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A review on the Mullins effect

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Diani, Julie, Fayolle, Bruno, Gilormini, Pierre·2009·European Polymer Journal
DOI 10.1016/j.eurpolymj.2008.11.017
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Research works printed but not linked: 81

  1. Mullins, 1969, Softening of rubber by deformation, Rubber Chem Technol, 42, 339, 10.5254/1.3539210 · DOI · Paper page
  2. Bouasse, 1903, Courbes de traction du caoutchouc vulcanisé, Ann Fac Sci Toulouse, 5, 257, 10.5802/afst.205 · doi:10.5802/afst.205
  3. Harwood, 1966, Stress softening in natural rubber vulcanizates. Part II. Stress softening effects in pure gum and filler loaded rubbers, Rubber Chem Technol, 39, 814, 10.5254/1.3547145 · doi:10.5254/1.3547145
  4. Harwood, 1966, Stress softening in natural rubber vulcanizates III. Carbon black filled vulcanizates, J Appl Polymer Sci, 10, 315, 10.1002/app.1966.070100212 · DOI
  5. Mullins, 1957, Theoretical model for the elastic behavior of filler reinforced vulcanized rubbers, Rubber Chem Technol, 30, 555, 10.5254/1.3542705 · DOI
  6. Mullins, 1948, Effect of stretching on the properties of rubber, J Rubber Res, 16, 275
  7. Dorfmann, 2004, A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber, Int J Solids Struct, 41, 1855, 10.1016/j.ijsolstr.2003.11.014 · DOI
  8. Mars, 2004, Observations of the constitutive response and characterization of filled natural rubber under monotonic and cyclic multiaxial stress states, J Engng Mat Technol, 126, 19, 10.1115/1.1631432 · doi:10.1115/1.1631432
  9. Németh I, Schleinzer G, Ogden RW, Holzapfel GA. On the modelling of amplitude and frequency-dependent properties in rubberlike solids. In: Austrell PE, Kari L, editors. In constitutive models for rubber IV. Balkema, 2005. p. 285–92. · doi:10.1201/9781315140216-47
  10. Dall’Asta, 2006, Experimental tests and analytical model of high daming rubber dissipating devices, Engng Struct, 28, 1874, 10.1016/j.engstruct.2006.03.025 · DOI
  11. Diani, 2006, A damage directional constitutive model for Mullins effect with permanent set and induced anisotropy, Eur J Mech Solids/A, 25, 483, 10.1016/j.euromechsol.2005.09.011 · DOI
  12. Klüppel, 2000, A generalized tube model of rubber elasticity and stress softening of filler reinforced elastomer systems, Macromol Theory Simul, 9, 742, 10.1002/1521-3919(20001201)9:9<742::AID-MATS742>3.0.CO;2-4 · DOI · Paper page
  13. Heinrich, 2002, Reinforcement of elastomers, Curr Opinion Solids St Mat Sci, 6, 195, 10.1016/S1359-0286(02)00030-X · DOI · Paper page
  14. Kakavas, 1996, Mechanical properties of bonded elastomer discs subjected to triaxial stress, J Appl Polym Sci, 59, 251, 10.1002/(SICI)1097-4628(19960110)59:2<251::AID-APP9>3.0.CO;2-W · doi:10.1002/(sici)1097-4628(19960110)59:2<251::aid-app9>3.0.co;2-w
  15. Clément, 2001, On the Mullins effect in silica-filled polydimethylsiloxane networks, Rubber Chem Technol, 74, 846, 10.5254/1.3547657 · doi:10.5254/1.3547657
  16. Stevenson, 2001, Influence of SiO2 fillers on the radiation ageing of silicone rubbers, Polymer, 42, 9287, 10.1016/S0032-3861(01)00470-0 · doi:10.1016/s0032-3861(01)00470-0
  17. Hanson, 2005, Stress softening experiments in silica-filled polydimethylsiloxane provide insight into a mechanism for the Mullins effect, Polymer, 46, 10989, 10.1016/j.polymer.2005.09.039 · DOI · Paper page
  18. Amin, 2002, An improved hyperelasticity relation in modelling viscoelasticity response of natural and high damping rubbers in compression: experiments, parameter identification and numerical verification, Mech Mater, 34, 75, 10.1016/S0167-6636(01)00102-8 · DOI
  19. Dorfmann, 2003, Stress softening of elastomers in hydrostatic tension, Acta Mech, 165, 117, 10.1007/s00707-003-0034-5 · DOI
