基于近场动力学的单晶冰弹性各向异性数值模拟方法

黄焱; 王建平; 孙剑桥

doi:10.6052/0459-1879-22-064

基于近场动力学的单晶冰弹性各向异性数值模拟方法

doi: 10.6052/0459-1879-22-064

天津大学水利工程仿真与安全国家重点实验室, 天津 300350

基金项目: 国家自然科学基金资助项目(52192690, 52192691, 52101327)

详细信息

作者简介:
孙剑桥, 助理研究员, 主要研究方向: 冰力学与冰工程学. E-mail: sun1008@tju.edu.cn

中图分类号: O343.8, P731.15
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- 文章访问数: 441
- HTML全文浏览量: 128
- PDF下载量: 93
- 被引次数: 0
出版历程
- 收稿日期: 2022-02-09
- 录用日期: 2022-04-22
- 网络出版日期: 2022-04-23
- 刊出日期: 2022-06-18

A NUMERICAL SIMULATION METHOD FOR THE ELASTIC ANISOTROPY OF SINGLE CRYSTAL ICE BASED ON PERIDYNAMICS

State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300350, China

摘要

摘要: 天然冰材料在变形与破坏行为上的各向异性特征是冰与结构相互作用中产生复杂载荷过程的关键诱因, 而天然冰各向异性的根源则在于单晶冰的各向异性. 目前, 学术界针对单晶冰各向异性的数值模拟方法研究仍较为缺乏. 为了准确再现天然冰材料的特殊力学性质, 本文基于近场动力学理论, 提出了一种单晶冰弹性各向异性的数值模拟方法. 该方法的核心思想是将单晶冰杨氏模量沿不同加载方向的变化规律引入到近场动力学力密度向量的影响函数中. 以前人实验测试得到的杨氏模量值为参考, 通过开展与C轴呈0°, 45°和90°三个加载方向的单晶冰单轴压缩数值模拟实验, 提出了针对该影响函数的修正和辅助参数标定方法, 最终在15°, 30°, 60°和75°等其他四个加载方向进行了验证. 结果表明: 本文提出的针对影响函数的修正与参数标定方法, 能够较为便捷地找到数值模型杨氏模量与参考杨氏模量相一致的影响函数最优解, 即本文提出的基于影响函数的近场动力学数值模拟方法, 能够合理、准确地模拟单晶冰的弹性各向异性行为. 本文研究成果可为后续多晶冰各向异性数值模拟方法的建立提供基础性参考.
- 近场动力学 /
- 单晶冰 /
- 弹性 /
- 各向异性 /
- 影响函数
Abstract: The anisotropy in the deformation and failure of natural ice, originating from the anisotropy of single crystal ice, is the main reason of the complex loading process during the ice-structure interaction. However, studies on the numerical simulation method of the anisotropy of single crystal ice are still rare in the academic community. To simulate such mechanical property of ice, a numerical simulation method for the elastic anisotropy of single crystal ice is proposed in this paper based on the theory of peridynamics. In the present method, the variation of Young's modulus of single crystal ice along different loading directions with respect to the c-axis obtained from published experimental results is adopted in the influence function of the force density vector in the state-based peridynamic model. Based on the numerical simulations of the uniaxial compression of single crystal ice along the loading directions of 0°, 45° and 90° with respect to the c-axis, correction method for the influence function of the peridynamic model, as well as the calibration procedure for the related auxiliary parameters, are proposed in this paper. Furthermore, validations of the Young's modulus for other loading directions including 15°, 30°, 60° and 75° are made, and good agreement has been achieved according to the comparison between the numerical and the reference experimental values. The results show that the correction method and calibration procedure presented in this paper can efficiently find the optimal solution to the influence function for the consistency between the Young's modulus of the numerical model and the reference Young's modulus from the published experiments, which indicates that the proposed numerical method based on peridynamic theory can sensibly simulate the elastic anisotropy behavior of single crystal ice. The main findings in this paper can provide basic reference for the future development of the numerical simulation method for the anisotropy of polycrystalline ice.
- peridynamics /
- single crystal ice /
- elastic /
- anisotropy /
- influence function

HTML全文

图 1 S2冰的水平向与垂向晶体切片^[15]

Figure 1. Horizontal and vertical sections of S2 ice^[15]

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图 2 单晶冰弹性各向异性表征图^[9]

Figure 2. Reference Young's modulus as a function of orientation^[9]

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图 3 各向同性模型及载荷条件(单位: mm)

Figure 3. Isotropic model and loading conditions (unit: mm)

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图 4 各粒子间距模型中心轴Z向位移与有限元结果的对比

Figure 4. Displacement variation along the loading direction

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图 5 恒定应变率加载模型(单位: mm)

Figure 5. Constant strain rate loading model (unit: mm)

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图 6 名义应力-名义应变曲线

Figure 6. Nominal stress-nominal strain curve

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图 7 两种不同α时的杨氏模量对比

Figure 7. Comparison of Young's modulus for two different α

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图 8 α, β, γ及三个方向杨氏模量的相对误差随着迭代次数的变化

Figure 8. α, β, γ and the relative error of Young's modulus as a function of iteration number

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图 9 总误差随着迭代次数的变化

Figure 9. Total error as a function of iteration number

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图 10 杨氏模量随加载方向的变化趋势对比

Figure 10. Graphic comparison of Young's modulus under different loading directions

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表 1 四个加载方向的杨氏模量计算结果及其相对误差

Table 1. Young's modulus of the numerical model under different loading directions and the relative error

Φ/(°) Young's modulus
of model/GPa Young's modulus
in Ref. [9]/GPa Relative
error/%

15 10.51 10.98 4.24
30 9.394 9.598 2.12
60 8.778 8.796 0.203
75 9.222 9.299 0.832

下载: 导出CSV

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