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

FANG Jun; WU Yishi

doi:10.21656/1000-0887.450073

Volume 46 Issue 6

Jun. 2025

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FANG Jun, WU Yishi. Strong-Weak Non-Local Medium Constitutive Modeling Based on the Spatial Fractional Derivative[J]. Applied Mathematics and Mechanics, 2025, 46(6): 764-780. doi: 10.21656/1000-0887.450073

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

doi: 10.21656/1000-0887.450073

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

Received Date: 2024-03-22
Rev Recd Date: 2024-05-06
Publish Date: 2025-06-01

Abstract

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

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References

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