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Bir Fenomenolojik Yapısal Modelin Kauçuk Tipi Malzemeler İçin Sonlu Elemanlar Yöntemi Uygulaması

Year 2021, Issue: 24, 359 - 363, 15.04.2021
https://doi.org/10.31590/ejosat.901867

Abstract

Bu makalede, kauçuk tipi malzemelerin yapısal olarak modellenmesi için yakın zamanda önerilmiş olan bir fenomenolojik model sürekli ortamlar mekaniği ve kauçuk elastisitesi temellerine dayanarak sonlu elemanlar yöntemi içerisine adapte edilmiştir. Model, ilk önce saf silikon kauçuğun beş farklı yükleme altında gösterdiği hiperelastik davranışlara göre kalibre edilmiştir. Sonrasında modeli sonlu elemanlar yöntemi yazılımına adapte etmek için altprogram yazılmış ve üzerinde delikler olan saf silikon kauçuk levha yazılım içerisinde nümerik olarak modellenmiştir. Meunier ve diğerlerinin (Meunier, Chagnon, Favier, Orgéas, & Vacher, 2008) deneylerde yaptığı gibi kauçuk levha simülasyon içerisinde 57.2 mm dikey deplasmana maruz bırakılmıştır. Yapılan ölçümlerde nümerik modelin ve deneysel verilerin örtüştüğü görülmüştür.

References

  • Blaise, B. B., Bien-aimé, L. K., Betchewe, G., Marckman, G., & Beda, T. (2020). A phenomenological expression of strain energy in large elastic deformations of isotropic materials. Iranian Polymer Journal, 29(6),, 525-533.
  • Boyce, M. C., & Arruda, E. M. (2000). Constitutive models of rubber elasticity: a review. Rubber chemistry and technology, 73, 504-523.
  • Carroll, M. M. (2011). A strain energy function for vulcanized rubbers. Journal of Elasticity, 103, 173-187.
  • Darijani, H., & Naghdabadi, R. .. (2010). Hyperelastic materials behavior modeling using consistent strain energy density functions. Acta mechanica, 213(3), 235-254.
  • Diani, J., Fayolle, B., & Gilormini, P. (2009). A review on the Mullins effect. European Polymer Journal, 45, 601. doi:10.1016/j.eurpolymj.2008.11.017
  • Flory, P. J. (1961). Thermodynamic relations for high elastic materials. Transactions of the Faraday Society 57, 829-838.
  • Gent, A. N. (1996). A new constitutive relation for rubber. Rubber Chemistry and Technology, 69, 59.
  • Khiêm, V. N., & Itskov, M. (2016). Analytical network-averaging of the tube model: Rubber elasticity. Journal of the Mechanics and Physics of Solids, 95, 254-269.
  • Külcü, İ. D. (2020). A hyperelastic constitutive model for rubber-like materials. Archive of Applied Mechanics, 90, 615-622.
  • Mansouri, M., & Darijani, H. (2014). Constitutive modeling of isotropic hyperelastic materials in an exponential framework using a self-contained approach. International Journal of Solids and Structures 51(25–26), 4316–4326.
  • Meunier, L., Chagnon, G., Favier, D., Orgéas, L., & Vacher, P. (2008). Mechanical experimental characterisation and numerical modelling of an unfilled silicone rubber. Polymer testing, 27, 765-777.
  • Mooney, M. (1940). A theory of large elastic deformation. Journal of applied physics, 11, 582-592.
  • Ogden, R. W. (1972). Large deformation isotropic elasticity--on the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 326, 565-584.
  • Sasso, M., Palmieri, G., Chiappini, G., & Amodio, D. (2008). Characterization of hyperelastic rubber-like materials by biaxial and uniaxial stretching tests based on optical methods. Polymer Testing 27(8), 995–1004.
  • Steinmann, P., Hossain, M., & Possart, G. (2012). Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar’s data. Archive of Applied Mechanics, 82, 1183-1217.
  • Storm, C., Pastore, J., MacKintosh, F., Lubensky, T., & Janmey, P. (2005). Nonlinear elasticity in biological gels. Nature 435(7039), 191.
  • Sun, J.-Y., Zhao, X., Illeperuma, W. R., Chaudhuri, O., Oh, K. H., Mooney, D. J., . . . Suo, Z. (2012). Highly stretchable and tough hydrogels. Nature, 489, 133-136.
  • Treloar, L. R. (1944). Stress-strain data for vulcanized rubber under various types of deformation. . Rubber Chemistry and Technology, 17(4), 813-825.
  • Yeoh, O. H. (1990). Characterization of elastic properties of carbon-black-filled rubber vulcanizates. Rubber chemistry and technology, 63, 792-805.
  • Yeoh, O. H., & Fleming, P. D. (1997). A new attempt to reconcile the statistical and phenomenological theories of rubber elasticity. Journal of Polymer Science Part B: Polymer Physics, 35(12)., 1919-1931.

