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

doi:10.1007/s10483-022-2825-8

Abstract

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.

Key words: symplectic approach, viscoelastic material, fractional Kelvin-Zener model, crack, fracture parameter

2010 MSC Number:

74D05
74R99

Chenghui XU, Sen LENG, Zhenhuan ZHOU, Xinsheng XU, Zichen DENG. Accurate and straightforward symplectic approach for fracture analysis of fractional viscoelastic media. Applied Mathematics and Mechanics (English Edition), 2022, 43(3): 403-416.

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