Investigation on stress wave propagation in mesoscopic discontinuous medium

YUAN Liangzhu; CHEN Meiduo; XIE Yushan; LU Jianhua; WANG Pengfei; XU Songlin

doi:10.11883/bzycj-2023-0365

Volume 44 Issue 9

Sep. 2024

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Article Navigation > Explosion And Shock Waves > 2024 > 44(9): 091422

YUAN Liangzhu, CHEN Meiduo, XIE Yushan, LU Jianhua, WANG Pengfei, XU Songlin. Investigation on stress wave propagation in mesoscopic discontinuous medium[J]. Explosion And Shock Waves, 2024, 44(9): 091422. doi: 10.11883/bzycj-2023-0365

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YUAN Liangzhu, CHEN Meiduo, XIE Yushan, LU Jianhua, WANG Pengfei, XU Songlin. Investigation on stress wave propagation in mesoscopic discontinuous medium[J]. Explosion And Shock Waves, 2024, 44(9): 091422. doi: 10.11883/bzycj-2023-0365

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Investigation on stress wave propagation in mesoscopic discontinuous medium

doi: 10.11883/bzycj-2023-0365

1.
CAS Key Laboratory for Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei 230027, Anhui, China
2.
United Laboratory of High-Pressure Physics and Earthquake Science, Institute of Earthquake Forecasting, China Earthquake Administration, Beijing 100036, China

Received Date: 2023-10-09
Rev Recd Date: 2023-12-14

Available Online: 2024-02-04

Publish Date: 2024-09-20

Abstract

Abstract

Solid mediums, like rocks, concretes, shells and porous materials, etc., has the characteristics of microscopic discontinuity and macroscopic continuity. It is of great significance for material design, safety protection and other fields to reveal the influence of the meso-discontinuity on the dynamic response of the material. In this paper, based on the generalized Taylor’s formula under fractional definition, the governing equation of 1-D wave propagation in discontinuous medium is derived. Equivalent fractional order is introduced and the simplified form of the governing equation is presented for easily calculating. By using the finite difference method, the numerical solution of the governing equation is obtained. The influence of equivalent fractional order on wave propagation are analyzed. By the time domain analysis, the smaller the equivalent fractional order, the greater the degree of attenuation of the calculated waveform. By the frequency domain analysis, both high frequency wave and low frequency wave exhibit attenuation, and the attenuation of high frequency wave is higher than that of low frequency wave, which makes the pulse duration of the wave being larger. It is obvious that the equivalent fractional order has a certain relationship with the spatial structure of discontinuous medium. Based on the structural characteristics of some meso-discontinuous medium, e.g., porous materials and rocks, a randomly distributed pores model is established by using ABAQUS to verify the reliability of the governing equation and study the wave propagation of meso-discontinuous medium. The effects of porosity, material properties and input waves on wave propagation are analyzed. The degree of wave attenuation is positively related to the porosity of the medium, and negatively related to the wave velocity and the pulse duration of input wave. However, the equivalent fractional order is only related to the porosity and pore distribution of the discontinuous medium. When the spatial structure of the discontinuous medium remains unchanged, the corresponding equivalent fractional order does not change with the material property and the pulse duration of the input wave. By the randomly distributed pores model with various porosities, it is found that the equivalent fractional order decreases with the increase of porosity. Under the same porosity, the heterogeneity of pore distribution will result in different waveforms, while with the increase of porosity, this difference becomes more obvious, but the corresponding equivalent fractional order only has little difference. The statistical relation between equivalent fractional order and porosity is approximately linear when the pore distribution is almost the same. Compared with the randomly distributed pores medium, the statistical relation between equivalent fractional order and porosity of discontinuous medium with uniform distribution of different porosity shifts upward, indicating that the attenuation effect of random structure on wave is higher than that of uniform structure. This paper provides a new approach to investigate wave propagation in meso-discontinuous medium such as porous materials, rocks, shells, etc. It can be used as a basis to evaluate the dynamic response of discontinuous medium.
- fractional derivative,
- meso-discontinuous,
- wave propagation,
- finite difference method,
- equivalent fractional order

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