The damping function in rheology

Rheologica Acta

Volumn 48, Issue 3, 2009, Pages 245-284

  Rolón Garrido, Víctor H ^a   Wagner, Manfred H ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Damping function; Rheology; Viscoelastic fluid; Viscoelasticity; Wagner model

Indexed keywords

DAMPING FUNCTION; FOOD RHEOLOGY; HOMOPOLYMERS; MICELLAR SYSTEMS; NON-LINEAR VISCOELASTICITY; PHYSICAL INTERPRETATION; POLYMER COMPOSITE; RUBBER MATERIAL; RUBBERLIKE MATERIALS; VISCO-ELASTIC FLUID; WAGNER MODELS;

BLOCK COPOLYMERS; DAMPING; ELASTICITY; LIQUID CRYSTAL POLYMERS; LIQUID CRYSTALS; PLASTICITY; POLYMER BLENDS; POLYMER MELTS; POLYMERS; RHEOLOGY; RUBBER; STEADY FLOW; VISCOELASTICITY;

VISCOSITY;

EID: 63449134579     PISSN: 00354511     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00397-008-0308-x     Document Type: Review

References (255)

1. Aoki Y, Hatano A, Tanaka T, Watanabe H (2001) Nonlinear stress relaxation of ABS polymers in the molten state. Macromolecules 34:3100-3107
2. Archer LA (1999) Separability criteria for entangled polymer liquids. J Rheol 43(6):1555-1571
3. Archer LA, Juliani (2004) Linear and nonlinear viscoelasticity of entangled multiarm (pom-pom) polymer liquids. Macromolecules 37:1076-1088
4. Archer LA, Mhetar VR (1998) Differential constitutive equation for entangled polymers with partial strand extension. Rheol Acta 37:170-181
5. Archer LA, Varshney SK (1998) Synthesis and relaxation dynamics of multiarm polybutadiene melts. Macromolecules 31:6348-6355
6. Archer LA, Chen YL, Larson RG (1995) Delayed slip after step strains in highly entangled polystyrene solutions. J Rheol 39(3):519-525
7. Archer LA, Sanchez-Reyes J, Juliani (2002) Relaxation dynamics of polymer liquids in nonlinear step shear. Macromolecules 35:10216-10224
8. Astarita G, Marrucci G (1974) Principles of non-Newtonian fluid mechanics. McGraw Hill, Great Britain
9. Barrera MA, Vega JF, Aguilar M, Martínez-Salazar J (2006) Melt flow index on high molecular weight polyethylene: A comparative study of experiments and simulation. J Mater Process Technol 174:171-177
10. Barroso VC, Maia JM (2002) Evaluation by means of stress relaxation (after a step strain) experiments of the viscoelastic behaviour of polymer melts in uniaxial extension. Rheol Acta 41:257-264
11. Barroso VC, Ribeiro SP, Maia JM (2003) Stress relaxation after a step strain in uniaxial extension of polyisobutylene and polyethylene. Rheol Acta 42:345-354
12. Bastian H (2001) Non-linear viscoelasticity of linear and long-chain-branched polymer melts in shear and extensional flows, Ph.D. Thesis, Stuttgart University, Germany. http://elib.uni-stuttgart.de/opus/ volltexte/2001/894
13. Bengoechea C, Puppo MC, Romero A, Cordobés F, Guerrero A (2008) Linear and non-linear viscoelasticity of emulsions containing carob protein as emulsifier. J Food Eng 87:124-135
14. Bernstein B, Kearsley EA, Zapas LJ (1963) A study of stress relaxation with finite strain. Trans Soc Rheol 7:391-410
15. Bick DK, McLeish TCB (1996) Topological contributions to nonlinear elasticity in branched polymers. Phys Rev Lett 76(14):2587-2590
16. Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids, vol 1. Fluid mechanics. Wiley and Sons, USA
17. Bishko G, McLeish TCB, Harlen OG, Larson RG (1997) Theoretical molecular rheology of branched polymers in simple and complex flows: The pom-pom model. Phys Rev Lett 79(12):2352-2355
