Modelling of frequency- and amplitude-dependent material properties of filler-reinforced rubber. (English) Zbl 1273.74065
Summary: Filler-reinforced elastomers are extremely complicated materials with pronounced deformation and temperature history-dependent material properties. In the current paper, the dynamic material behaviour is investigated and modelled. To this end, a carbon black-filled rubber compound is loaded with harmonic deformations under different frequencies and amplitudes and the stationary stress response is evaluated in terms of the storage and the loss modulus or, equivalently, in terms of the dynamic modulus and the loss angle. In this essay, detailed experimental investigations of the dynamic material properties of carbon black-filled elastomers are provided and a new three-dimensional constitutive approach of finite nonlinear viscoelasticity to represent the observed material behaviour is developed.
MSC:
| 74E30 | Composite and mixture properties |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
References:
| [1] | Arruda, E. M.; Boyce, M. C., A three-dimensional constitutive model for the large stretch behaviour of rubber elastic materials, Journal of the Mechanics and Physics of Solids, 41, 2, 389-412 (1993) · Zbl 1355.74020 |
| [2] | Bergström, J. S.; Boyce, M. C., Constitutive modelling of large strain time-dependent behaviour of elastomers, Journal of the Mechanics and Physics of Solids, 46, 5, 931-954 (1998) · Zbl 1056.74500 |
| [3] | Coleman, B. D.; Mizel, V. J., On the general theory of fading memory, Archive for Rational Mechanics and Analysis, 29, 1, 18-31 (1968) · Zbl 0167.24704 |
| [4] | Göktepe, S.; Miehe, C., A new micromechanical based approach for the elastic response of rubber-like materials at large strains, Proceedings of Applied Mathematics and Mechanics, 3, 174-175 (2003) · Zbl 1354.74192 |
| [5] | Govindjee, S.; Reese, S., A presentation and comparison of two large deformation viscoelasticity models, Journal of Engineering Materials and Technology, 119, 251-255 (1997) |
| [6] | Govindjee, S.; Simo, J., Mullins’ effect and the strain amplitude dependence of the storage modulus, International Journal of Solids and Structures, 29, 14/15, 1737-1751 (1992) · Zbl 0764.73073 |
| [7] | Haupt, P., Continuum Mechanics and Theory of Materials (2002), Springer: Springer Berlin · Zbl 0993.74001 |
| [8] | Haupt, P.; Lion, A., On finite linear viscoelasticity of incompressible isotropic materials, Acta Mechanica, 159, 87-124 (2002) · Zbl 1143.74312 |
| [9] | Haupt, P.; Lion, A.; Backhaus, E., On the dynamic behaviour of polymers under finite strains: constitutive modelling and identification of parameters, International Journal of Solids and Structures, 37, 3633-3646 (2000) · Zbl 0997.74013 |
| [10] | Heimes, T., 2005. Finite thermoinelastizität. Ph.D. Thesis, Institut für Mechanik, Universität der Bundeswehr München.; Heimes, T., 2005. Finite thermoinelastizität. Ph.D. Thesis, Institut für Mechanik, Universität der Bundeswehr München. |
| [11] | Heinrich, G., Härtel, V., Tschimmel, J., Klüppel, M., 2004. Kinetics of filler structures in reinforced polymer networks. In: Polymeric Materials 2004.; Heinrich, G., Härtel, V., Tschimmel, J., Klüppel, M., 2004. Kinetics of filler structures in reinforced polymer networks. In: Polymeric Materials 2004. |
| [12] | Höfer, P., 2007. Strain-induced nonlinearities of filler-reinforced rubber under cyclic deformations: experiments and modelling. In: Constitutive Models of Rubber.; Höfer, P., 2007. Strain-induced nonlinearities of filler-reinforced rubber under cyclic deformations: experiments and modelling. In: Constitutive Models of Rubber. |
| [13] | Holzapfel, G. A., Nonlinear Solid Mechanics—A Continuum Approach for Engineering (2000), Wiley: Wiley New York · Zbl 0980.74001 |
| [14] | Huber, G.; Vilgis, T.; Heinrich, G., Universal properties in the dynamical deformation of filled rubbers, Journal of Physics: Condensed Matter, 8, L409-L412 (1996) |
| [15] | Ihlemann, J., 2004. Kontinuumsmechanische nachbildung hochbelasteter technischer Gummiwerkstoffe. Dissertation, Institut für Mechanik der Universität Hannover, Fortschritt-Berichte VDI, Reihe 18, Nr. 288pp.; Ihlemann, J., 2004. Kontinuumsmechanische nachbildung hochbelasteter technischer Gummiwerkstoffe. Dissertation, Institut für Mechanik der Universität Hannover, Fortschritt-Berichte VDI, Reihe 18, Nr. 288pp. |
