基于非局部微分算子的近场动力学及固体材料应力数值模拟

李树忱; 马鹏飞; 王修伟; 刘祥坤

doi:10.6052/j.issn.1000-4750.2021.07.0520

基于非局部微分算子的近场动力学及固体材料应力数值模拟

doi: 10.6052/j.issn.1000-4750.2021.07.0520

山东大学岩土与结构工程研究中心，山东，济南 250061

基金项目: 国家自然科学基金项目(51879150，41831278)

详细信息

作者简介:
李树忱(1973−)，男，黑龙江人，教授，博士，博导，主要从事深部岩体破坏机理研究(E-mail: shuchenli@sdu.edu.cn)

王修伟(1997−)，男，山东人，博士生，主要从事岩土工程数值模拟方面的研究(E-mail: wxwsdu@126.com)

刘祥坤(1997−)，男，山东人，硕士生，主要从事深部岩体破坏机理研究(E-mail: 15965610971@163.com)

通讯作者:
马鹏飞(1994−)，男，山东人，博士生，主要从事岩土工程数值模拟方面的研究(E-mail: mapengfeisdu@163.com)

中图分类号: O346.1+1
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- 被引次数: 0
出版历程
- 收稿日期: 2021-07-10
- 录用日期: 2021-12-10
- 修回日期: 2021-12-01
- 网络出版日期: 2021-12-10
- 刊出日期: 2022-11-01

PERIDYNAMICS AND NUMERICAL SIMULATION OF SOLID MATERIAL STRESS BASED ON NONLOCAL DIFFERENTIAL OPERATOR

Geotechnical and Structural Engineering Research Center, Shandong University, Jinan, Shandong 250061, China

摘要

摘要: 在经典近场动力学模型的基础上引入非局部微分算子求解理论，建立近场动力学微弹性应力分析模型。在近场动力学模型物质点处进行泰勒级数展开，利用正交非局部函数构建微分算子的数值积分方程并且根据矩阵正交性求解函数未知系数，最终由平衡方程等价性建立近场动力学应力求解模型。采用所提出的方法对固体材料变形破坏过程中的应力进行模拟，并将计算结果与理论解对比以验证方法有效性，同时对粒子离散间距、泰勒项数及权函数的数值收敛性进行分析。结果表明：该文提出的方法可以较准确的反映完整及非完整固体脆性材料在荷载作用下的应力分布，并且离散间距及权函数对数值收敛结果具有显著影响，可为使用近场动力学方法模拟变形破坏时提供新的应力分析思路，有着较为广泛的应用前景。
- 数值模拟 /
- 非局部方法 /
- 近场动力学 /
- 微分算子 /
- 应力分析
Abstract: Based on the classical peridynamic model, the nonlocal differential operator solution theory is introduced to establish the peridynamic micro-elastic stress analysis model. Taylor series expansion is carried out at the material point of the peridynamic model. The numerical integral equation of the differential operator is constructed by using the orthogonal nonlocal function, and the unknown coefficients of the function are solved according to the orthogonality of the matrix. Finally, the peridynamic stress solution model is established by the equivalence of the equilibrium equation. The proposed method is used to simulate the stress distribution in the deformation and failure process of solid materials, and the calculated results are compared with the theoretical solution to verify the effectiveness of the method proposed. At the same time, the numerical convergence of the particle discrete distance, Taylor term number and the weight function are analyzed. The simulation results show that the proposed method can accurately reflect the stress distribution of holonomic and nonholonomic solid brittle materials under loads. Moreover, the discrete distance and weight function have a significant influence on the numerical convergence. It can provide a new idea for stress analysis when using the extended peridynamics method to simulate deformation and failure and, has a wide application prospect.
- numerical simulation /
- nonlocal method /
- peridynamics /
- differential operator /
- stress analysis

HTML全文

图 1 物质点相互作用

Figure 1. Interaction of material points

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图 2 平板拉伸模型　/mm

Figure 2. Model of plate tension

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图 3 平板拉伸结果

Figure 3. Result of plate tension

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图 4 含圆孔平板模型　/mm

Figure 4. Model of plate with hole

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图 5 含圆孔平板计算结果

Figure 5. Calculation result of plate with hole

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图 6 含圆孔平板结果对比

Figure 6. Result comparison of plate with hole

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图 7 含裂隙平板模型　/mm

Figure 7. Model of plate with crack

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图 8 含裂隙平板计算结果

Figure 8. Calculation result of plate with crack

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图 9 局部结果对比

Figure 9. Comparison of local result

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图 10 裂纹渐进破坏

Figure 10. Crack progressive failure

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图 11 离散间距影响

Figure 11. Influence of particle discrete distance

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图 12 泰勒项数影响

Figure 12. Influence of Taylor term number

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图 13 权函数影响

Figure 13. Influence of weight function

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