基于空间分数阶导数的强-弱非局部连续介质本构建模

方俊; 吴一石

doi:10.21656/1000-0887.450073

基于空间分数阶导数的强-弱非局部连续介质本构建模

doi: 10.21656/1000-0887.450073

方俊^1, ,,
吴一石²

1.
南京工业职业技术大学公共基础课部，南京 210023
2.
中国华电集团有限公司上海分公司，上海 200100

基金项目:

江苏省高校自然科学基金(面上项目) 21KJB510005

详细信息

通讯作者:
方俊(1986—)，男，副教授，博士(通讯作者. E-mail: 346801730@qq.com)

中图分类号: O345;O302
计量
- 文章访问数: 49
- HTML全文浏览量: 13
- PDF下载量: 6
- 被引次数: 0
出版历程
- 收稿日期: 2024-03-22
- 修回日期: 2024-05-06
- 刊出日期: 2025-06-01

Strong-Weak Non-Local Medium Constitutive Modeling Based on the Spatial Fractional Derivative

FANG Jun^{1
, ,},
WU Yishi²

1.
Department of General Foundation Requisite, Nanjing Vocational University of Industry Technology, Nanjing 210023, P.R.China
2.
China Huadian Corporation Shanghai Branch, Shanghai 200100, P.R.China

摘要

摘要: 研究了以空间分数阶导数为基础的非局部介质本构建模方法，为研究复杂非局部材料的力学性能提供了理论指导. 首先，通过扩展Chen-Holm分数阶Laplace算子的定义，得到了新型0~4阶空间分数阶导数算子. 然后，基于强-弱非局部连续介质理论，建立了含该算子的非局部介质本构关系，并以此构建了新的力学元件. 通过对力学元件的不同组合，可以得到几类非局部分数阶导数本构模型：Kelvin模型、Maxwell模型和Zener模型. 此后，基于散射波方程与介质本构方程之间的关联性，确定了模型各参数的表达式及物理意义，并研究了部分模型的蠕变和应力松弛. 最后，通过含砂软土蠕变的实例研究，验证了非局部Kelvin模型的有效性.
- 分数阶导数 /
- 非局部介质 /
- 本构建模 /
- 散射波方程 /
- 蠕变柔量
Abstract: The non-local medium constitutive modeling method based on the spatial fractional derivative was studied, which provides a theoretical guidance for studying the mechanical properties of complex non-local materials. Firstly, the definition of the Chen-Holm fractional-order Laplace operator was extended, to obtain a new-type 0th- to 4th-order spatial fractional derivative operator. Then the constitutive relation of the non-local medium containing the new operator was established based on the strong-weak non-local continuum theory, with some new mechanical elements constructed. Through different combinations of mechanical elements, several types of non-local fractional derivative constitutive models were obtained: the Kelvin model, the Maxwell model and the Zener model. Based on the correlation between the scattered wave equations and the medium constitutive equations, the expressions and physical meanings of the model parameters were determined, and the creep and stress relaxation of some models were studied. Finally, the effectiveness of the non-local Kelvin model was verified by the case study of creep in sand-bearing soft soil.
- fractional derivative /
- non-local medium /
- constitutive modeling /
- scattering wave equation /
- creep flexibility

HTML全文

图 1 非局部弹簧元件

Figure 1. The non-local spring element

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图 2 非局部阻尼元件

Figure 2. The non-local damper element

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图 3 非局部Kelvin模型

Figure 3. The non-local Kelvin model

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图 4 修正的非局部Kelvin模型

Figure 4. The modified non-local Kelvin model

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图 5 非局部Maxwell模型

Figure 5. The non-local Maxwell model

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图 6 非局部Zener模型

Figure 6. The non-local Zener model

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图 7 当d=10⁴时，不同分数阶阶数s对应的非局部Kelvin模型在空间频域的蠕变曲线

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 7. For d=10⁴, the creep curves of the non-local Kelvin model corresponding to different fractional orders s in the spatial frequency domain

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图 8 当s=0.1时，不同杂质平均尺寸d对应的非局部Kelvin模型在空间频域的蠕变曲线

Figure 8. For s=0.1, the creep curves of the non-local Kelvin model corresponding to different average sizes d of impurities in the spatial frequency domain

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图 9 当d=10时，不同分数阶阶数s对应的非局部Maxwell模型在空间频域的应力松弛曲线

Figure 9. For d=10, the stress relaxation curves of the non-local Maxwell model corresponding to different fractional orders s in the spatial frequency domain

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图 10 当s=0.1时，不同杂质平均尺寸d对应的非局部Maxwell模型在空间频域的应力松弛曲线

Figure 10. For s=0.1, the stress relaxation curves of the non-local Maxwell model corresponding to different average sizes d of impurities in the spatial frequency domain

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图 11 非局部Kelvin模型与经典Kelvin模型对含砂软土蠕变柔量的拟合曲线(荷载37.5 kPa)

Figure 11. Fitting curves for the creep flexibility of sand-bearing soft soil according to the non-local Kelvin model and the classical Kelvin model(37.5 kPa)

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图 12 非局部Kelvin模型与经典Kelvin模型对含砂软土蠕变柔量的拟合曲线(荷载87.5 kPa)

Figure 12. Fitting curves for the creep flexibility of sand-bearing soft soil according to the non-local Kelvin model and the classical Kelvin model(87.5 kPa)

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