软岩三维非线性统一弹粘塑性本构模型有限元分析

FEM Analysis of Three Dimensional Unified Elastic ViscoPlastic Model of soft rock

在作者已建立的软岩三维非线性统一弹粘塑性软化本构模型基础上,讨论了软岩三维非线性统一弹粘塑性本构模型有限元分析过程,即推导了软岩三维非线性统一弹粘塑性屈服面(破坏面)的流动矢量表达式,便于编程与通用的有限元程序接口,进行二次开发;利用张量求导的原则,导出了流动矢量对应力求导公式中关键矩阵的具体表达式,并结合平面应力、平面应变和轴对称问题的特点进行了简化,得出了适合于分析二维问题的关键矩阵的表达式;采用流动矢量奇异性的统一处理方法,有效地处理了各种角点奇异性问题;最后给出了有限元分析的流程图,便于编制有限元程序。

A three dimensional nonlinear elastic viscoplastic softening constitutive model is established,and the expression of triaxial condition is derived.The simulation result shows the model describes the strain softening behavior of soft rock very well and the simulation result has good agreement with the experimental one.The FEM analysis of the three dimensional nonlinear unified elastic viscoplastic model is carried out,where the matrix for solving the strain increment is established,and a flow vector formulation of yield surface of the model is derived.The key matrixes are derived and simplified with the condition of two dimensional problems.The singularity of the angular point of limited line on π plane is effectively solved by the unified method.The idiographic process of elastic viscoplastic FEM analysis is listed.