| [16] | Ihlemann, J., Richtungsabhängigkeit beim Mullins-effekt, Kautschuk Gummi Kunststoffe, 58, 438-447 (2005) |
| [17] | Kaliske, M.; Heinrich, G., Eine formulierung von gummielastizität und viskoelastizität mit schädigung für finite-elemente-simulationen, Kautschuk Gummi Kunststoffe, 53, 110-117 (2000) |
| [18] | Klüppel, M.; Heinrich, G., Physics and engineering of reinforced elastomers: from molecular mechanisms to industrial applications, Kautschuk Gummi Kunststoffe, 58, 217-224 (2005) |
| [19] | Kraus, G., Mechanical losses in carbon-black-filled rubbers, Journal of Applied Polymer Science: Applied Polymer Symposium, 39, 75-92 (1984) |
| [20] | Lion, A., A constitutive model for carbon black-filled rubber: experimental investigations and mathematical modeling, Continuum Mechanics and Thermodynamics, 8, 153-169 (1996) |
| [21] | Lion, A., On the large deformation behaviour of reinforced rubber at different temperatures, Journal of the Mechanics and Physics of Solids, 45, 1805-1834 (1997) |
| [22] | Lion, A., Thixotropic behaviour of rubber under dynamic loading histories: experiments and theory, Journal of the Mechanics and Physics of Solids, 46, 895-930 (1998) · Zbl 1056.74503 |
| [23] | Lion, A.; Höfer, P., On the phenomenological representation of curing phenomena in continuum mechanics, Archives of Mechanics, 59, 59-89 (2007) · Zbl 1175.74012 |
| [24] | Lion, A.; Kardelky, C., The Payne effect in finite viscoelasticity: constitutive modelling based on fractional derivatives and intrinsic time scales, International Journal of Plasticity, 20, 1313-1345 (2004) · Zbl 1066.74524 |
| [25] | Malvern, L., Introduction to the Mechanics of a Continuous Medium (1969), Prentice-Hall: Prentice-Hall New Jersey |
| [26] | Miehe, C., Discontinuous and continuous damage evolution in ogden-type large-strain elastic materials, European Journal of Mechanics A/Solids, 14, 5, 697-720 (1995) · Zbl 0837.73054 |
| [27] | Mullins, L., Softening of rubber by deformation, Rubber Chemistry and Technology, 42, 1, 339-362 (1969) |
| [28] | Ogden, R. W., Non-Linear Elastic Deformations (1997), Dover Publications, Inc. · Zbl 0938.74014 |
| [29] | Payne, A., Dynamic mechanical properties of filler loaded vulcanisates, Rubber and Plastics Age, 42, 963-967 (1961) |
| [30] | Qi, H. J.; Boyce, M. C., Constitutive model for stretch-induced softening of the stress-stretch behavior of elastomeric materials, Journal of the Mechanics and Physics of Solids, 52, 2187-2205 (2004) · Zbl 1115.74311 |
| [31] | Rabkin, M., Brüger, T., 2001. A constitutive model of elastomers in the case of cyclic load with amplitude-dependent internal damping. In: Constitutive Models for Rubber.; Rabkin, M., Brüger, T., 2001. A constitutive model of elastomers in the case of cyclic load with amplitude-dependent internal damping. In: Constitutive Models for Rubber. |
| [32] | Reese, S.; Govindjee, S., A theory of finite viscoelasticity and numerical aspects, International Journal of Solids and Structures, 35, 26-27, 3455-3482 (1998) · Zbl 0918.73028 |
| [33] | Robertson, C.; Wang, X., Spectral hole burning to probe the nature of unjamming (payne effect) in particle-filled elastomers, Europhysics Letters, 76, 278-284 (2006) |
| [34] | Roland, C., Dynamic mechanical behaviour of filled rubber at small strains, Journal of Rheology, 34, 25-34 (1990) |
| [35] | Ulmer, J., Strain dependence of dynamic mechanical properties of carbon black-filled rubber compounds, Rubber Chemistry and Technology, 69, 15-47 (1996) |
| [36] | von Tobolsky, A., 1967. Mechanische eigenschaften und struktur von polymeren. Berliner Union Stuttgart, deutsche Übersetzung bearbeitet und ergänzt von M. Hoffmann.; von Tobolsky, A., 1967. Mechanische eigenschaften und struktur von polymeren. Berliner Union Stuttgart, deutsche Übersetzung bearbeitet und ergänzt von M. Hoffmann. |
| [37] | Wrana, C.; Fischer, C.; Härtel, V., Dynamische messungen an gefüllten elastomersystemen bei mono- und bimodaler sinusförmiger anregung, Kautschuk Gummi Kunststoffe, 56, 437-443 (2003) |
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