Characterizing the creep of viscoelastic materials by fractal derivative models |
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| Affiliation: | 1. Department of Mechanics, University of Novi Sad, Serbia;2. Department of Otorhinolaryngology, University of Novi Sad, Serbian;1. School of Civil Engineering, Lanzhou University of Technology, Lanzhou, Gansu 730050, China;2. Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of Education, Lanzhou, Gansu 730050, China;1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 210098, China;2. College of Mechanical and Electrical Engineering, Hohai University, Changzhou 213022, China |
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| Abstract: | In this paper, we make the first attempt to apply the fractal derivative to modeling viscoelastic behavior. The methodology of scaling transformation is utilized to obtain the creep modulus and relaxation compliance for the proposed fractal Maxwell and Kelvin models. Comparing with the fractional derivatives reported in the literature, the fractal derivative as a local operator has lower calculation costs and memory storage requirements. Moreover, numerical results show that the proposed fractal models require fewer parameters, have simpler mathematical expression and result in higher accuracy than the classical integer-order derivative models. Results further confirm that the proposed fractal models can characterize the creep behavior of viscoelastic materials. |
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| Keywords: | Fractal derivative Viscoelastic materials Scaling transformation Creep |
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