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结构性软土弹塑性模型的隐式算法实现

耿大将 Peijun Guo 周顺华

耿大将, Peijun Guo, 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): 78-86. doi: 10.6052/0459-1879-16-340
引用本文: 耿大将, Peijun Guo, 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): 78-86. doi: 10.6052/0459-1879-16-340
Dajiang Geng, Peijun Guo, Shunhua Zhou. Implicit numerical integration of an elasto-plastic constitutive model for structured clays[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(1): 78-86. doi: 10.6052/0459-1879-16-340
Citation: Dajiang Geng, Peijun Guo, Shunhua Zhou. Implicit numerical integration of an elasto-plastic constitutive model for structured clays[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(1): 78-86. doi: 10.6052/0459-1879-16-340

结构性软土弹塑性模型的隐式算法实现

doi: 10.6052/0459-1879-16-340
基金项目: 国家重点研发计划(2017YFB1201204)资助项目
详细信息
    作者简介:

    null

    作者简介:耿大将,博士研究生,主要研究方向:结构性软土的本构模型及数值实现。E-mail:1410704@tongji.edu.cn

    通讯作者:

    耿大将

  • 中图分类号: TU432;

Implicit numerical integration of an elasto-plastic constitutive model for structured clays

  • 摘要: 对于考虑软土结构性的高度非线性弹塑性本构模型,在采用Newton-CPPM隐式算法对模型进行数值实现的过程中容易出现Jacobian矩阵奇异和不收敛问题。为此,本文提出了两种改进隐式算法。考虑到Newton-CPPM隐式算法是局部收敛性算法,因此引入大范围收敛的同伦延拓算法对Newton-CPPM算法的迭代初值进行改进,形成了同伦-Newton-CPPM算法。考虑到Newton-CPPM隐式算法单个迭代步的计算量过大,因此借鉴显式算法的思想提出一种两阶段迭代算法,第一阶段先求出一致性参数,第二阶段采用类似于显示算法的方法进行回代得出状态变量的值。然后,以考虑软土结构性的SANICLAY模型为例,从弹塑性本构模型的组成和算法的特点两个角度分析了引起Jacobian矩阵奇异和不收敛问题的原因,并且在单单元计算的基础上,对全显式算法、传统隐式算法和两种改进隐式算法在计算收敛性、计算精度和计算效率方面进行了对比。最后,将同伦-Newton-CPPM算法和传统隐式算法用于地基承载力多单元计算中,结果表明该算法能够有效地解决Jacobian矩阵奇异和不收敛问题。

     

