结构性软土弹塑性模型的隐式算法实现

摘要

对于考虑软土结构性的高度非线性弹塑性本构模型,在采用Newton-CPPM隐式算法对模型进行数值实现的过程中容易出现Jacobian矩阵奇异和不收敛问题.为此,本文提出了两种改进隐式算法.考虑到Newton-CPPM隐式算法是局部收敛性算法,因此引入大范围收敛的同伦延拓算法对Newton-CPPM算法的迭代初值进行改进,形成了同伦–Newton-CPPM算法.考虑到Newton-CPPM隐式算法单个迭代步的计算量过大,因此借鉴显式算法的思想提出一种两阶段迭代算法,第一阶段先求出一致性参数,第二阶段采用类似于显示算法的方法进行回代得出状态变量的值.然后,以考虑软土结构性的SANICLAY模型为例,从弹塑性本构模型的组成和算法的特点两个角度分析了引起Jacobian矩阵奇异和不收敛问题的原因,并且在单单元计算的基础上,对全显式算法、传统隐式算法和两种改进隐式算法在计算收敛性、计算精度和计算效率方面进行了对比.最后,将同伦–Newton-CPPM算法和传统隐式算法用于地基承载力多单元计算中,结果表明该算法能够有效地解决Jacobian矩阵奇异和不收敛问题.%Compared with the general constitutive models,the highly nonlinear elasto-plastic constitutive models for structured clays are more complex,which leads to the problems of Jacobian matrix singularity and nonconvergence more easily when the implicit algorithm of Newton-CPPM is used for the numerical implementation.To solve the problems,two implicit algorithms are proposed in this paper.Considering the Newton-CPPM implicit algorithm is a local convergence algorithm,the homotopy continuation algorithm of global convergence is introduced to improve the iterative initial value of the Newton-CPPM algorithm,so the method can be called as homotopy-Newton-CPPM algorithm.Considering that the calculation of every iteration for the Newton-CPPM implicit algorithm is too large,a two-stage iterative algorithm based on the idea of the fully explicit algorithm is presented.The consistency parameter is calculated in the first-stage,taking the consistency parameter as a known quantity and the algorithm similar to the explicit algorithm is used to solve the values of state variables in the second-stage.Then,taking the SANICLAY model that including destructuration as an example,from the two aspects of the composition of the elasto-plastic constitutive model and the characteristics of the algorithm,the reasons for Jacobian matrix singularity and nonconvergence are analyzed.The convergence,accuracy and cost of four algorithms,including the explicit algorithm,traditional implicit algorithm and two kinds of improved implicit algorithms,are compared with reference to the numerical simulations of single element tests.Finally,the homotopy-Newton-CPPM algorithm and the traditional implicit algorithm are applied to the multi-element calculation of subgrade bearing capacity.The results show that the homotopy-Newton-CPPM algorithm can effectively improve convergence and avoid singularity of Jacobian matrix compared with the traditional implicit algorithm.