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Finite element implementation of a microstructure-based model for filled elastomers. (English) Zbl 1426.74290

Summary: To describe the inelastic mechanical behavior of filled elastomers a microstructure-based material model for uniaxial loadings has been developed. The generalization of this one-dimensional material description to a fully three-dimensional constitutive model has been accomplished by using the concept of representative directions. The generalized model shows a very good agreement with cyclic uniaxial tension and compression tests as well as simple shear measurements for several rubber compounds. The FE-implementation enables finite element simulations of technical components though the original input model predicts the material behavior for uniaxial loadings only.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74E30 Composite and mixture properties
74Q15 Effective constitutive equations in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
Full Text: DOI

References:

[1] Ahmadi, H.R., Gough, J., Muhr, A.H., 1999. Bi-axial experimental techniques highlighting the limitations of strain-energy description of rubber. In: Dorfmann, A., Muhr, A. (Eds.), Constitutive Models for Rubber, pp. 65 – 71.
[2] Ahrendts, J.; Baehr, H. D.: Die anwendung nichtlinearer regressionsverfahren bei der aufstellung thermodynamischer zustandsgleichungen, Forsch. ing. Wes. 45, 51-56 (1979)
[3] Ames, N. M.; Srivastava, V.; Chester, S. A.; Anand, L.: A thermo-mechanically coupled theory for large deformations of amorphous polymers, Part II: appl. Int. J. Plast. 25, 1495-1539 (2009) · Zbl 1272.74083
[4] Anand, L.; Ames, N. M.; Srivastava, V.; Chester, S. A.: A thermo-mechanically coupled theory for large deformations of amorphous polymers. Part I: Formulation., Int. J. Plast. 25, 1474-1494 (2009) · Zbl 1165.74011 · doi:10.1016/j.ijplas.2008.11.004
[5] Anand, L.; Ames, N. M.: On modeling the micro-indentation response of an amorphous polymer, Int. J. Plast. 22, 1123-1170 (2006) · Zbl 1176.74038 · doi:10.1016/j.ijplas.2005.07.006
[6] Ayoub, G.; Zairi, F.; Nait-Abdelaziz, M.; Gloaguen, J. M.: Modelling large deformation behaviour under loading – unloading of semicrystalline polymers: application to a high density polyethylene, Int. J. Plast. 26, 329-347 (2010) · Zbl 1452.74023
[7] Besdo, D.; Ihlemann, J.: A phenomenological constitutive model for rubberlike materials and its numerical applications, Int. J. Plast. 19, 1019-1036 (2003) · Zbl 1090.74526 · doi:10.1016/S0749-6419(02)00091-8
[8] Besdo, D., Ihlemann, J., Kingston, J.G.R., Muhr, A.H., 2003. Modelling inelastic stress – strain phenomena and a scheme for efficient experimental characterization. In: Busfield, J., Muhr, A. (Eds.), Constitutive Models for Rubber III, pp. 309 – 317.
[9] Boukamel, A.: A thermo-viscoelastic model for elastomeric behaviour and its numerical application, Arch. appl. Mech. 71, 785-801 (2001) · Zbl 1016.74014 · doi:10.1007/s004190100191
[10] Chaboche, J.: Constitutive equations for cyclic plasticity and cyclic viscoplasticity, Int. J. Plast. 5, 247-302 (1989) · Zbl 0695.73001 · doi:10.1016/0749-6419(89)90015-6
[11] Dienes, J. K.: A statistical theory of fragmentation, Proceedings of the 19th US symposium on rock mechanics, 51-55 (1978)
[12] Dienes, J. K.: A unified theory of flow, hot spots, and fragmentation with an application to explosive sensitivity, High pressure shock compression of solids II, 66-398 (1996) · Zbl 0845.73060
[13] Dorfmann, A.; Ogden, R. W.: A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber, Int. J. Solids struct. 41, 1855-1878 (2004) · Zbl 1074.74021 · doi:10.1016/j.ijsolstr.2003.11.014
[14] Dusunceli, N.; Colak, O. U.: Modelling effects of degree of crystallinity on mechanical behavior of semicrystalline polymers, Int. J. Plast. 24, 1224-1242 (2008) · Zbl 1419.74081
[15] Einstein, A.: Eine neue bestimmung der molekldimensionen, Ann. phys. 19, 289-306 (1906) · JFM 37.0811.01
[16] Freund, M.; Ihlemann, J.: Generalization of one-dimensional material models for the finite element method, Z. angew. Math. mech. 90, No. 5, 399-417 (2010) · Zbl 1208.74005 · doi:10.1002/zamm.200900352
[17] Gent, A. N.: Simple rotary dynamic testing machine, Br. J. Appl. phys. 11, 165-167 (1960)
