Dynamic properties of oyster shells based on a fractional-order model

YUAN Liangzhu; LU Jianhua; MIAO Chunhe; WANG Pengfei; XU Songlin

doi:10.11883/bzycj-2022-0318

Volume 43 Issue 1

Jan. 2023

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YUAN Liangzhu, LU Jianhua, MIAO Chunhe, WANG Pengfei, XU Songlin. Dynamic properties of oyster shells based on a fractional-order model[J]. Explosion And Shock Waves, 2023, 43(1): 011101. doi: 10.11883/bzycj-2022-0318

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YUAN Liangzhu, LU Jianhua, MIAO Chunhe, WANG Pengfei, XU Songlin. Dynamic properties of oyster shells based on a fractional-order model[J]. Explosion And Shock Waves, 2023, 43(1): 011101. doi: 10.11883/bzycj-2022-0318

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Dynamic properties of oyster shells based on a fractional-order model

doi: 10.11883/bzycj-2022-0318

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: 2022-07-21
Rev Recd Date: 2022-10-11

Available Online: 2022-11-21

Publish Date: 2023-01-05

Abstract

Abstract

Natural materials such as shells and oysters have attracted extensive attention in the field of material design due to their lightweight and high-strength mechanical properties. However, due to the complex structure of shells, it is very difficult to study their mechanical behavior. In recent years, fractional-order models have been successful in studying the mechanical properties of materials. Compared with the traditional constitutive model, the fractional model can better characterize the relationship between the complex media’s stress or strain and time. Therefore, based on wave propagation theory and by using the time-dependent fractional-order model as the material constitutive model, the complex medium is simplified to the uniform medium, and its governing equation is obtained by then. The analytic solution of the governing equation which is a function of space coordinate x and Laplace variable s is obtained by the Laplace transform. It is hard to obtain the analytical solution of space coordinate x and time t directly through the inverse Laplace transform, so the numerical inverse Laplace transform is used to obtain the numerical solution of the governing equation in the time domain. The sensitivity of wave attenuation to parameters in the fractional model is analyzed. The inertial properties, which are different from the elastic and viscous properties of materials, are also discussed by analyzing the attenuation characteristics of stress waves when the order α is 0, 1.0, and 2.0 respectively. Then, based on the analytical solution of the governing equation and a variety of experimental test signals, a fitting formula is given to obtain the parameters of the fractional model. Oyster material with layered structure is taken as the research object. To obtain the local dynamic mechanical properties of oyster samples, the CO₂ pulse laser was used to carry out the impact loading of the small sample due to the high variability of the density distribution of oyster samples, and the two-point laser interferometer velocimetry system (VISAR) was used to measure the surface particle velocity. The particle velocity time history curve of the oyster sample with different densities and thicknesses was obtained. Combined with the above fitting formula, the parameters of the Abel model and Maxwell fractional differential model of oyster samples were obtained by fixing and unfixing the values of fractional order α, and the model parameters reflected the fine microstructure characteristics of oyster samples. The results show that the higher the density of the oyster sample is, the higher the proportion of nacre with brick and mortar structure in fine and micro, the greater the velocity attenuation, and the greater the viscosity of the oyster sample. The laser wavelength emitted by the CO₂ laser pulse is similar to the size of the gap between brick and mortar structures in the nacre of the oyster sample, so the laser has a large scattering when it impacts the nacre of the oyster sample, which causes the velocity attenuation. This study has a good reference significance for the study of the dynamic properties of meso-isomeric and macro-continuous complex media.
- fractional derivative,
- constitutive model,
- oyster shell,
- pulse laser,
- dynamic properties

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References(33)

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