18. Booij HC, Palmen JHM (1982) Some aspects of linear and nonlinear viscoelastic behaviour of polymer melts in shear. Rheol Acta 21:376-387
19. Bruker I (1986) Measurements of the first normal-stress difference in a new Rheo-dilatometer for molten polymers: Triple-step-shear-strain tests for all K-BKZ constitutive equations. Rheol Acta 25:501-506
20. Byars JA, Jong L (2009) Flow properties of natural rubber composites filled with defatted soy flour. J Appl Polym Sci 111:2049-2055
21. Campanella OH, Peleg M (1987) Analysis of the transient flow of mayonnaise in coaxial viscometer. J Rheol 31(6):439-452
22. Caram Y, Bautista F, Puig JE, Manero O (2006) On the rheological modeling of associative polymers. Rheol Acta 46:45-57
23. Callaghan PT, Cates ME, Rofe CJ, Smeulders JBAF (1996) A study of the "spurt effect" in wormlike micelles using nuclear magnetic resonance microscopy. J Phys II France 6:375-393
24. Carriere CJ, Thomas AJ, Inglett GE (2002) Prediction of the nonlinear transient and oscillatory rheological behavior of flour suspensions using a strain-separable integral constitutive equation. Carbohydr Polym 47:219-231
25. Chang H, Lodge AS (1972) Comparison of rubberlike-liquid theory with stress-growth data for elongation of a low-density branched polyethylene melt. Rheol Acta 11:127-219
26. Chang WV, Bloch R, Tschoegl NW (1976) On the theory of the viscoelastic behaviour of soft polymers in moderately large deformations. Rheol Acta 15:367-378
27. Chen CY, Wu SM, Chen ZR, Huang TJ, Hua CC (2003) Nonlinear stress relaxation of an entangled linear polystyrene in single step-strain flow: A quantitative theoretical investigation. J Polym Sci B Polym Phys 41:1281-1293
28. Chodankar CD, Schieber JD, Venerus DC (2003a) Pom-pom theory evaluation in double-step strain flows. J Rheol 47(2):413-427
29. Chodankar CD, Schieber JD, Venerus DC (2003b) Evaluation of rheological constitutive equations for branched polymers in step shear strain flows. Rheol Acta 42:123-131
30. Clemeur N, Debbaut B (2007) A pragmatic approach for deriving constitutive equations endowed with pom-pom attributes. Rheol Acta 46:1187-1196
31. de Gennes PG (1971) Reptation of a polymer chain in the presence of fixed obstacles. J Chem Phys 55(2):572-579
32. Dealy JM, Wissbrun KF (1999) Melt rheology and its role in plastics processing. Theory and applications. Kluver Academic Publishers, Netherlands
33. Demarmels A, Meissner J (1986) Multiaxial elongations of polyisobutylene and the predictions of several network theories. Colloid Polym Sci 264:829-846
34. Demarquette NR, Dealy JM (1992) Nonlinear viscoelasticity of concentrated polystyrene solutions: Sliding plate rheometer studies. J Rheol 36(6):1007-1032
35. Doi M (1980) Stress relaxation of polymeric liquids after double-step strain. J Polym Sci B Polym Phys 18:1891-1905
36. Doi M, Edwards SF (1978a) Dynamics of concentrated polymer systems. Part 1.-Brownian motion in the equilibrium state. Trans Faraday Soc 20:1789-1801
37. Doi M, Edwards SF (1978b) Dynamics of concentrated polymer systems. Part 2.-Molecular motion under flow. Trans Faraday Soc 20:1802-1817
38. Doi M, Edwards SF (1978c) Dynamics of concentrated polymer systems. Part 3.-The constitutive equations. Trans Faraday Soc 20:1818-1832
39. Doi M, Edwards SF (1979) Dynamics of concentrated polymer systems. Part 4.- Rheological properties. Trans Faraday Soc 20:38-54
