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Home > Archive>Volume 49, Issue 2, 2021 >173-179. DOI:10.11908/j.issn.0253-374x.20076
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Application of Conjugate Gradient Method in Numerical Implementation of Elasto-plastic Model
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1.Key Laboratory of Road and Traffic Engineering of the Ministry of Education， Tongji University， Shanghai 201804，China;2.Shanghai Key Laboratory of Rail Infrastructure Durability and System Safety， Tongji University， Shanghai 201804，China;3.Shanghai Second Branch of Seazen Holdings Co.， Ltd.， Shanghai 201800， China;4.Department of Civil Engineering， McMaster University， Hamilton L8S4L7， Canada

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TU431

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    Abstract:

    Based on the singularity and non-convergence characteristics of the Jacobian matrix， the composition and the algorithm of the elasto-plastic constitutive model were comprehensively analyzed. The problem of solving the highly nonlinear equations in Newton-closest point projection method（Newton-CPPM） implicit algorithm was transformed into a seeking minimum value problem by the conjugate gradient method， and the improvement of traditional implicit method was eventually accomplished. Finally， according to the calculations of single unit， the Saniclay model considering the structural properties of soft soils was set as an example， which is involved in different strain paths and initial stress states. In this process， the calculation convergence， the accuracy and the efficiency between traditional implicit algorithm and improved implicit algorithm were separately compared. In addition， the differences between traditional and improved implicit algorithm were examined by engineering example. Results show that， compared with the traditional implicit algorithm， the improved implicit algorithm can effectively improve the computational efficiency and convergence.

