Accurate and straightforward symplectic approach for fracture analysis of fractional viscoelastic media |
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Authors: | Xu Chenghui Leng Sen Zhou Zhenhuan Xu Xinsheng Deng Zichen |
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Institution: | 1. MIIT Key Laboratory of Dynamics and Control of Complex Systems, Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, China;2. State Key Laboratory of Structure Analysis of Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, Liaoning Province, China |
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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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Keywords: | symplectic approach viscoelastic material fractional Kelvin-Zener model crack fracture parameter |
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