A Finite Element Implementation of A Phenomenological Constitutive Model for Rubber-like Materials

Year 2021, Issue: 24, 359 - 363, 15.04.2021
https://doi.org/10.31590/ejosat.901867

Abstract

In this paper, a finite element implementation of a recently proposed phenomenological constitutive model for rubber-like materials is represented based on the fundamentals of continuum mechanics and rubber elasticity. The phenomenological model is first fitted to the hyperelastic behavior of an unfilled silicon rubber subjected to five different uniform deformations. Then, a subroutine is written to import the model into the finite element software and an unfilled silicon rubber sheet is numerically modeled in the commercial finite element software. As performed in the experiments by Meunier et al (Meunier, Chagnon, Favier, Orgéas, & Vacher, 2008)., the rubber sheet is deformed 57.2 mm along the vertical axes in the simulations. Good agreement between the numerical model and experimental data is obtained.

References

  • Blaise, B. B., Bien-aimé, L. K., Betchewe, G., Marckman, G., & Beda, T. (2020). A phenomenological expression of strain energy in large elastic deformations of isotropic materials. Iranian Polymer Journal, 29(6),, 525-533.
  • Boyce, M. C., & Arruda, E. M. (2000). Constitutive models of rubber elasticity: a review. Rubber chemistry and technology, 73, 504-523.
  • Carroll, M. M. (2011). A strain energy function for vulcanized rubbers. Journal of Elasticity, 103, 173-187.
  • Darijani, H., & Naghdabadi, R. .. (2010). Hyperelastic materials behavior modeling using consistent strain energy density functions. Acta mechanica, 213(3), 235-254.
  • Diani, J., Fayolle, B., & Gilormini, P. (2009). A review on the Mullins effect. European Polymer Journal, 45, 601. doi:10.1016/j.eurpolymj.2008.11.017
  • Flory, P. J. (1961). Thermodynamic relations for high elastic materials. Transactions of the Faraday Society 57, 829-838.
  • Gent, A. N. (1996). A new constitutive relation for rubber. Rubber Chemistry and Technology, 69, 59.
  • Khiêm, V. N., & Itskov, M. (2016). Analytical network-averaging of the tube model: Rubber elasticity. Journal of the Mechanics and Physics of Solids, 95, 254-269.
  • Külcü, İ. D. (2020). A hyperelastic constitutive model for rubber-like materials. Archive of Applied Mechanics, 90, 615-622.
  • Mansouri, M., & Darijani, H. (2014). Constitutive modeling of isotropic hyperelastic materials in an exponential framework using a self-contained approach. International Journal of Solids and Structures 51(25–26), 4316–4326.
  • Meunier, L., Chagnon, G., Favier, D., Orgéas, L., & Vacher, P. (2008). Mechanical experimental characterisation and numerical modelling of an unfilled silicone rubber. Polymer testing, 27, 765-777.
  • Mooney, M. (1940). A theory of large elastic deformation. Journal of applied physics, 11, 582-592.
  • Ogden, R. W. (1972). Large deformation isotropic elasticity--on the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 326, 565-584.
  • Sasso, M., Palmieri, G., Chiappini, G., & Amodio, D. (2008). Characterization of hyperelastic rubber-like materials by biaxial and uniaxial stretching tests based on optical methods. Polymer Testing 27(8), 995–1004.
  • Steinmann, P., Hossain, M., & Possart, G. (2012). Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar’s data. Archive of Applied Mechanics, 82, 1183-1217.
  • Storm, C., Pastore, J., MacKintosh, F., Lubensky, T., & Janmey, P. (2005). Nonlinear elasticity in biological gels. Nature 435(7039), 191.
  • Sun, J.-Y., Zhao, X., Illeperuma, W. R., Chaudhuri, O., Oh, K. H., Mooney, D. J., . . . Suo, Z. (2012). Highly stretchable and tough hydrogels. Nature, 489, 133-136.
  • Treloar, L. R. (1944). Stress-strain data for vulcanized rubber under various types of deformation. . Rubber Chemistry and Technology, 17(4), 813-825.
  • Yeoh, O. H. (1990). Characterization of elastic properties of carbon-black-filled rubber vulcanizates. Rubber chemistry and technology, 63, 792-805.
  • Yeoh, O. H., & Fleming, P. D. (1997). A new attempt to reconcile the statistical and phenomenological theories of rubber elasticity. Journal of Polymer Science Part B: Polymer Physics, 35(12)., 1919-1931.
There are 20 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

İsmail Doğan Külcü 0000-0001-5431-7802

Publication Date April 15, 2021
Published in Issue Year 2021 Issue: 24

Cite

APA Külcü, İ. D. (2021). A Finite Element Implementation of A Phenomenological Constitutive Model for Rubber-like Materials. Avrupa Bilim Ve Teknoloji Dergisi(24), 359-363. https://doi.org/10.31590/ejosat.901867