Constitutive equation with fractional derivatives for the generalized UCM model |
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| Authors: | Pan Yang Yee Cheong Lam Ke-Qin Zhu |
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| Institution: | 1. Institute for Polymers and Composites/i3N, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal;2. Instituto de Ciências Exatas e Naturais, Faculdade de Matemática, Universidade Federal do Pará, 66075-110 Belem, PA, Brasil;1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and Materials, Hohai University, Nanjing 210098, China;2. Department of Geological Sciences, University of Alabama, Tuscaloosa, AL 35487, United States;3. Department of Civil and Architectural Engineering, University of Wyoming, 1000 E. University Ave., Laramie, WY 82071, United States;4. School of Environmental Science & Engineering, Southern University of Science and Technology, Shenzhen 518055, China;1. Institute of Structures and Materials Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 211100, China;2. School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA |
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| Abstract: | A fundamental problem on the constitutive equation with fractional derivatives for the generalized upper convected Maxwell model (UCM) is studied. The existing investigations on the constitutive equation are reviewed and their limitations or deficiencies are highlighted. By utilizing the convected coordinates approach, a mathematically rigorous constitutive equation with fractional derivatives for the generalized UCM model is proposed, which has an explicit expression for the stress tensor. This model can be reduced to the linear generalized Maxwell model with fractional derivatives, the UCM model and some other existing models. In addition, the rheological properties of this proposed model in the start-up of simple shear and elongation flows are investigated. It is shown that this generalized UCM model can describe the various stress evolution processes and the strain hardening effect of the viscoelastic fluids. |
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