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| An implicit return mapping algorithm for coupled viscoelastic-Perzyna viscoplastic finite element method |
| Received:September 29, 2017 Revised:November 29, 2017 |
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| DOI：10.7511/jslx20170929001 |
| KeyWord:viscoelasticity Perzyna viscoplasticity return mapping algorithm consistent tangent operator FEM |
| Author | Institution |
| 闫富有 |
郑州大学 土木工程学院, 郑州 |
| 崔昊 |
郑州大学 土木工程学院, 郑州 |
| 张晓婉 |
郑州大学 土木工程学院, 郑州 |
| 刘忠玉 |
郑州大学 土木工程学院, 郑州 |
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| Abstract: |
| 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. |
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