Viscoelastic materials are widely used as devices for vibration control in modern engineering applications. They exhibit both viscous and elastic characteristic when undergoing deformation. They are mainly characterized by three time-dependent mechanical properties such as creep, stress relaxation and hysteresis. Among them, stress relaxation is one of the most important features in the characterization of viscoelastic materials. This phenomenon is defined as a time-dependent decrease in stress under a constant strain. Due to the inherent nonlinearity shown by the material response over a certain range of strain when viscoelastic materials are subjected to external loads, nonlinear rheological models are needed to better describe the experimental data. In this study, a singlenonlinear differential constitutive equation is derived froma nonlinear rheological model composed of a generalized nonlinear Maxwell fluid model in parallel with a nonlinear spring obeying a power law for the prediction of the stress relaxation behavior in viscoelastic materials. Under a constant strain-history, the time-dependent stress is analytically derived in the cases where the positive power law exponent, α ˂ 1 and α ˃1. The Trust Region Method available in MATLAB Optimization Toolbox is used to identify the material parameters. Significant correlations are found between the experimental relaxation data taken from literature and exact analytical predictions. The obtained results show that the developed rheological model with integer and non-integer orders nonlinearities accurately describes the experimental relaxation data of some viscoelastic materials.
| Published in | International Journal of Materials Science and Applications (Volume 12, Issue 1) |
| DOI | 10.11648/j.ijmsa.20231201.11 |
| Page(s) | 1-7 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2023. Published by Science Publishing Group |
Nonlinear Rheological Model, Integer and Non-Integer Orders Nonlinearities, Stress Relaxation, Viscoelastic Materials
| [1] |
APA Style
Kpomahou, Y. J. F., Agbélélé, K. J., Yamadjako, A. E., Ambelohoun, B. K. A. (2023). A Rheological Model with Integer and Non-Integer Orders Nonlinearities for Predicting Stress Relaxation Behavior in Viscoelastic Materials. International Journal of Materials Science and Applications, 12(1), 1-7. https://doi.org/10.11648/j.ijmsa.20231201.11
ACS Style
Kpomahou, Y. J. F.; Agbélélé, K. J.; Yamadjako, A. E.; Ambelohoun, B. K. A. A Rheological Model with Integer and Non-Integer Orders Nonlinearities for Predicting Stress Relaxation Behavior in Viscoelastic Materials. Int. J. Mater. Sci. Appl. 2023, 12(1), 1-7. doi: 10.11648/j.ijmsa.20231201.11
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Download@article{10.11648/j.ijmsa.20231201.11,
author = {Yélomè Judicaël Fernando Kpomahou and Koffi Judicaël Agbélélé and Arnaud Edouard Yamadjako and Bachir Koladé Adélakoun Ambelohoun},
title = {A Rheological Model with Integer and Non-Integer Orders Nonlinearities for Predicting Stress Relaxation Behavior in Viscoelastic Materials},
journal = {International Journal of Materials Science and Applications},
volume = {12},
number = {1},
pages = {1-7},
doi = {10.11648/j.ijmsa.20231201.11},
url = {https://doi.org/10.11648/j.ijmsa.20231201.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmsa.20231201.11},
abstract = {Viscoelastic materials are widely used as devices for vibration control in modern engineering applications. They exhibit both viscous and elastic characteristic when undergoing deformation. They are mainly characterized by three time-dependent mechanical properties such as creep, stress relaxation and hysteresis. Among them, stress relaxation is one of the most important features in the characterization of viscoelastic materials. This phenomenon is defined as a time-dependent decrease in stress under a constant strain. Due to the inherent nonlinearity shown by the material response over a certain range of strain when viscoelastic materials are subjected to external loads, nonlinear rheological models are needed to better describe the experimental data. In this study, a singlenonlinear differential constitutive equation is derived froma nonlinear rheological model composed of a generalized nonlinear Maxwell fluid model in parallel with a nonlinear spring obeying a power law for the prediction of the stress relaxation behavior in viscoelastic materials. Under a constant strain-history, the time-dependent stress is analytically derived in the cases where the positive power law exponent, α ˂ 1 and α ˃1. The Trust Region Method available in MATLAB Optimization Toolbox is used to identify the material parameters. Significant correlations are found between the experimental relaxation data taken from literature and exact analytical predictions. The obtained results show that the developed rheological model with integer and non-integer orders nonlinearities accurately describes the experimental relaxation data of some viscoelastic materials.},
year = {2023}
}
TY - JOUR T1 - A Rheological Model with Integer and Non-Integer Orders Nonlinearities for Predicting Stress Relaxation Behavior in Viscoelastic Materials AU - Yélomè Judicaël Fernando Kpomahou AU - Koffi Judicaël Agbélélé AU - Arnaud Edouard Yamadjako AU - Bachir Koladé Adélakoun Ambelohoun Y1 - 2023/03/04 PY - 2023 N1 - https://doi.org/10.11648/j.ijmsa.20231201.11 DO - 10.11648/j.ijmsa.20231201.11 T2 - International Journal of Materials Science and Applications JF - International Journal of Materials Science and Applications JO - International Journal of Materials Science and Applications SP - 1 EP - 7 PB - Science Publishing Group SN - 2327-2643 UR - https://doi.org/10.11648/j.ijmsa.20231201.11 AB - Viscoelastic materials are widely used as devices for vibration control in modern engineering applications. They exhibit both viscous and elastic characteristic when undergoing deformation. They are mainly characterized by three time-dependent mechanical properties such as creep, stress relaxation and hysteresis. Among them, stress relaxation is one of the most important features in the characterization of viscoelastic materials. This phenomenon is defined as a time-dependent decrease in stress under a constant strain. Due to the inherent nonlinearity shown by the material response over a certain range of strain when viscoelastic materials are subjected to external loads, nonlinear rheological models are needed to better describe the experimental data. In this study, a singlenonlinear differential constitutive equation is derived froma nonlinear rheological model composed of a generalized nonlinear Maxwell fluid model in parallel with a nonlinear spring obeying a power law for the prediction of the stress relaxation behavior in viscoelastic materials. Under a constant strain-history, the time-dependent stress is analytically derived in the cases where the positive power law exponent, α ˂ 1 and α ˃1. The Trust Region Method available in MATLAB Optimization Toolbox is used to identify the material parameters. Significant correlations are found between the experimental relaxation data taken from literature and exact analytical predictions. The obtained results show that the developed rheological model with integer and non-integer orders nonlinearities accurately describes the experimental relaxation data of some viscoelastic materials. VL - 12 IS - 1 ER -
Normal High School of Technical Teaching (ENSET) of Lokossa, National University of Sciences Technologies, Engineering and Mathematics (UNSTIM) of Abomey, Abomey, Benin
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