    Fig.1 Improved implicit algorithm
    Fig.6 Comparison of convergence between two algorithms
    Fig.7 Geometric model (unit：m)
    Fig.8 Calculation results of surface settlement
    Reference
    [1] SLOAN S W， ABBO A J， SHENG D C. Refined explicit integration of elastoplastic models with automatic error control[J]. Engineering Computations， 2001， 18：121.
    [2] GONZALEZ N A， GENS A. Evaluation of a constitutive model for unsaturated soils： stress variables and numerical implementation[C]//Fifth International Conference on Unsaturated Soils. New York：Taylor and Francis Group， 2011： 829-836.
    [3] LLORET C M， SLOAN S W， SHENG D C， et al. Error behaviour in explicit integration algorithms with automatic substepping[J]. International Journal for Numerical Methods in Engineering， 2016，108（9）：1030.
    [4] BICANIC N， PEARCE C J. Computational aspects of a softening plasticity model for plain concrete[J]. Mechanics of Cohesive-Frictional Materials， 1996， 1（1）：75.
    [5] STUPKIEWICZ S， DENZER R， PICCOLROAZ A， et al. Implicit yield function formulation for granular and rock-like materials[J]. Computational Mechanics， 2014， 54（5）：1163.
    [6] VALENTINI B， HOFSTETTER G. Review and enhancement of 3D concrete models for large-scale numerical simulations of concrete structures[J]. International Journal for Numerical and Analytical Methods in Geomechanics， 2013， 37（3）：221.
    [7] JIA J L. Integration algorithm for a modified Yoshida-Uemori model to simulate cyclic plasticity in extremely large plastic strain ranges up to fracture[J]. Computers and Structures， 2014， 145：36.
    [8] MAJID M T， KARMA Y. On implementation and performance of an anisotropic constitutive model for clays[J]. International Journal of Computational Methods， 2014， 11（2）：1.
    [9] PENASA M， PICCOLROAZ A， ARGANI L， et al. Integration algorithms of elasto-plasticity for ceramic powder compaction[J]. Journal of the European Ceramic Society， 2014， 34（11）：2775.
    [10] WANG W， DATCHEVA M， SCHANZ T， et al. A sub-stepping approach for elasto-plasticity with rotational hardening[J]. Computational Mechanics， 2006， 37（3）：266.
    [11] LEE J，KIM D，QUAGLIATO L，et al. Change of the yield stress in roll formed ERW pipes considering the Bauschinger effect[J]. Journal of Materials Processing Technology， 2017， 244： 304.
    [12] HERNANDEZ J A， OLIVER J， CANTE J C， et al. A robust approach to model densification and crack formation in powder compaction processes[J]. International Journal for Numerical Methods in Engineering， 2011， 87（8）：735.
    [13] 耿大将， GUO Peijun， 周顺华. 结构性软土弹塑性模型的隐式算法实现[J]. 力学学报， 2018， 50（1）：78.
    [14] HOMEL M A， BRANNON R M. Relaxing the multi-stage nested return algorithm for curved yield surfaces and nonlinear hardening laws[J]. International Journal of Fracture， 2015， 194（1）：1.
    [15] HOMEL M A， GUILKEY J E， BRANNON R M. Numerical solution for plasticity models using consistency bisection and a transformed-space closest-point return： a nongradient solution method[J]. Computational Mechanics， 2015， 56（4）：565.
    [16] SHARIFIAN M， SHARIFIAN M， KRYSL P， et al. Stress-update algorithms for Bigoni-Piccolroaz yield criterion coupled with a generalized function of kinematic hardening laws[J]. European Journal of Mechanics A：Solids， 2018， 67： 1.
    [17] BILOTTA A， LEONETTI L， GARCEA G. An algorithm for incremental elastoplastic analysis using equality constrained sequential quadratic programming[J]. Computers and Structures， 2012， 102：97.
    [18] PLACIDI L. A variational approach for a nonlinear 1-dimensional second gradient continuum damage model[J]. Continuum Mechanics and Thermodynamics， 2015， 27（4/5）： 623.
    [19] ARMORO F. Elastoplastic and viscoplastic deformations in solids and structures[M]//Encyclopedia of Computational Mechanics. New York： John Wiley & Sons Ltd.， 2018： 227-264.
    [20] FLETCHER R， REEVES C M. Function minimization by conjugate gradients[J]. Computer Journal， 1964， 7（2）：149.
    [21] LUCAMBIO L R， PRUDENTE L F. Nonlinear conjugate gradient methods for vector optimization[J]. SIAM Journal on Optimization， 2018， 28（3）： 2690.
    [22] AWWAL A M， KUMAM P， ABBAKAR A B. A modified conjugate gradient method for monotone nonlinear equations with convex constraints[J]. Applied Numerical Mathematics， 2019， 145： 507.
    [23] 祝恩阳， 姚仰平. 结构性土UH模型[J]. 岩土力学，2015，11：3101.
    [24] SUEBSUK J， HORPIBULSUK S， LIU M D. Modified structured cam clay： a generalised critical state model for destructured， naturally structured and artificially structured clays[J]. Computers and Geotechnics， 2010， 37：956.
    [25] DAFALIAS Y F， MANZARI M T， AKAISHI M. A simple anisotropic clay plasticity model[J]. Mechanics Research Communications， 2002， 29（4）：241.
    [26] TAIEBAT M， DAFALIAS Y F， PEEK R. A destructuration theory and its application to SANICLAY model[J]. International Journal for Numerical and Analytical Methods in Geomechanics， 2010， 34（10）：1009.
    [27] ROSCOE K H， BURLAND J B. On the generalised stress-strain behaviour of ‘wet’ clay[M]//Engineering Plasticity. Cambridge： Cambridge University Press，1968：535-609.
    [28] DENNIS J E. A characterization of superlinear convergence and its application to quasi-Newton methods[J]. Mathematics of Computation， 1974， 28（126）： 549.
    [29] ZHANG L， ZHOU W J. Spectral gradient projection method for solving nonlinear monotone equations[J]. Journal of Computational and Applied Mathematics， 2017，196（2）：478.
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DAI Ning, GENG Dajiang, GUO Peijun, ZHOU Shunhua, DI Honggui. Application of Conjugate Gradient Method in Numerical Implementation of Elasto-plastic Model[J].同济大学学报(自然科学版),2021,49(2):173~179

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  • Received:March 11,2020
  • Online: March 18,2021
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