zbMATH — the first resource for mathematics

Mullins effect and cyclic stress softening of filled elastomers by internal sliding and friction thermodynamics model. (English) Zbl 1217.74018
Summary: Elastomers are characterized by their ability to undergo large elastic deformation. Nevertheless, their behavior exhibits stress softening, hysteresis and cyclic softening. The first phenomenon, known as Mullins effect, is commonly assumed to be either the result of an evolution in the hard and soft domain microstructure whereby the effective volume fraction of the soft domain increases with stretch or the result of irreversible damage in the material or combination of both. Hysteresis and cyclic stress softening are often considered as the result of the effect of stress relaxation. Based on the physical structure of filled elastomers, the present study shows that the Mullins effect, hysteresis and cyclic softening can be modeled by dissipative friction phenomena due to internal sliding of the macromolecular chains and to sliding of the connecting chains on the reinforcing filler particles. This implies that the three effects are in fact related to one single deformation process. The proposed analysis allows to identify the state variables and to build a thermodynamic potential which accounts for the nonlinearity of the material behavior and for a time independent hysteresis. The constitutive model is 3D. Written in a rate form it applies to complex loadings: monotonic, cyclic, random fatigue, etc. Filled elastomers hysteresis loops and cyclic softening are represented with no need to introduce neither damage nor viscosity. The model was implemented in a Finite Element software to simulate a metal/elastomer lap joint. Good agreement with experiment was achieved.

74B20 Nonlinear elasticity
74A15 Thermodynamics in solid mechanics
74M10 Friction in solid mechanics
Full Text: DOI
[1] Armstrong, P.J., Frederick, C.O.,1966. A mathematical representation of the multiaxial Bauschinger effect. CEBG R.D./B/N731. Central Electricity Generating Board.
[2] Andrieux, F.; Saanouni, K.; Sidoroff, F.: Sur LES solides hyperélastiques à compressibilité induite par l’endommagement, CR acad. Sci. Paris ser. Iib 324, 281-288 (1997)
[3] Arruda, E. M.; Boyce, M. C.: A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials, J. mech. Phys. solids 41, 389-412 (1993) · Zbl 1355.74020
[4] Beatty, M. F.; Krishnaswamy, S.: Theory of stress-softening in incompressible isotropic materials, J. mech. Phys. solids 48, No. 9, 1931-1965 (2000) · Zbl 0983.74014 · doi:10.1016/S0022-5096(99)00085-X
[5] Besson, J.; Cailletaud, G.; Chaboche, J. L.; Forest, S.: Mécanique des matériaux solides, Hermes sci. (2001)
[6] Bueche, F.: Molecular basis for Mullins effect, J. appl. Polym. sci. 4, No. 10, 107-114 (1960)
[7] Burr, A.; Hild, F.; Leckie, F. A.: Continuum description of damage in ceramic – matrix composites, Eur. J. Mech. A 16, No. 1, 53-78 (1997) · Zbl 0887.73047
[8] Cantournet, S., 2002. Endommagement et fatigue des élastomères, Ph.D. Thesis, Univ. Paris VI.
[9] Dannenberg, E. M.: The effet of surface chemical interactions on the properties of filler-reinforced rubbers, Rubber chem. Technol. 44, 440-478 (1975)
[10] Doll, S.; Schweizerhof, K.: On the development of volumetric strain energy functions, J. appl. Mech. trans. ASME 67, 17-21 (2000) · Zbl 1110.74418 · doi:10.1115/1.321146
[11] Dragon, A.; Halm, D.: An anisotropic model of damage and frictional sliding for brittle materials, Eur. J. Mech. A 17, No. 3, 439-460 (1998) · Zbl 0933.74055 · doi:10.1016/S0997-7538(98)80054-5
[12] Flory, P. J.: Thermodynamic relations for high elastic materials, Trans. Faraday soc. 57, 829-838 (1961)
[13] Godvindjee, S.; Simo, J.: A micro-mechanically based continuum damage model for carbon black-filled rubbers incorporating Mullins effect, J. mech. Phys. solids 29, No. 1, 87-112 (1991) · Zbl 0734.73066 · doi:10.1016/0022-5096(91)90032-J
[14] Halphen, B.: Sur LES matériaux standards généralisés, J. mecanique 14, 39-63 (1975) · Zbl 0308.73017
[15] Harwood, J. A. C.; Payne, A. R.: Stress-softening in natural rubber vulcanizates. Part III: Carbon black-filled vulcanizates, J. appl. Polym. sci. 10, 315-324 (1966)
[16] Harwood, J. A. C.; Payne, A. R.: Hysteresis and strength of rubbers, J. appl. Polym. sci. 12, 889-901 (1968)
[17] Holzapfel, G. A.: Nonlinear solid mechanics: A continuum approach for engineering, (2001) · Zbl 0980.74001
[18] Hughes, T. J. R.: Generalization of selective integration procedures to anisotropic and non-linear media, Int. J. Numer. meth. Eng. 15, 1413-1418 (1980) · Zbl 0437.73053 · doi:10.1002/nme.1620150914
[19] Johnson, M. A.; Beatty, M. F.: The Mullins effect in uniaxial extension and its influence on the transverse vibration of a rubber string, Continuum mech. Thermodyn. 5, 83-115 (1993)
[20] Lambert-Diani, J.; Rey, C.: New phenomenological behavior laws for rubbers and thermoplastic elastomers, Eur. J. Mech. A 18, 1027-1043 (1999) · Zbl 0969.74513 · doi:10.1016/S0997-7538(99)00147-3
[21] Lapra, A., 1999. Caractérisation moléculaire et propriétés mécaniques des réseaux élastomères sbr renforcés par la silice, Ph.D. Thesis, Univ. Paris VI.