40. Doi M, Edwards SF (1986) Theory of polymer dynamics. Oxford University Press
41. Doi M, Takimoto J (2003) Molecular modelling of entanglement. Phil Trans R Soc Lond A 361:641-652
42. Ehrecke P, Wagner MH (1995) Untersuchungen zur Irreversibilität von Netzwerkentschlaufungen beim fließen von Polymerschmelzen. Macromol Chem Phys 196:2989-3004
43. Einaga Y, Osaki K, Kurata M, Kimura S, Tamura M (1971) Stress relaxation of polymer solutions under large strain. Polymer J 2(4):550-552
44. Einaga Y, Osaki K, Kurata M, Kimura S, Yamada N, Tamura M (1973) Stress relaxation of polymer solutions under large strain. Polymer J 5(1):91-96
45. Erchiqui F (2005) Thermodynamic approach of inflation process of K-BKZ polymer sheet with respect to thermoforming. Polym Eng Sci 45(10):1319-1335
46. Erchiqui F (2006) A new hybrid approach using the explicit dynamic finite element method and thermodynamic law for the analysis of the thermoforming and blow molding processes for polymer materials. Polym Eng Sci 46(11):1554-1564
47. Fan Y, Liao H (2008) Experimental studies on the relaxation behavior of commercial polymer melts. J Appl Polym Sci 110:1520-1530
48. Fan B, Kazmer DO, Bushko WC, Theriault RP, Poslinski AJ (2004) Birefringence prediction of optical media. Polym Eng Sci 44:814-824
49. Feigl K, Öttinger HC, Meissner J (1993) A failure of a class of K-BKZ equations based on principal stretches. Rheol Acta 32:438-446
50. Ferri JD (1980) Viscoelastic properties of polymers. John Wiley and Sons, USA
51. Ferri D, Greco F (2006) Nonlinear stress relaxation of molten polymers: experimental verification of a new theoretical approach. Macromolecules 39:5931-5938
52. Fukuda M, Osaki K, Kurata M (1975) Nonlinear viscoelasticity of polystyrene solutions. I. Strain-dependent relaxation modulus. J Polym Sci Polym Phys Ed 13:1563-1576
53. Furuichi K, Nonomura Ch, Masubuchi Y, Ianniruberto G, Greco F, Marrucci G (2007) Primitive chain network simulations of damping functions for shear, uniaxial, biaxial and planar deformations. Nihon Reoroji Kakkaishi 35(2):73-77
54. Gallegos C, Berjano M (1992) Linear viscoelastic behavior of commercial and model mayonnaise. J Rheol 36(3):465-478
55. Gevgilili H, Kalyon DM (2001) Step strain flow: Wall slip effects and other error sources. J Rheol 45(2):467-475
56. Gianotti G, Cicuta A, Romanini D (1980) Long chain branching in low-density polyethylene: 1. Molecular structure. Polymer 21:1087-1091
57. Gotsis AD, Zeevenhoven BLF, Tsenoglou C (2004) Effect of long branches on the rheology of polypropylene. J Rheol 48(4):895-914
58. Gottlieb M, Gaylord RJ (1987) Experimental tests of entanglement models of rubber elasticity. 3. Biaxial deformations. Macromolecules 20:130-138
59. Greco F (2004) Entangled polymeric liquids: Nonstandard statistical thermodynamics of a subchain between entanglement points and a new calculation of the strain measure tensor. Macromolecules 37:10079-10088
60. Green MS, Tobolsky AV (1946) A new approach to the theory of relaxing polymeric media. J Chem Phys 14(2):80-92
61. Goublomme A, Crochet MJ (1993) Numerical prediction of extrudate swell of a high-density polyethylene - Further results. J Non-Newton Fluid Mech 47:281-287
62. Goublomme A, Draily B, Crochet MJ (1992) Numerical prediction of extrudate swell of a high-density polyethylene. J Non-Newton Fluid Mech 44:171-195
