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Accurate and straightforward symplectic approach for fracture analysis of fractional viscoelastic media

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Abstract

An accurate and straightforward symplectic method is presented for the fracture analysis of fractional two-dimensional (2D) viscoelastic media. The fractional Kelvin-Zener constitutive model is used to describe the time-dependent behavior of viscoelastic materials. Within the framework of symplectic elasticity, the governing equations in the Hamiltonian form for the frequency domain (s-domain) can be directly and rigorously calculated. In the s-domain, the analytical solutions of the displacement and stress fields are constructed by superposing the symplectic eigensolutions without any trial function, and the explicit expressions of the intensity factors and J-integral are derived simultaneously. Comparison studies are provided to validate the accuracy and effectiveness of the present solutions. A detailed analysis is made to reveal the effects of viscoelastic parameters and applied loads on the intensity factors and J-integral.

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Authors and Affiliations

  1. MIIT Key Laboratory of Dynamics and Control of Complex Systems, Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an, 710072, China

    Chenghui Xu, Sen Leng & Zichen Deng

  2. State Key Laboratory of Structure Analysis of Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning Province, 116024, China

    Zhenhuan Zhou & Xinsheng Xu

Authors
  1. Chenghui Xu
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  2. Sen Leng
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  3. Zhenhuan Zhou
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  4. Xinsheng Xu
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  5. Zichen Deng
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Correspondence to Zichen Deng.

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Citation: XU, C. H., LENG, S., ZHOU, Z. H., XU, X. S., and DENG, Z. C. Accurate and straightforward symplectic approach for fracture analysis of fractional viscoelastic media. Applied Mathematics and Mechanics (English Edition), 43(3), 403–416 (2022) https://doi.org/10.1007/s10483-022-2825-8

Project supported by the National Natural Science Foundation of China (Nos. 11872303 and 11702221), the China Postdoctoral Science Foundation (No. 2017M613198), and the Fundamental Research Funds for the Central Universities of China (No. G2020KY05402)

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Xu, C., Leng, S., Zhou, Z. et al. Accurate and straightforward symplectic approach for fracture analysis of fractional viscoelastic media. Appl. Math. Mech.-Engl. Ed. 43, 403–416 (2022). https://doi.org/10.1007/s10483-022-2825-8

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  • DOI: https://doi.org/10.1007/s10483-022-2825-8

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