Study On Return Mapping Algorithm For Viscoelastic-viscoplastic Finite Element Method On Geological Materials

Rheology is a main property for most geotechnical materials.Viscoelastic-viscoplastic models are used to describe the constitutive relation of rheology property.And the finite element method(FEM)is the most popular,convenient and important numerical analysis method.The accuracy,efficiency of computation,stability and the convergence of solution by FEM are depended on,to a large degree,the constitutive integration algorithm.The constitutive integration algorithm which is also called return mapping algorithm is an important part of FEM.It consists of two tasks: compute return mapping and consistent tangent operator.The former influence the accuracy and efficiency of computation directly,while the stability and convergence of the later determine the convergence of FEM in iteration of unbalance equation.When studying the return mapping algorithm,none of the two aspects could be ignored.In this text,return mapping algorithm for viscoelastic-viscoplastic Finite element method is researched.A viscoelastic-viscoplastic constitutive model based on Drucker-Prager yield criterion is proposed,which can describe the viscoelastic,plastic hardening,non-associated flow and viscoplastic properties.This model is valid for numerical calculation in geotechnical engineering.By considering viscoelastic strain history and quasi-linearization of the genetic integral equation,assume the rate of deviatoric strain tensor and volumetric strain as constants in one time step.The recursive formulas of deviatoric strain tensor and volumetric strain are derived with the shear relaxation modulus and bulk relaxation modulus.The equivalent shear modulus and equivalent bulk modulus are defined,by which the viscoelastic problem can be transferred into similar elastic problems and it is convenient to couple with other models.The strict implicit algorithm of the viscoplastic constitutive integration algorithm based on Drucker-Prager model is obtained,and the relative formulas are derived.The process of calculation proves that the proposed return mapping algorithm is of good convergence because there are only general algebraic calculations in iterationprocess.The calculation results shows that the sensitivity index has a great influence on the deformation for Perzyna viscoplastic model.Deformation decreases with the increase of the sensitivity index.The deformation results of Viscoelastic models are much smaller than that of Bingham model.When the sensitivity index inscreases to a certain value,the calculation result of the displacement based on elastic-viscoplastic models are approximately the same as that based on Viscoelastic models.