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An implicit return mapping algorithm for coupled viscoelastic-Perzyna viscoplastic finite element method[J].计算力学学报,2018,35(5):611~618

An implicit return mapping algorithm for coupled viscoelastic-Perzyna viscoplastic finite element method
An implicit return mapping algorithm for coupled viscoelastic-Perzyna viscoplastic finite element method

DOI：10.7511/jslx20170929001

 作者 单位 E-mail 闫富有 郑州大学 土木工程学院, 郑州 450001 yfy@zzu.edu.cn 崔昊 郑州大学 土木工程学院, 郑州 450001 张晓婉 郑州大学 土木工程学院, 郑州 450001 刘忠玉 郑州大学 土木工程学院, 郑州 450001

黏弹-黏塑性耦合模型的黏弹性部分由弹簧、黏壶和Kelvin链串联而成，黏塑性部分为双曲线型Drucker-Prager屈服函数、各向同性硬化和Perzyna黏塑性流动模型。基于黏弹性蠕变柔度，通过定义与弹性问题相对应的与时间增量相关的黏弹性剪切模量和体积模量，导出增量递推形式的本构方程。为保证算法的收敛和稳定性，把Perzyna黏塑性流动方程转化为与弹塑性相似的一致性条件，建立黏塑性增量因子单侧逼近其收敛值的N-R迭代算法。最后，给出应力更新完全隐式算法和最终计算公式。分别采用黏弹性、黏弹-塑性和黏弹-黏塑性本构关系对一地基蠕变模型进行三维有限元分析和比较，结果表明，本文算法具有较高的计算效率和稳定性。

A fully implicit stress updating algorithm is proposed for the coupled viscoelastic-viscoplastic model,and the final formulas are derived in closed form in this paper.The viscoelastic part of the model is consists of the Kelvin chains,a spring and a dashpot in series,and the viscoplastic part is the hyperbolic Drucker-Prager plasticity-based model with isotropic hardening and Perzyna's viscoplastic flow law.Firstly,based on the creep compliance,the viscoelastic shear modules and bulk modules,corresponding to the ones in elasticity,are defined as functions of the time increment.The recursive formulas for the relations between stress increments and viscoelastic strain increments are also derived.Then,an extended viscoplastic consistency condition,analogous to that of the rate-independence plasticity,is given from Perzyna law in order to avoid the instability in the computer implementation.A simple successive approximation scheme with monotonic convergence property is given for the solution of the equation on the incremental viscoplastic multiplier using the Newton-Raphson iterative method.Finally,a creep model for the foundation was computed using three-dimensional FEM with the viscoelastic,the viscoelastic-rate-independent plastic and the viscoelastic-viscoplastic constitutive relations,respectively.The results show that this algorithm has a higher computational efficiency and stability.