An 8-chain model for rubber-like materials accounting for non-affine chain deformations and topological constraints

Journal of Elasticity

Volumn 102, Issue 2, 2011, Pages 99-116

  Kroon, Martin ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Elastomer; Hyperelastic; Non affine; Rubber; Strain energy; Tube model

Indexed keywords

BIAXIAL TENSIONS; CHAIN MODELS; ELASTIC SPRINGS; EXPERIMENTAL DATA; EXPERIMENTAL STUDIES; FINITE ELEMENT; HYPER ELASTIC; MODEL PARAMETERS; NEW COMPONENTS; NON-AFFINE; PLANE DEFORMATION; POLYMER CHAINS; POLYMER NETWORKS; PREDICTIVE ABILITIES; RUBBERLIKE MATERIALS; TOPOLOGICAL CONSTRAINTS; TRANSVERSE MOTIONS; TUBE MODEL; UNIAXIAL TENSIONS;

DEFORMATION; ELASTOMERS; FINITE ELEMENT METHOD; INDUSTRIAL APPLICATIONS; KNOWLEDGE BASED SYSTEMS; POLYMERS; RUBBER; RUBBER APPLICATIONS; STRAIN ENERGY;

TOPOLOGY;

EID: 79851515095     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10659-010-9264-7     Document Type: Article

References (46)