63. Guerrero A, Partal P, Gallegos C (2000) Linear and non-linear viscoelasticity of low-in-cholesterol mayonnaise. Food Sci Tech Int 6(2):165-172
64. Guth E, Wack PE, Anthony RL (1946) Significance of the equation of state for rubber. J Appl Phys 17:347-351
65. Halley PJ, Mackay ME (1994) The effect of metals on the processing of LLDPE through a slit die. J Rheol 38(1):41-51
66. Han CD, Kim SS (1994) Transient rheological behavior of a thermotropic liquid-crystalline polymer. III. Step strain experiment and shear stress relaxation modulus. J Rheol 38(1):31-40
67. Harry-O'kuru RE, Carriere CJ (2002) Synthesis, rheological characterization, and constitutive modeling of polyhydroxy triglycerides derived from milkweed oil. J Agric Food Chem 50:3214-3221
68. Hepperle J, Münstedt H (2006) Rheological properties of branched polystyrene: Nonlinear shear and extensional behaviour. Rheol Acta 45:717-727
69. Holmqvist P, Castelletto V, Hamley IW, Hermsdorf N, Almdal K (2001) Stress relaxation experiments on a lamellar polystyrene-polyisoprene diblock copolymer melt. Polymer 42:7203-7208
70. Huang SX, Lu CJ (2006) Stress relaxation characteristics and extrudate swell of the IUPAC-LDPE melt. J Non-Newton Fluid Mech 136:147-156
71. Inoue T, Uematsu T, Yamashita Y, Osaki K (2002) Significance of the longest Rouse relaxation time in the stress relaxation process at large deformation of entangled polymer solutions. Maromolecules 35:4718-4724
72. Isaki T, Takahashi M, Urakawa O (2003) Biaxial damping function of entangled monodisperse polystyrene melts: Comparison with the Mead7-Larson-Doi model. J Rheol 47(5):1201-1210
73. Islam MT, Archer LA (2001) Nonlinear rheology of highly entangled polymer solutions in start-up and steady shear flow. J Poly Sci B Polym Phys 39:2275-2289
74. Islam MT, Sanchez-Reyes J, Archer LA (2001) Nonlinear rheology of highly entangled polymer liquids: Step shear damping function. J Rheol 45(1):61-82
75. Isono Y, Ferry JD (1985) Stress relaxation and differential dynamic modulus of polyisobutylene in large shearing deformations. J Rheol 29(3):273-280
76. Isono Y, Nishitake T (1995) Stress relaxation and change in entanglement structure of polyisobutylene in large shearing deformations. Polymer 36(8):1635-1638
77. Isono Y, Itoh K, Komiyatani T, Fujimoto T (1991a) Differential dynamic modulus of polyisobutylene with high molecular weight 1. Single-step large shearing deformations. Macromolecules 24:4429-4432
78. Isono Y, Shizuru K, Fujimoto T (1991b) Differential dynamic modulus of polyisobutylene with high molecular weight 2. Double-step large shearing deformations. Macromolecules 24:4433-4436
79. Isono Y, Ohashi N, Kase T (1995) Chain contraction and change in entanglement structure of well-entangled polymer in large shearing deformations. Macromolecules 28:5154-5155
80. Isono Y, Kamohara T, Takano A, Kase T (1997) Nonlinear viscoelastic properties and change in entanglement structure of linear polymer. 1. Single-step large shearing deformations. Rheol Acta 36:245-251
81. Iza M, Bousmina M (2000) Nonlinear rheology of immiscible polymer blends: Step strain experiments. J Rheol 44(6):1363-1384
82. Iza M, Bousmina M (2005) Damping function for narrow and large molecular weight polymers: Comparison with the force-balanced network model. Rheol Acta 44:372-378
