适用于弹黏塑性本构模型的修正切面算法

李舰; 蔡国庆; 尹振宇

doi:10.11779/CJGE202002006

适用于弹黏塑性本构模型的修正切面算法 English Version

李舰^{1, 2,},
蔡国庆^{1, 2},
尹振宇^3, ,

1.
北京交通大学城市地下工程教育部重点实验室,北京　100044
2.
北京交通大学土木建筑工程学院,北京　100044
3.
香港理工大学土木与环境工程学系,香港

基金项目:

中央高校基本科研业务费专项资金项目 2019JBM083

详细信息

作者简介:
李舰（1985— ）,男,博士,讲师,主要从事土的本构模型及其数值计算方面的研究工作。E-mail：jianli@bjtu.edu.cn

通讯作者:
尹振宇, E-mail：zhenyu.yin@polyu.edu.hk

中图分类号: TU43
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出版历程
- 收稿日期: 2019-07-06
- 网络出版日期: 2022-12-07
- 刊出日期: 2020-01-31

Modified cutting-plane integration scheme for elasto-viscoplastic models

LI Jian^{1, 2,},
CAI Guo-qing^{1, 2},
YIN Zhen-yu^3, ,

1.
Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China
2.
School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China
3.
Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China

摘要

摘要: 针对弹黏塑性本构模型将原始切面算法进行了修正。该弹黏塑性本构模型结合了修正剑桥模型和过应力理论。首先对弹黏塑性本构模型的应力-应变关系式进行了调整,基于过应力理论给出了动态加载面硬化参数的演化方程。其次,利用切面算法对整理后应力-应变关系式进行了数值实现。在弹性试算过程中,该算法假设黏塑性应变率为常数,以此确保时间增量引起的当前应力点与动态加载面间的偏离。在塑性修正过程中,对动态加载面函数进行泰勒级数展开,依此获得黏塑性应变率增量。再次,提出了一种自动分步方法,有效地稳定了大应变步情况下算法的计算精度和收敛性。最后,对变应变率的固结试验和三轴剪切不排水试验进行了模拟,分析了修正切面算法的计算能力。
- 黏塑性 /
- 本构模型 /
- 切面算法 /
- 半隐式算法 /
- 数值积分
Abstract: The elasto-viscoplastic model can be regarded as a combination of the modified Cam-clay model and the overstress theory. Firstly, the stress-strain formulas for the model are rearranged, in which an evolution equation for the hardening parameter of dynamic loading surface is deduced based on the overstress theory. Secondly, the rearranged stress-strain formulas are numerically implemented by the cutting-plane integration scheme. In an elastic prediction process, the viscoplastic strain rate is assumed to be constant, which guarantees the deviation of the current stress state from dynamic loading surface due to time increments. In a plastic corrector process, a Taylor series approximation of the dynamic loading function is used to obtain the increment of viscoplastic multiplier rate. Thirdly, an adaptive substepping method is proposed to maintain the accuracy and convergence of the proposed algorithm at a large loading step. Finally, the performances of the modified cutting-plane algorithm are analyzed by the calculated results of step-changed oedometer tests and undrained triaxial tests.
- viscoplasticity /
- constitutive model /
- cutting-plane algorithm /
- semi-implicit scheme /
- numerical integration

HTML全文

图 1 EVP-MCC模型的动态加载面和参考面

Figure 1. Dynamic loading surface and reference surface of EVP-MCC model

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图 2 变应变率固结试验计算结果

Figure 2. Calculated results of step-changed oedometer tests

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图 3 3种算法变应变率固结试验

Figure 3. Comparison of calculation errors and total iteration number of three kinds of algorithms for step-changed oedometer tests

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图 4 变应变率三轴剪切不排水试验

Figure 4. Calculated results of deviatoric stress and pore-water pressure for step-changed undrained triaxial tests

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图 5 两种算法变应变率三轴试验

Figure 5. Comparison of calculation errors and total iteration number of two kinds of algorithms for step-changed undrained triaxial tests

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表 1 Saint-Herblain黏土模型参数和状态变量初值

Table 1 Values of parameters and state constants of Saint-Herblain clay

$p_{m0}^{r}$ $p_{m0}^{r}$ /kPa	e₀	$μ$ $μ$	κ	λ	M	Cα_ae
39	2.26	0.2	0.038	0.48	1.2	0.034

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