EI、Scopus 收录
中文核心期刊
快速检索 年期检索 高级检索

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
shu
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
shu
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. CSTR: 32045.14.0459-1879-16-340
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. CSTR: 32045.14.0459-1879-16-340
shu
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. CSTR: 32045.14.0459-1879-16-340
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. CSTR: 32045.14.0459-1879-16-340
shu

结构性软土弹塑性模型的隐式算法实现

  • 1 同济大学,道路与交通工程教育部重点实验室,上海,201804

  • 2 McMaster University, Department of Civil Engineering, Hamilton, L8S4L7

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

  • 1 Key Laboratory of Road and Traffic Engineering of the Ministry of Education,Tongji University,Shanghai 201804,China

  • 2 Department of Civil Engineering,McMaster University,Hamilton L8S4L7,Canada

HTML全文

    摘要
  • 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。
    Abstract: ：Compared with the general constitutive models, the highly nonlinear elasto-plastic constitutive models for structured clays are more complex, which leads to the problems of Jacobian matrix singularity and nonconvergence more easily when the implicit algorithm of Newton-CPPM is used for the numerical implementation. To solve the problems, two implicit algorithms are proposed in this paper. Considering the Newton-CPPM implicit algorithm is a local convergence algorithm, the homotopy continuation algorithm of global convergence is introduced to improve the iterative initial value of the Newton-CPPM algorithm, so the method can be called as homotopy-Newton-CPPM algorithm. Considering that the calculation of every iteration for the Newton-CPPM implicit algorithm is too large, a two-stage iterative algorithm based on the idea of the fully explicit algorithm is presented. The consistency parameter is calculated in the first-stage, taking the consistency parameter as a known quantity and the algorithm similar to the explicit algorithm is used to solve the values of state variables in the second-stage. Then, taking the SANICLAY model that including destructuration as an example, from the two aspects of the composition of the elasto-plastic constitutive model and the characteristics of the algorithm, the reasons for Jacobian matrix singularity and nonconvergence are analyzed. The convergence, accuracy and cost of four algorithms, including the explicit algorithm, traditional implicit algorithm and two kinds of improved implicit algorithms, are compared with reference to the numerical simulations of single element tests. Finally, the homotopy-Newton-CPPM algorithm and the traditional implicit algorithm are applied to the multi-element calculation of subgrade bearing capacity. The results show that the homotopy-Newton-CPPM algorithm can effectively improve convergence and avoid singularity of Jacobian matrix compared with the traditional implicit algorithm.
    • HTML全文
    • 参考文献(1)
  • 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.
    • 相关文章
    • 施引文献(9)

  • 期刊类型引用(7)

    1. 付子才. 新型串珠状溶洞预处理施工技术的研究与应用. 四川水泥. 2024(07): 137-139 . 百度学术
    2. 罗志机，龙琰. 城市核心区水泵房沉井施工技术探讨. 江西建材. 2023(01): 320-321+326 . 百度学术
    3. 龙琰，罗志机. 基坑支护结构位移影响因素敏感性分析. 四川水泥. 2023(05): 74-76 . 百度学术
    4. 代宁，耿大将，郭培军，周顺华，狄宏规. 共轭梯度法在弹塑性模型数值实现中的应用. 同济大学学报(自然科学版). 2021(02): 173-179+297 . 百度学术
    5. 惠军. 剪切速率对边坡软弱夹层破坏机理的影响. 科技通报. 2021(12): 61-70 . 百度学术
    6. 谭琳，刘芳. 水平井降压法和热激法水合物开采对海底边坡稳定性的影响. 力学学报. 2020(02): 567-577 . 本站查看
    7. 万征，孟达. 复杂加载条件下的砂土本构模型. 力学学报. 2018(04): 929-948 . 本站查看

    其他类型引用(2)

    • 资源附件(0)
计量
  • 文章访问数:  1568
  • HTML全文浏览量:  210
  • PDF下载量:  388
  • 被引次数: 9
出版历程
  • 收稿日期:  2017-11-20
  • 刊出日期:  2018-01-17

目录

摘要
HTML全文
    参考文献(1)
    相关文章
    施引文献
    资源附件(0)

    /

    返回文章
    返回

    下载中心

    作者中心

    版权所有 © 《力学学报》编辑部备案号：京ICP备05039218号-1

    通讯地址：北京市海淀区北四环西路15号邮政编码：100190

    联系电话：010-62536271

    邮箱：lxxb@cstam.org.cn

    微信公众号
    RSS

    本系统由 北京仁和汇智信息技术有限公司 开发  百度统计