83. Juliani, Archer LA (2001) Linear and nonlinear rheology of bidisperse polymer blends. J Rheol 45(3):691-708
84. Kajiwara T, Tomiyama H, Sueyoshi Y, Yamamura M, Adachi K (2001) Numerical simulation of extrudate swell problem and evaluation of applicability of viscoelastic constitutive models 1. A study of axisymmetric extrudate swell from a straight die. Nihon Reoroji Gakkaishi 29(1):47-52
85. Kalyon DM, Yu DW, Moy FH (1988) Rheology and processing of linear low density polyethylene resins as affected by alpha-olefin comonomers. Polym Eng Sci 28(23):1542-1550
86. Kasehagen LJ, Macosko CW (1998) Nonlinear shear and extensional rheology of long-chain randomly branched polybutadiene. J Rheol 42(6):1303-1327
87. Kawamura T, Urayama K, Kohjiya S (2001) Multiaxial deformations of end-linked poly(dimethylsiloxane) networks. 1. Phenomenological approach to strain energy density function. Macromolecules 34:8252-8260
88. Kaye A (1962) College of Astronautics. Cranford, U.K., Note No. 134
89. Khan SA, Larson RG (1987) Comparison of simple constitutive equations for polymer melts in shear and biaxial and uniaxial extensions. J Rheol 31(3):207-234
90. Khan MMK, Tanner RI (1990) Rheology of an LDPE melt in reversing multi-step shear and elongational flows. Rheol Acta 29:281-297
91. Khan SA, Prud'homme RK, Larson RG (1987) Comparison of the rheology of polymer melts in shear, biaxial and uniaxial extensions. Rheol Acta 26:144-151
92. Kolkka RW, Malkus DS, Rose TR (1991) Finite rise time step strain modelling of nearly monodisperse polymer melts and solutions. Rheol Acta 30:430-446
93. Kontou E (1994) Nonlinear viscoelasticity of a vulcanized elastomer. J Appl Polym Sci 54:1873-1877
94. Kotsilkova R (2002) Rheology-structure relationship of polymer/layered silicate hybrids. Mech Time-Dependent Mater 6:283-300
95. Kuhn R, Krömer H, Roßmanith G (1974) Struktur und Eigenschaften verschieden hergestellter Hochdruckpolyäthylene. Ang Makrom Chem 40/41:361-389
96. Kurose T, Takahashi T, Sugimoto M, Taniguchi T, Koyama K (2005) Uniaxial elongational viscosity of PC/A small amount of PTFE blend. J Soc Rheol Japan 33(4):173-182
97. Kwon Y, Cho KS (2001) Time-strain nonseparability in viscoelastic constitutive equations. J Rheol 45(6):1441-1452
98. Larson RG (1984) A constitutive equation for polymer melts based on partially extending strand convection. J Rheology 28(5):545-571
99. Larson RG (1985) Nonlinear shear relaxation modulus for a linear low-density polyethylene. J Rheol 29(6):823-831
100. Larson RG (1988) Constitutive equations for polymer melts and solutions. Buttherworths, USA
101. Larson RG (1999) The structure and rheology of complex fluids. Oxford University Press, USA
102. Larson RG, Monroe K (1984) The BKZ as an alternative to the Wagner model for shifting shear and elongational flow data of an LDPE melt. Rheol Acta 23:10-13
103. Larson RG, Monroe K (1987) Correction. Rheol Acta 26:208-209
104. Larson RG, Valesano VA (1986) Are polymer melts visco-anelastic? J Rheol 30(6):1093-1108
105. Laun HM (1978) Description of the non-linear shear behaviour of a low density polyethylene melt by means of an experimentally determined strain dependent memory function. Rheol Acta 17:1-15
106. Laun HM, Wagner MH, Janeschitz-Kriegl H (1979) Model analysis of nonlinear viscoelastic behaviour by use of a single integral constitutive equation: Stresses and birefringence of a polystyrene melt in intermittent shear flows. Rheol Acta 18:615-622