  • 1 Callisto L, Rampello S.Shear strength and small-strain stiffness of a natural clay under general stress conditions. Geotechnique, 2002, 52(8):547-560.
    2 于亚磊, 叶冠林, 熊永林. 上海第4层黏土力学特性的弹塑性本构模拟. 岩土力学,2016,9:2541-2546
    2 Yu Yalei, Ye Guanlin, Xiong Yonglin.Elasto-plastic constitutive modelling for mechanical behavior of Shanghai 4th layer clay. Rock and Soil Mechanics, 2016,9: 2541-2546(in Chiniese)
    3 Liu WZ, Shi ML, Miao LC, et al.Constitutive modeling of the destructuration and anisotropy of natural soft clay. Computers and Geotechnics, 2013, 51:24-41.
    4 Panayides S, Rouainia M, Woodd M.Influence of degradation of structure on the behaviour of a full-scale embankment. Canadian Geotechnical Journal, 2012, 49(3):344-356.
    5 Rocchi G, Vaciago G, Fontana M, et al.Understanding sampling disturbance and behaviour of structured clays through constitutive modelling. Soils and Foundations, 2013, 53(2):315-334.
    6 Taiebat M, Dafalias YF, Peek R.A destructuration theory and its application to SANICLAY model. International Journal for Numerical and Analytical Methods in Geomechanics, 2010, 34(10):1009-1040.
    7 Suebsuk J, Horpibulsuk S, Liu MD.Modified Structured Cam Clay: A generalised critical state model for destructured, naturally structured and artificially structured clays. Computers and Geotechnics, 2010, 37:956-968.
    8 Cotecchia F, Chandler RJ.A general framework for the mechanical behaviour of clays. Geotechnique, 2000, 50(4):431-447.
    9 Callisto L, Gajo A, Wood DM.Simulation of triaxial and true triaxial tests on natural and reconstituted Pisa clay. Geotechnique, 2002, 52(9):649-666.
    10 10祝恩阳, 姚仰平. 结构性土UH模型. 岩土力学,2015, 11:3101-3110
    10 Zhu Enyang, Yao Yangping, A UH constitutive model for structured soils. Rock and Soil Mechanics, 2015,11: 3101-3110(in Chiniese)
    11 Lloret CM, Sloan SW, Sheng DC, et al.Error behaviour in explicit integration algorithms with automatic substepping. International Journal for Numerical Methods in Engineering, 2016,108(9):1030-1053.
    12 Bicanic N, Pearce CJ.Computational aspects of a softening plasticity model for plain concrete. Mechanics of Cohesive-frictional Materials, 1996, 1(1):75-94.
    13 Stupkiewicz S, Denzer R, Piccolroaz A, et al.Implicit yield function formulation for granular and rock-like materials. Computational Mechanics, 2014, 54(5):1163-1173.
    14 Valentini B, Hofstetter G.Review and enhancement of 3D concrete models for large-scale numerical simulations of concrete structures. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(3):221-246.
    15 Jiu JL.Integration algorithm for a modified Yoshida-Uemori odel to simulate cyclic plasticity in extremely large plastic strain ranges up to fracture. Computers and Structures, 2014, 145:36-46.
    16 Majid MT, Karma Y.On implementation and performance of an anisotropic constitutive model for clays. International Journal of Computational Methods, 2014, 11(2):1-31.
    17 Penasa M, Piccolroaz A, Argani L, et al.Integration algorithms of elastoplasticity for ceramic powder compaction. Journal of the European Ceramic Society, 2014, 34(11):2775-2788.
    18 Crouch SC, Tahar B.Application of a stress return algorithm for elasto-plastic hardening-softening models with high yield surface curvature. In: Proceedings of European Congress on Computational Methods in Applied Sciences and Engineering. Barcelona, 11-14, September 2000.
    19 Wang W, Datcheva M, Schanz T, et al.A sub-stepping approach for elasto-plasticity with rotational hardening. Computational Mechanics, 2006, 37(3):266-278.
    20 Hernandez JA, Oliver J, Cante JC, et al.A robust approach to model densification and crack formation in powder compaction processes. International Journal for Numerical Methods in Engineering, 2011, 87(8):735-767.
    21 Brannon RM, Leelavanichkul S.A multi-stage return algorithm for solving the classical damage component of constitutive models for rocks, ceramics, and other rock-like media. International Journal of Fracture, 2010, 163:133-149.
    22 Homel MA, Brannon RM.Relaxing the multi-stage nested return algorithm for curved yield surfaces and nonlinear hardening laws. International Journal of Fracture, 2015, 194(1):1-7.
    23 Homel MA, Guilkey JE, Brannon RM.Numerical solution for plasticity models using consistency bisection and a transformed-space closest-point return: a nongradient solution method. Computational Mechanics, 2015, 56(4):565-584.
    24 Bilotta A, Leonetti L, Garcea G.An algorithm for incremental elastoplastic analysis using equality constrained sequential quadratic programming. Computers and Structures, 2012, 102:97-107.
    25 Contrafatto L, Cuomo A.A globally convergent numerical algorithm for damaging elasto-plasticity based on the Multiplier method. International Journal for Numerical Methods in Engineering, 2005, 63(8):1089-1125.
    26 Perez FA, Armero F.On the formulation of closest-point projection algorithms in elastoplasticity-part II: Globally convergent schemes. International Journal for Numerical Methods in Engineering, 2002, 53(2):331-374.
    27 Dafalias YF, Manzari MT, Akaishi M.A simple anisotropic clay plasticity model. Mechanics Research Communications, 2002, 29(4):241-245.
    28 Ortiz M, Popov EP.Accuracy and stability of integration algorithms for elastoplastic constitutive relations. International Journal for Numerical Methods in Engineering, 1985, 21(9):1561-1576.
    29 Ortiz M, Simo JC.An analysis of a new class of integration algorithms for elastoplastic constitutive relations. International Journal for Numerical Methods in Engineering, 1986, 23(3):353-366.
    30 Abbasbandy S, Tan Y, Liao SJ.Newton-homotopy analysis method for nonlinear equations. Applied Mathematics and Computation, 2007, 188(2):1794-1800.
    31 石玉仁, 许新建, 吴枝喜, 等. 同伦分析法在求解非线性演化方程中的应用. 物理学报,2006,55(4):1555-1560
    32 Shi Yuren, Xu Xinjian, Wu Zhixi, et al.Application of the homotopy analysis method to solving nonlinear evolution equations. ACTA PHYSICA SINICA 2006,55(4):1555-1560(in Chiniese)
    32 Wu Y, Cheung KF.Two-parameter homotopy method for nonlinear equations. Numerical Algorithms, 2010, 53(4):555-572.
    33 Wu TM.Solving the nonlinear equations by the Newton-homotopy continuation method with adjustable auxiliary homotopy function. Applied Mathematics and Computation, 2006, 173(1):383-388.
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出版历程
  • 收稿日期:  2017-11-21
  • 刊出日期:  2018-01-18

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