Fractional Burgers models in creep and stress relaxation tests |
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| Institution: | 1. Department of Mechanics, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21000 Novi Sad, Serbia;2. Mathematical Institute, Serbian Academy of Arts and Sciences, Kneza Mihaila 36, 11000 Belgrade, Serbia;3. Department of Physics, Faculty of Sciences, University of Novi Sad, Trg D. Obradovića 4, 21000 Novi Sad, Serbia;1. Dublin City University, Dublin, Ireland;2. University of Oslo, Oslo, Norway;1. Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, Novi Sad, Serbia;2. Department of Physics, Faculty of Sciences, University of Novi Sad, Trg D. Obradovića 4, Novi Sad, Serbia;3. Mathematical Institute, Serbian Academy of Arts and Sciences, Kneza Mihaila 36, Belgrade, Serbia;1. Department of Physics, Faculty of Sciences, University of Ngaoundéré, P.O. Box 454, Ngaoundéré, Cameroon;2. Department of Mechanical Petroleum and Gas Engineering, Faculty of Mines and Petroleum Industries University of Maroua, P.O. Box 46, Maroua, Cameroon;3. Department of Petroleum and Gas Engineering, School of Geology and Mining Engineering, University of Ngaoundéré, P.O. Box 454, Ngaoundéré, Cameroon |
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| Abstract: | Classical and thermodynamically consistent fractional Burgers models are examined in creep and stress relaxation tests. Using the Laplace transform method, the creep compliance and relaxation modulus are obtained in integral form, that yielded, when compared to the thermodynamical requirements, the narrower range of model parameters in which the creep compliance is a Bernstein function while the relaxation modulus is completely monotonic. Moreover, the relaxation modulus may even be oscillatory function with decreasing amplitude. The asymptotic analysis of the creep compliance and relaxation modulus is performed near the initial time-instant and for large time as well. |
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