1. E. Guth H. Mark 1934 Zur innermolekularen, statistik, insbesondere bei Kettenmolekülen i Monatsh. Chem. 65 93 121 10.1007/BF01522052
2. W. Kuhn 1934 Über die gestalt fadenförmiger moleküle in lösungen Kolloid-Zeitschrift 68 2 15 10.1007/BF01451681
3. W. Kuhn 1936 Beziehungen zwischen molekülgrösse, statistischer molekülgestalt und elastischen eigenschaften hochpolymerer stoffe Kolloid-Zeitschrift 76 258 271 10.1007/BF01451143
4. W. Kuhn F. Grün 1942 Beziehungen zwischen elastischen konstanten und dehnungsdoppelbrechung hochelastischer stoffe Kolloid-Zeitschrift 101 248 271 10.1007/BF01793684
5. H.M. James E. Guth 1943 Theory of elastic properties of rubber J. Chem. Phys. 11 455 481 10.1063/1.1723785 1943JChPh..11..455J
6. R.L. Jernigan P.J. Flory 1969 Distribution functions for chain molecules J. Chem. Phys. 50 4185 4200 10.1063/1.1670884 1969JChPh..50.4185J
7. M.C. Wang E. Guth 1952 Statistical theory of networks of non-Gaussian flexible chains J. Chem. Phys. 20 1144 1157 10.1063/1.1700682 49777 1952JChPh..20.1144W
8. P.J. Flory J. Rehner Jr. 1943 Statistical mechanics of cross-linked polymer networks J. Chem. Phys. 11 512 526 10.1063/1.1723791 1943JChPh..11..512F
9. L.R.G. Treloar 1946 The elasticity of a network of long-chain molecules Trans. Faraday Soc. 42 83 94 10.1039/tf9464200083 15693
10. E.M. Arruda M.C. Boyce 1993 A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials J. Mech. Phys. Solids 41 389 412 10.1016/0022-5096(93)90013-6 1993JMPSo..41..389A
11. A. Elias-Zuniga M.F. Beatty 2002 Constitutive equations for a (Pubitemid 35433381)
12. L.R.G. Treloar 1954 The photoelastic properties of short-chain molecular networks Trans. Faraday Soc. 50 881 896 10.1039/tf9545000881
13. L.R.G. Treloar G. Riding 1979 A non-Gaussian theory of rubber in biaxial strain. I. Mechanical properties Proc. R. Soc. Lond. A 369 261 280 10.1098/rspa.1979.0163 1979RSPSA.369..261T
14. P.D. Wu E. van der Giessen 1993 On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers J. Mech. Phys. Solids 41 427 456 0825.73103 10.1016/0022-5096(93)90043-F 1993JMPSo..41..427W
15. M.F. Beatty 2003 An average-stretch full-network model for rubber elasticity J. Elast. 70 65 86 1073.74013 10.1023/B:ELAS.0000005553.38563.91 2059928
16. C. Miehe S. Göktepe F. Lulei 2004 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 1091.74008 10.1016/j.jmps.2004.03. 011 2096575 2004JMPSo..52.2617M
17. G. Ronca G. Allegra 1975 An approach to rubber elasticity with internal constraints J. Chem. Phys. 63 4990 4997 10.1063/1.431245 1975JChPh..63.4990R
18. P.J. Flory 1976 Theory of elasticity of polymer networks Proc. R. Soc. Lond. A 351 351 380 10.1098/rspa.1976.0146 1976RSPSA.351..351F
19. P.J. Flory 1977 Theory of elasticity of polymer networks. The effect of local constraints on junctions J. Chem. Phys. 66 5720 5729 10.1063/1.433846 1977JChPh..66.5720F
20. B. Erman P.J. Flory 1978 Theory of elasticity of polymer networks. II. The effect of geometric constraints on junctions J. Chem. Phys. 68 5363 5369 10.1063/1.435714 1978JChPh..68.5363E
21. P.J. Flory B. Erman 1982 Theory of elasticity of polymer networks Macromolecules 15 800 806 10.1021/ma00231a022 1982MaMol..15..800F
22. R.T. Deam S.F. Edwards 1976 The theory of rubber elasticity Philos. Trans. R. Soc. A 280 317 353 10.1098/rsta.1976.0001 406296 1976RSPTA.280..317D
23. S.F. Edwards R.A. Vilgis 1988 The tube model theory of rubber elasticity Rep. Prog. Phys. 51 243 297 10.1088/0034-4885/51/2/003 927072 1988RPPh...51..243E
24. G. Heinrich E. Straube 1983 On the strength and deformation dependence of the tube-like topological constraints of polymer networks, melts and concentrated solutions. I. The polymer network case Acta Polym. 34 589 594 10.1002/actp.1983.010340909
25. G. Heinrich E. Straube 1984 On the strength and deformation dependence of the tube-like topological constraints of polymer networks, melts and concentrated solutions. II. Polymer melts and concentrated solutions Acta Polym. 35 115 119 10.1002/actp.1984.010350201
26. G. Heinrich E. Straube G. Helmis 1988 Rubber elasticity of polymer networks: theories Adv. Polym. Sci. 85 33 87 10.1007/BFb0024050
27. C.O. Horgan G. Saccomandi 2006 Phenomenological hyperelastic strain-stiffening constitutive models for rubber Rubber Chem. Technol. 79 152 169 (Pubitemid 44972154)
28. M. Mooney 1940 A theory of large elastic deformation J. Appl. Phys. 11 582 592 10.1063/1.1712836 1940JAP....11..582M
29. R.S. Rivlin 1948 Large elastic deformations of isotropic materials IV. Further developments of the general theory Philos. Trans. R. Soc. A 241 379 397 0031.42602 10.1098/rsta.1948.0024 27674 1948RSPTA.241..379R
30. A.N. Gent 1996 A new constitutive relation for rubber Rubber Chem. Technol. 69 59 61 1396825 (Pubitemid 126598076)
31. A.N. Gent 2005 Extensibility of rubber under different types of deformation J. Rheol. 49 271 275 10.1122/1.1835343 2005JRheo..49..271G (Pubitemid 43066250)
32. O.H. Yeoh 1993 Some forms of the strain energy function for rubber Rubber Chem. Technol. 66 754 771
33. T. Beda 2007 Modeling hyperelastic behavior of rubber: A novel invariant-based and a review of constitutive models J. Polym. Sci., Polym. Phys. 45 1713 1732 10.1002/polb.20928 2007JPoSB..45.1713B (Pubitemid 47146884)
34. K.C. Valanis R.F. Landel 1967 The strain-energy function of a hyperelastic material in terms of the extension ratios J. Appl. Phys. 38 2997 3002 10.1063/1.1710039 1967JAP....38.2997V
35. R.W. Ogden 1972 Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids Proc. R. Soc. Lond. A 326 565 584 0257.73034 10.1098/rspa.1972.0026 1972RSPSA.326..565O
36. E. Fried 2002 An elementary molecular-statistical basis for the Mooney and Rivlin-Saunders theories of rubber elasticity J. Mech. Phys. Solids 50 571 582 1002.74012 10.1016/S0022-5096(01)00086-2 1892739 2002JMPSo..50..571F (Pubitemid 34220976)
37. Doi, M., Edwards, S.F.: The Theory of Polymer Dynamics, 1st edn. Clarendon Press, Oxford (1986)
38. C.O. Horgan G. Saccomandi 1999 Simple torsion of isotropic, hyperelastic, incompressible materials with limiting chain extensibility J. Elast. 56 159 170 0982.74011 10.1023/A:1007606909163 1799932
39. E. Pucci G. Saccomandi 2002 A note on the Gent model for rubber-like materials Rubber Chem. Technol. 75 839 852
40. A. Wineman 2005 Some results for generalized neo-Hookean elastic materials Int. J. Non-Linear Mech. 40 271 279 05138585 10.1016/j.ijnonlinmec. 2004.05.007 2005IJNLM..40..271W
41. L.R.G. Treloar 1944 Stress-strain data for vulcanized rubber under various types of deformation Trans. Faraday Soc. 40 59 70 10.1039/tf9444000059
42. R.W. Ogden G. Saccomandi I. Sgura 2004 Fitting hyperelastic models to experimental data Comput. Mech. 34 484 502 1109.74320 10.1007/s00466-004-0593-y
43. Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes in C. The Art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge (1994)
44. A.G. James A. Green G.M. Simpson 1975 Strain energy functions of rubber. I. Characterization of gum vulcanizates J. Appl. Polym. Sci. 19 2033 2058 10.1002/app.1975.070190723
45. S. Kawabata M. Matsuda K. Tei H. Kawai 1981 Experimental survey of the strain energy density function of isoprene rubber vulcanizate Macromolecules 14 154 162 10.1021/ma50002a032 1981MaMol..14..154K
46. M.C. Boyce E.M. Arruda 2000 Constitutive models of rubber elasticity: a review Rubber Chem. Technol. 73 504 523 (Pubitemid 32300941)