107. Le Meins JF, Moldenaers P, Mewis J (2002) Suspensions in polymer melts. 1. Effect of particle size on the shear flow behavior. Ind Eng Chem Res 41:6297-6304
108. Leblans PJR (1987) Nonlinear viscoelasticity of polymer melts in different types of flow. Rheol Acta 26:135-143
109. Leblans PJR, Sampers J, Booij HC (1985) Rheological properties of some polyolefine melts in transient uniaxial elongational flow, described with a special type of constitutive equation. J Non-Newton Fluid Mech 19:185-207
110. Lee JH, Orfanou K, Driva P, Iatrou H, Hadjichristidis N, Lohse DJ (2008) Linear and nonlinear rheology of dendritic star polymers: Experiment. Macromolecules 41:9165-9178
111. Lefebvre J (2006) An outline of the non-linear viscoelastic behaviour of wheat flour dough in shear. Rheol Acta 45:525-538
112. Li TQ, Wolcott MP (2006) Rheology of wood plastics melt, part 3: nonlinear nature of the flow. Polym Eng Sci 46(1):114-121
113. Lin YH, Das AK (2007) Monte Carlo simulations of stress relaxation of entanglement-free Fraenkel chains. II. Nonlinear polymer viscoelasticity. J Chem Phys 126:074903
114. Lodge AS (1964) Elastic liquids. An introductory vector treatment of finite-strain polymer rheology. Academic Press, Great Britain
115. Lodge AS (1968) Constitutive equation from molecular network theories for polymer solutions. Rheol Acta 7(4):379-392
116. Luo XL, Tanner RI (1988) Finite element simulation of long and short circular die extrusion experiments using integral models. Int J Numer Methods Eng 25(1):9-22
117. Mackley MR, Marshall RTJ, Smeulders JBAF, Zhao FD (1994) The rheological characterization of polymeric and colloidal fluids. Chem Eng Sci 49(16):2551-2565
118. Macosko WCh (1994) Rheology. Principles, measurements, and applications. Wiley-VCH, USA
119. Malkin AY, Isayev AI (2006) Rheology. Concepts, methods and applications. ChemTec Publisching, Toronto
120. Marini L, Georgakis Ch (1984) Low-density polyethylene vessel reactors. Part I: Steady state and dynamic modelling. AIChE 30(3):401-408
121. Marrucci G, Grizzuti N (1983) The free energy function of the Doi-Edwards theory: Analysis of the instabilities in stress relaxation. J Rheol 27(5):433-450
122. Marrucci G, Ianniruberto G (2003) Flow-induced orientation and stretching of entangled polymers. Phil Trans R Soc Lond A 361:677-688
123. Marrucci G, Greco F, Ianniruberto G (2000a) Possible role of force balance on entanglements. Macromol Symp 158:57-64
124. Marrucci G, Greco F, Ianniruberto G (2000b) Simple strain measure for entangled polymers. J Rheol 44(4):845-854
125. Matsumiya Y, Watanabe H (2004) Nonlinear relaxation behaviour of diblock copolymer micellar dispersions: Effects of corona-matrix and corona-corona entanglements. Macromolecules 37:9861-9871
126. McLeish TCB, Larson RG (1998) Molecular constitutive equations for a class of branched polymers: The pom-pom polymer. J Rheol 42(1):81-110
127. Menezes EV (1980) Some relations and tests on a constitutive equation with a factorized memory function. J Non-Newton Fluid Mech 7:45-62
128. Mhetar V, Archer LA (1999) Nonlinear viscoelasticity of entangled polymeric liquids. J Non-Newton Fluid Mech 81:71-81
129. Milner ST, McLeish TCB, Likhtman AE (2001) Microscopy theory of convective constraint release. J Rheol 45(2):539-563
