算法  

NUMERICAL MODEL AND NUMERICAL ALGORITHM OF GENERALIZED GRADIENT-DEPENDENT PLASTICY MODEL

作　　者：赵冰[1] 李宁[2] 盛国刚[1] 郑颖人[3] 

机构地区：[1]长沙理工大学桥梁与结构工程学院,湖南长沙410076 [2]西安理工大学岩土工程研究所,陕西西安710048 [3]后勤工程学院,重庆400041

出　　处：《岩石力学与工程学报》2007年第4期825-832,共8页Chinese Journal of Rock Mechanics and Engineering

基　　金：湖南省自然科学基金资助项目(04JJ40032);湖南省教育厅资助科研项目(04C119)

摘　　要：广义塑性梯度模型在双屈服函数中分别考虑塑性剪切应变和塑性体积应变的拉普拉斯项,用虚功方程和屈服函数的一致性条件建立控制微分方程。它有望在较全面地反映岩土介质基本力学性质的同时,也合理解释岩土介质的应变局部化现象。为得到上述控制方程的数值解答,同时对位移和塑性乘子进行离散,得到以节点位移和节点塑性乘子为基本未知量的非线性方程组,建立塑性乘子的边界条件,给出求解上述方程组的增量算法。数值算例表明:(1)发生应变局部化时,塑性剪切应变和塑性体积应变主要集中在应变局部化带中;(2)网格密度变化时,网格敏感性问题不再出现;(3)当模型的局部化参数增大时,应变局部化带的带宽也明显增宽。　Considering the Laplace operator of plastic strains in the double yield functionst,he control equations of the generalized gradient-dependent plasticity model are established to describe both the strain localization characteristics and the basic mechanical characteristics of geomaterials.In order to get the numerical solution of the control equations,the displacement and the plastic multiplier are discretized by virtual work equation and the consistency condition of yield functions separately.A set of nonlinear equations taking the displacements and the plastic factors of nodes as the unknown variables are obtained;and the boundary conditions and the increment algorithm of the equations are given.The numerical examples indicate that：（1） when strain localization appears,the plastic shear strain and the plastic bulk strain mainly concentrate in localization band（;2） the mesh-dependency does not appear any more when the size of mesh changes（;3） when the parameters reflecting localization increase,the width of the strain localization band will be widened obviously.

关 键 词：数值分析 软化 岩土介质 应变局部化 广义塑性梯度 数值模型 算法 

分 类 号：O242[理学—计算数学]