[22] Lemaitre, J.; Chaboche, J. L.: Mécanique des matériaux solides, (1985)
[23] Lemaitre, J.; Desmorat, R.: Engineering damage mechanics: ductile, creep, fatigue and brittle failures, (2005)
[24] Miehe, C.: Discontinuous and continuous damage evolution in ogden-type large-strain elastic materials, Eur. J. Mech. A 14, No. 5, 697-720 (1995) · Zbl 0837.73054
[25] Miehe, C.; Keck, J.: Superimposed finite elastic-viscoelastic – plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic implementation, J. mech. Phys. solids 48, 323-365 (2000) · Zbl 0998.74014 · doi:10.1016/S0022-5096(99)00017-4
[26] Mullins, L.: Effect of stretching on the properties of rubber, J. rubber res. 16, 275-289 (1947)
[27] Mullins, L., Tobin, N.R., 1954. Theoretical model for the elastic behavior of filler-reinforced vulcanized rubbers. In: Proceedings of the Third Rubber Technological Conference, W. Heffer and Sons Ltd., pp. 397 – 412.
[28] Mullins, L.; Tobin, N. R.: Stress softening in rubber vulcanizates. Part I, J. appl. Polym. sci. 9, 2993-3009 (1965)
[29] Oden, J. T.: Finite elements of nonlinear continua, (1972) · Zbl 0235.73038
[30] Ogden, R.W., 1982. Elastic deformation of rubberlike solids, In: Mechanics of Solids, vol. 6, The Rodney Hill 60th Anniversary Volume, Pergamon Press, Oxford, pp. 499 – 537.
[31] Ogden, R. W.; Roxburgh, D. G.: A pseudo-elastic model for the Mullins effect in filled rubber, Proc. roy. Soc. lond. A 455, 2861-2877 (1999) · Zbl 0971.74011 · doi:10.1098/rspa.1999.0431
[32] Penn, R. W.: Volume changes accompanying the extension of rubber, Trans. soc. Rheol. 14, No. 4, 509-517 (1970)
[33] Qi, H. J.; Boyce, M. C.: Constitutive model for stretch-induced softening of the stress-stretch behavior of elastomeric materials, J. mech. Phys. solids 52, No. 10, 2187-2205 (2004) · Zbl 1115.74311 · doi:10.1016/j.jmps.2004.04.008
[34] Rivlin, R. S.: Large elastic deformations of isotropic materials, Philos. trans. Roy. soc. Lond. A 240, 459-481 (1948) · Zbl 0029.32605 · doi:10.1098/rsta.1948.0002
[35] Simo, J. C.: On a fully three-dimensional finite-strain visco-elastic damage model: formulation and computational aspects, Comput. meth. Appl. mech. Eng. 60, 153-173 (1987) · Zbl 0588.73082 · doi:10.1016/0045-7825(87)90107-1
[36] Simo, J. C.; Taylor, R. L.; Pister, K. S.: Variational and projection methods for the volume constraint in finite deformation elastoplasticity, Comput. meth. Appl. mech. Eng. 51, 177-208 (1985) · Zbl 0554.73036 · doi:10.1016/0045-7825(85)90033-7
[37] Taylor, R. L.: A mixed-enhanced formulation for tetrahedral finite elements, Int. J. Numer. meth. Eng. 47, 205-227 (2000) · Zbl 0985.74074 · doi:10.1002/(SICI)1097-0207(20000110/30)47:1/3<205::AID-NME768>3.0.CO;2-J
[38] Truesdell, C.; Noll, W.: The non-linear field theories of mechanics, Handbuch der physik, III 3 (1965) · Zbl 0779.73004
[39] Vidal, A.; Donnet, J. B.: Carbon black: surface properties and interactions with elastomers, Adv. polym. Sci. 76, 104-106 (1986)
[40] Zuniga, A. E.; Beatty, M. F.: A new phenomenological model for stress-softening in elastomers, Z. angew. Math. phys. 53, No. 5, 794-814 (2002) · Zbl 1030.74012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.