  20. Johnson, 1995, The Mullins effect in equibiaxial extension and its influence on the inflation of a balloon, Int J Engng Sci, 33, 223, 10.1016/0020-7225(94)E0052-K · doi:10.1016/0020-7225(94)e0052-k
  21. Li, 2008, A constitutive model dealing with damage due to cavity growth and the Mullins effect in rubber-like materials under triaxial loading, J Mech Phys Solids, 56, 953, 10.1016/j.jmps.2007.06.009 · doi:10.1016/j.jmps.2007.06.009
  22. Diani, 2006, Observation and modeling of anisotropic visco-hyperelastic behavior of a rubberlike material, Int J Solids Struct, 43, 3044, 10.1016/j.ijsolstr.2005.06.045 · doi:10.1016/j.ijsolstr.2005.06.045
  23. Boyce, 2001, Deformation of thermoplastic vulcanizates, J Mech Phys Solids, 49, 1073, 10.1016/S0022-5096(00)00066-1 · DOI
  24. Qi, 2005, Stress–strain behavior of thermoplastic polyurethanes, Mech Mat, 37, 817, 10.1016/j.mechmat.2004.08.001 · DOI · Paper page
  25. Webber, 2007, Large strain hysteresis and Mullins effect of tough double-network hydrogels, Macromolecules, 40, 2919, 10.1021/ma062924y · DOI · Paper page
  26. Dorfmann, 2008, Muscle performance in a soft-bodied terrestrial crawler: constitutive modeling of strain-rate dependency, J R Soc Interface, 5, 336, 10.1098/rsif.2007.1076 · DOI
  27. Muñoz, 2008, An experimental study of the Mouse skin behaviour: damage and inelastic aspects, J Biomech, 41, 93, 10.1016/j.jbiomech.2007.07.013 · DOI
  28. Rubod, 2008, Biomechanical properties of vaginal tissue preliminary results, Int Urogynecol J, 19, 811, 10.1007/s00192-007-0533-3 · DOI
  29. Treloar, 1941, Crystallization phenomena in raw rubber, Trans Faraday Soc, 37, 84, 10.1039/tf9413700084 · doi:10.1039/tf9413700084
  30. Gent, 1955, Crystallization and the relaxation of stress in stretched natural-rubber vulcanizates, Trans Faraday Soc, 50, 521, 10.1039/tf9545000521 · DOI · Paper page
  31. Trabelsi, 2003, Crystallization and melting processes in vulcanized stretched natural rubber, Macromolecules, 36, 7624, 10.1021/ma030224c · doi:10.1021/ma030224c
  32. Trabelsi, 2003, Effective local deformation in stretched filled rubber, Macromolecules, 36, 9093, 10.1021/ma0303566 · doi:10.1021/ma0303566
  33. Albouy, 2005, Chain orientation in natural rubber, Part I: the inverse yielding effect, Eur Phys J, 17, 247
  34. Rault, 2006, Stress-induced crystallization and reinforcement in filled natural rubbers: 2H NMR study, Macromolecules, 39, 8356, 10.1021/ma0608424 · doi:10.1021/ma0608424
  35. Mullins, 1965, Stress softening in rubber vulcanizates. Part I. Use of a strain amplification factor to describe elastic behavior of filler-reinforced vulcanized rubber, J Appl Polymer Sci, 9, 2993, 10.1002/app.1965.070090906 · DOI · Paper page
  36. Mullins, 1949, Permanent set in vulcanized rubber, India Rubber World, 120, 63
  37. Laraba-Abbes, 2003, A new ‘Taylor-made’ methodology for the mechanical behaviour analysis of rubber-like materials: II. Application to the hyperelastic behaviour characterization of a carbon-black filled natural rubber vulcanizate, Polymer, 44, 821, 10.1016/S0032-3861(02)00719-X · doi:10.1016/s0032-3861(02)00719-x
  38. Harwood, 1966, Stress softening in natural rubber vulcanizates. IV. Unfilled vulcanizates, J Appl Polymer Sci, 10, 1203, 10.1002/app.1966.070100811 · doi:10.1002/app.1966.070100811
  39. Rigbi, 1980, Reinforcement of rubber by carbon black, Adv Polym Sci, 36, 21, 10.1007/3-540-10204-3_2 · DOI
  40. Simo, 1987, On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects, Comput Methods Appl Mech Engrg, 60, 153, 10.1016/0045-7825(87)90107-1 · DOI · Paper page
  41. Kachanov, 1958, Time of the rupture process under creep conditions, Izvestiya Akad Nauk SSR Otd Tekh Nauk, 58, 26
  42. Miehe, 1995, Discontinuous and continuous damage evolution in Ogden-type large-strain elastic materials, Eur J Mech A/Solids, 14, 697