130. Minegishi A, Nishioka A, Takahashi T, Masubuchi Y, Takimoto J, Koyama K (2001) Uniaxial elongational viscosity of PS/a small amount of UHMW-PS blends. Rheol Acta 40:329-338
131. Mongruel A, Cartault M (2006) Nonlinear rheology of styrene-butadiene rubber filled with carbon-black or silica particles. J Rheol 50(2):115-135
132. Morrison FA, Larson RG (1992) A study of shear-stress relaxation anomalies in binary of monodisperse polystyrenes. J Polym Sci B Polym Phys 30:943-950
133. Muliawan EB, Hatzikiriakos SG (2008) The effect of refrigerated storage on the rheological properties of three commercial mozzarella cheeses. Int J Food Eng 4(4):1-19
134. Ng TSK, McKinley GH (2008) Power law gels at finite strains: The nonlinear rheology of gluten gels. J Rheol 52(2):417-449
135. Ng TSK, McKinley GH, Padmanabhan M (2006) Linear to non-linear rheology of wheat flour-water dough. Appl Rheol 16(5):265-274
136. Nielsen JK, Rasmussen HK, Hassager O, McKinley GH (2006a) Elongational viscosity of monodisperse and bidisperse polystyrene melts. J Rheol 50:453-476
137. Nielsen JK, Rasmussen HK, Denberg M, Almdal K, Hassager O (2006b) Nonlinear branch-point dynamics of multiarm polystyrene. Macromolecules 39:8844-8853
138. Nishioka A, Takahashi T, Masubuchi Y, Takimoto J, Koyama K (2000) Description of uniaxial, biaxial, and planar elongational viscosities of polystyrene melt by the K-BKZ model. J Non-Newton Fluid Mech 89:287-301
139. Nishioka A, Takahashi T, Masubuchi Y, Takimoto J, Koyama K (2002) Rheological characterization of ionic bounding in ethylene-ionomer melts with low neutralization degree. J Rheol 46(6):1325-1339
140. Nithi-Uthai N, Manas-Zloczower I (2002) Numerical studies of the effect of constitutive model parameters as reflecting polymer molecular structure on extrudate swell. Appl Rheol 12:252-259
141. Noll W (1958) A mathematical theory of the mechanical behavior of continuous media. Arch Ration Mech Anal 2:197-226
142. Odian G (1981) Principles of polymerization. Wiley, USA
143. Okamoto K, Takahashi M, Yamane H, Kashihara H, Watanabe H, Masuda T (1999) Shape recovery of a dispersed droplet phase and stress relaxation stress after application of step shear strains in a polystyrene/ polycarbonate blend melt. J Rheol 43(4):951-965
144. Osaki K (1993) On the damping function of shear relaxation modulus for entangled polymers. Rheol Acta 32:429-437
145. Osaki K (1999) Constitutive equation and damping function for entangled polymers. Korea-Australia Rheol J 11(4):287-291
146. Osaki K, Kurata M (1980) Experimental appraisal of the Doi-Edwards theory for polymer rheology based on the data for polystyrene solutions. Macromolecules 13:671-676
147. Osaki K, Ohta S, Fukuda M, Kurata M (1976) Nonlinear viscoelasticity of polystyrene solutions. III. Stress development at the start of steady shear flow and an experimental check of some constitutive models. J Polym Sci, Polym Phys Ed 14:1701-1715
148. Osaki K, Kim BS, Kurata M (1979) Rheology of copolymer solutions. IV. Nonlinear viscoelasticity of solutions of an SBS block copolymer. Polym J 11(1):33-42
149. Osaki K, Kimura S, Kurata M (1981) Relaxation of shear and normal stresses in double-step shear deformations for a polystyrene solution. A test of the Doi-Edwards theory for polymer rheology. J Rheol 25(5):549-562