[18] Heinrich, G.; Straube, E.; Helmis, G.: Rubber elasticity of polymer networks: theories, Adv. polym. Sci 85, 33-87 (1988)
[19] Höfer, P.; Lion, A.: Modelling of frequency- and amplitude-dependent material properties of filler-reinforced rubber, J. mech. Phys. solids 57, 500-520 (2009) · Zbl 1273.74065
[20] Hossain, M.; Possart, G.; Steinmann, P.: A small-strain model to simulate the curing of thermosets, Comput. mech. 43, 769-779 (2009) · Zbl 1162.74329 · doi:10.1007/s00466-008-0344-5
[21] Huber, G.; Vilgis, T. A.: Universal properties of filled rubbers: mechanisms for reinforcement on different length scales, Kautschuk gummi kunststoffe 52, 102-107 (1999)
[22] Ihlemann, J., 2003. Kontinuumsmechanische Nachbildung hochbelasteter technischer Gummiwerkstoffe. VDI, Düsseldorf.
[23] Julien, R.: The application of fractals and investigations of colloidal aggregation and fandom deposition, New J. Chem. 14, 239-253 (1990)
[24] Khan, A. S.; Lopez-Pamies, O.; Kazmi, R.: Thermo-mechanical large deformation response and constitutive modeling of viscoelastic polymers over a wide range of strain rates and temperatures, Int. J. Plast. 22, 581-601 (2006) · Zbl 1190.74006 · doi:10.1016/j.ijplas.2005.08.001
[25] Klüppel, M.: The role of disorder in filler reinforcement of elastomers on various length scales, Adv. polym. Sci. 164, 1-86 (2003)
[26] Klüppel, M.; Schramm, J.: A generalized tube model for rubber elasticity and stress softening of filler reinforced elastomer systems, Macromol. theory simul. 9, 742-754 (2000)
[27] Klüppel, M.; Schuster, R. H.; Heinrich, G.: Structure and properties of reinforcing fractal filler networks in elastomers, Rubber chem. Technol. 70, 243 (1997)
[28] Lion, A.: Constitutive modelling in finite thermoviscoplasticity: a physical approach based on nonlinear rheological elements, Int. J. Plast. 16, 469-494 (2000) · Zbl 0996.74022 · doi:10.1016/S0749-6419(99)00038-8
[29] Lorenz, H., Klüppel, M., 2009. A microstructure-based model of the stress – strain behavior of filled elastomers. In: G. Heinrich, M. Kaliske, A. Lion, S. Reese (Eds.), Constitutive Models for Rubber VI, pp. 423 – 428.
[30] Lorenz, H.; Meier, J.; Klüppel, M.: Micromechanics of internal friction of filler reinforced elastomers, Experiment and simulation, lecture notes in applied and computational mechanics 51, 27-53 (2010)
[31] Miehe, C.; Göktepe, S.; Lulei, F.: A micro – macro approach to rubber-like materials – part I: The non-affine micro-sphere model of rubber elasticity, J. mech. Phys. solids 52, 2617-2660 (2004) · Zbl 1091.74008 · doi:10.1016/j.jmps.2004.03.011
[32] Pawelski, H., 1998. Eigenschaften von Elastomerwerkstoffen mit Methoden der statistischen Physik. Shaker, Aachen.
[33] Reese, S.: A micromechanically motivated material model for the thermo-viscoelastic material behaviour of rubber-like polymers, Int. J. Plast. 19, 909-940 (2003) · Zbl 1090.74528 · doi:10.1016/S0749-6419(02)00086-4
[34] Rendek, M., Lion, A., 2009. Filler-reinforced rubber under transient and cyclic loadings: constitutive modelling and FEM-implementation for time domain simulations. In: G. Heinrich, M. Kaliske, A. Lion, S. Reese (Eds.), Constitutive Models for Rubber VI, pp. 39 – 45.
[35] Seelecke, S.: Equilibrium thermodynamics of pseudoelasticity and quasiplasticity, Contin. mech. Thermodyn. 8, 309-322 (1996) · Zbl 0938.74004 · doi:10.1007/s001610050046
[36] Shutov, A. V.; Kreißig, R.: Finite strain viscoplasticity with nonlinear kinematic hardening: phenomenological modeling and time integration, Comput. methods appl. Mech. eng. 197, 2015-2029 (2008) · Zbl 1194.74026 · doi:10.1016/j.cma.2007.12.017
[37] Sugihara, K.: Laguerre Voronoi diagram on the sphere, J. geom. Graphics 6, 69-81 (2002) · Zbl 1009.51007
[38] Witten, T. A.; Rubinstein, M.; Colby, R. H.: Reinforcement of rubber by fractal aggregates, J. phys. II France 3, 367-383 (1993)
[39] Zairi, F.; Nait-Abdelaziz, M. N.; Gloaguen, J. M.; Lefebvre, J. M.: Modelling of the elasto-viscoplastic damage behaviour of glassy polymers, Int. J. Plast. 24, 945-965 (2008) · Zbl 1135.74043 · doi:10.1016/j.ijplas.2007.08.001
[40] Zairi, F.; Woznica, K.; Nait-Abdelaziz, M.: Phenomenological nonlinear modelling of glassy polymers, CR mec. 333, 359-364 (2005)
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