  43. Miehe, 2000, Superimposed finite elastic–viscoelastic–plastoelastic stress response with damage in filled rubbery polymers. Experiments, modeling and algorithmic implementation, J Mech Phys Solids, 48, 323, 10.1016/S0022-5096(99)00017-4 · DOI · Paper page
  44. Kaliske, 2001, On damage modeling for elastic and viscoelastic materials at large strain, Comput Structures, 79, 2133, 10.1016/S0045-7949(01)00061-X · doi:10.1016/s0045-7949(01)00061-x
  45. Lin, 2003, A finite elastic–viscoelastic–elastoplastic material low with damage: theoretical and numerical aspects, Comput Methods Appl Mech Engrg, 192, 1591, 10.1016/S0045-7825(02)00649-7 · doi:10.1016/s0045-7825(02)00649-7
  46. Besdo, 2003, A phenomenological constitutive model for rubberlike materials and its numerical applications, Int J Plast, 19, 1019, 10.1016/S0749-6419(02)00091-8 · DOI
  47. Lion, 1996, A constitutive model for carbon black filled rubber: experimental investigations and mathematical representation, Continuum Mech Thermodyn, 8, 153, 10.1007/BF01181853 · DOI · Paper page
  48. Ernst, 1999, Hysteresis and time-dependent constitutive modeling of filled vulcanized rubber, J Phys IV France, 9, 63, 10.1051/jp4:1999907 · doi:10.1051/jp4:1999907
  49. Beatty, 2000, A theory of stress-softening in incompressible isotropic materials, J Mech Phys Solids, 48, 1931, 10.1016/S0022-5096(99)00085-X · doi:10.1016/s0022-5096(99)00085-x
  50. Laiarinandrasana, 2003, Visco-hyperelastic model with internal state variable coupled with discontinuous damage concept under total Lagrangian formulation, Int J Plast, 19, 977, 10.1016/S0749-6419(02)00089-X · DOI
  51. Chagnon, 2004, On the relevance of continuum damage mechanics as applied to the Mullins effect in elastomers, J Mech Mater Phys Solids, 52, 1627, 10.1016/j.jmps.2003.12.006 · DOI
  52. Ogden, 1999, A pseudo-elastic model for the Mullins effect in filled rubber, Proc R Soc Lond A, 455, 2861, 10.1098/rspa.1999.0431 · DOI · Paper page
  53. Zúñiga, 2002, A new phenomenological model for stress-softening in elastomers, Z Angew Math Phys, 53, 794, 10.1007/PL00022513 · DOI
  54. Horgan, 2004, A theory of stress softening of elastomers based on finite chain extensibility, Proc R Soc Lond A, A460, 1737, 10.1098/rspa.2003.1248 · DOI
  55. Elías-Zúñiga, 2006, A phenomenological energy-based model to characterize stress-softening effect in elastomers, Polymer, 46, 3496, 10.1016/j.polymer.2005.02.093 · DOI
  56. Kazakevičiūtė-Makovska, 2007, Experimentally determined properties of softening functions in pseudo-elastic models of the Mullins effect, Int J Solids Struct, 44, 4145, 10.1016/j.ijsolstr.2006.11.012 · doi:10.1016/j.ijsolstr.2006.11.012
  57. Krishnaswamy, 2000, The Mullins effect in compressible solids, Int J Engng Sci, 38, 1397, 10.1016/S0020-7225(99)00125-1 · doi:10.1016/s0020-7225(99)00125-1
  58. Qi, 2004, Constitutive model for stretch-induced softening of the stress-stretch behavior of elastomeric materials, J Mech Phys Solids, 52, 2187, 10.1016/j.jmps.2004.04.008 · doi:10.1016/j.jmps.2004.04.008
  59. De Tommasi, 2006, A micromechanics based model for the Mullins effect, J Rheol, 50, 495, 10.1122/1.2206706 · doi:10.1122/1.2206706
  60. Wineman, 1990, On a constitutive theory for materials undergoing microstructural changes, Arch of Mech, 42, 53
  61. De Tommasi, 2007, Mullins effect for a cylinder subjected to combined extension and torsion, J Elasticity, 86, 85, 10.1007/s10659-006-9087-8 · doi:10.1007/s10659-006-9087-8
  62. Blanchard, 1952, Breakage of carbon-rubber networks by applied stress, Ind Eng Chem, 44, 799, 10.1021/ie50508a034 · doi:10.1021/ie50508a034
  63. Bueche, 1960, Molecular basis for the Mullins effect, J Appl Polym Sci, 4, 107, 10.1002/app.1960.070041017 · DOI
  64. Houwink, 1956, Slipping of molecules during the deformation of reinforced rubber, Rubber Chem Technol, 29, 888, 10.5254/1.3542602 · doi:10.5254/1.3542602
  65. Kraus, 1966, Stress softening in carbon black reinforced vulcanizates. Strain rate and temperature effects, J Appl Polym Sci, 10, 229, 10.1002/app.1966.070100205 · DOI
  66. Fukahori, 2005, New progress in the theory and model of carbon black reinforcement of elastomers, J Appl Polym Sci, 95, 60, 10.1002/app.20802 · doi:10.1002/app.20802
  67. Suzuki, 2005, Effects of rubber/filler interactions on deformation behavior of silica filled SBR systems, Polymer, 46, 193, 10.1016/j.polymer.2004.10.066 · DOI · Paper page
  68. Alexendrov, 1944, Strength of amorphous and crystallizing rubber polymers, Doklady Akad Nauk SSSR, 45, 291
  69. Dannenberg, 1965, Strain-energy as a criterion for stress softening in carbon-black-filled vulcanizates, Rubber Chem Technol, 39, 597, 10.5254/1.3544867 · doi:10.5254/1.3544867
  70. Roland, 1989, Network recovery from uniaxial extension: the origin of the Mullins effect, Rubber Chem Technol, 62, 880, 10.5254/1.3536281 · doi:10.5254/1.3536281
  71. Santangelo, 1992, Chain ends and the Mullins effect in rubber, Rubber Chem Technol, 65, 965, 10.5254/1.3538654 · doi:10.5254/1.3538654
  72. Hamed, 1989, On the role of bound rubber in carbon-black reinforcement, Rubber Chem Technol, 62, 143, 10.5254/1.3536231 · doi:10.5254/1.3536231
  73. Fukahori, 2007, Generalized concept of the reinforcement of elastomers. Part 1: carbon black reinforcement of rubbers, Rubber Chem Technol, 80, 701, 10.5254/1.3548189 · doi:10.5254/1.3548189
  74. Besdo, 2003, Properties of rubberlike materials under large deformations explained by self organizing linkage patterns, Int J Plast, 19, 1001, 10.1016/S0749-6419(02)00090-6 · DOI
  75. Govindjee, 1991, A micro-mechanical continuum mechanical model for carbon black filled rubbers incorporating Mullins effect, J Mech Phys Solids, 39, 87, 10.1016/0022-5096(91)90032-J · DOI · Paper page
  76. Göktepe, 2005, A micro-macro approach to rubber-like materials. Part III: the micro-sphere model of anisotropic Mullins-type damage, J Mech Phys Solids, 53, 2259, 10.1016/j.jmps.2005.04.010 · DOI · Paper page
  77. Killian, 1994, Universal properties in filler-loaded rubbers, Rubber Chem Technol, 67, 1, 10.5254/1.3538664 · DOI
  78. Marckmann, 2002, A theory of network alteration for the Mullins effect, J Mech Phys Solids, 50, 2011, 10.1016/S0022-5096(01)00136-3 · DOI · Paper page
  79. Arruda, 1993, A three-dimensional constitutive model for the large deformation stretch behavior of rubber elastic materials, J Mech Phys Solids, 41, 389, 10.1016/0022-5096(93)90013-6 · DOI · Paper page
  80. Meissner, 2000, Description of the tensile stress–strain behavior of filler-reinforced rubber-like networks using a Langevin-theory-based approach. Part I, Polymer, 41, 7749, 10.1016/S0032-3861(00)00151-8 · DOI
  81. Gent, 1996, A new constitutive relation for rubber, Rubber Chem Technol, 69, 59, 10.5254/1.3538357 · DOI · Paper page

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Metadata

Authors
Diani, J., Fayolle, B., & Gilormini, P.
Venue
European Polymer Journal
Publisher
Elsevier BV
Published
2009-03
Volume
45
Issue
3
Pages
601-612
ISSN
0014-3057 (ISSN-L)
DOI
10.1016/j.eurpolymj.2008.11.017
OpenAlex
W2095122216
Cited by
1,249
References
1
FWCI
12.36
Type
journal article
Language
en
Open access
green
Licence
  • www.elsevier.com/tdm/userlicense/1.0/ (tdm)
  • www.elsevier.com/legal/tdmrep-license (tdm)

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Diani, J., Fayolle, B., & Gilormini, P. (2009). A review on the Mullins effect. European Polymer Journal. https://doi.org/10.1016/j.eurpolymj.2008.11.017

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