150. Osaki K, Nishizawa K, Kurata M (1982) Material time constant characterizing the nonlinear viscoelasticity of entangled polymeric systems. Macromolecules 15:1068-1071
151. Osaki K, Takatori E, Kurata M (1987) Nonlinear viscoelasticity of semidilute polystyrene solutions. Effect of molecular weight distribution. Macromolecules 20:1681-1687
152. Osaki K, Takatori E, Kurata M, Watanabe H, Yoshida H, Kotaka T (1990) Viscoelastic properties of solutions of star-branched polystyrene. Macromolecules 23:4392-4396
153. Osaki K, Takatori E, Watanabe H, Kotaka T (1993) Viscoelastic properties of semidilute poly(methyl methacrylate) solutions. Rheol Acta 32:132-139
154. Osaki K, Watanabe H, Inoue T (1996) Damping function of the shear relaxation modulus and the chain retraction process of entangled polymers. Macromolecules 29:3611-3614
155. Otsuki Y, Kajiwara T, Funatsu K (1997) Numerical simulations of annular extrudate swell of polymer melts. Polym Eng Sci 37(7):1171-1181
156. Otsuki Y, Kajiwara T, Funatsu K (1999) Numerical simulations of annular extrudate swell using various types of viscoelastic models. Polym Eng Sci 39(10):1969-1981
157. Papanastasiou AC, Scriven LE, Macosko CW (1983) An integral constitutive equation for mixed flows: Viscoelastic characterization. J Rheol 27(4):387-410
158. Partal P, Guerrero A, Berjano M, Gallegos C (1999) Transient flow of o/w sucrose palmitate emulsions. J Food Eng 41:33-41
159. Petrie CJS (1979) Measures of deformation and convected derivatives. J Non-Newton Fluid Mech 5:147-176
160. Phan-Thien N (2002) Understanding viscoelasticity. Basics of rheology. Springer, Germany
161. Pol HV, Joshi YM, Tapadia PS, Lele AK, Mashelkar RA (2007) A geometrical solution to the sharkskin instability. Ind Eng Chem Res 46:3048-3056
162. Raible T, Stephenson SE, Meissner J, Wagner MH (1982) Constant force elongational flow of a low-density polyethylene melt-experiment and theory. J Non-Newton Fluid Mech 11:239-256
163. Rasmussen HK, Nielsen JK, Bach A, Hassager O (2005) Viscosity overshoot in the start-up of uniaxial elongation of low density polyethylene melts. J Rheol 49(2):369-381
164. Ravindranath S, Wang SQ (2007) What are the origins of stress relaxation behaviors in step shear of entangled polymer solutions? Macromolecules 40:8031-8039
165. Ren J, Krishnamoorit R (2003) Nonlinear viscoelastic properties of layered-silicate-based intercalated nanocomposites. Macromolecules 36:4443-4451
166. Riscardo MA, Moros JE, Franco JM, Gallegos C (2005) Rheological characterization of salad-dressing-type emulsions stabilized by egg yolk/ sucrose distearate blends. Eur Food Res Technol 220:380-388
167. Rivlin RS, Sawyers KN (1971) Nonlinear continuum mechanics of viscoelastic fluids. Ann Rev Fluid Mech 3:117-146
168. Rolón-Garrido VH, Wagner MH (2007) The MSF model: Relation of nonlinear parameters to molecular structure of long-chain branched polymer melts. Rheol Acta 46:583-593
169. Roovers J (1984) Melt rheology of H-shaped polystyrenes. Macromolecules 17:1196-1200
170. Rubio P, Wagner MH (2000) LDPE melt rheology and the pom-pom model. J Non-Newton Fluid Mech 92:245-259
171. Samurkas T, Larson RG, Dealy JM (1989) Strong extensional and shearing flows of a branched polythylenes. J Rheol 33:559-578
172. Sanchez-Reyes J, Archer LA (2002) Step shear dynamics of entangled polymer liquids. Macromolecules 35:5194-5202
173. Shikata T, Hirata H, Takatori E, Osaki K (1988) Nonlinear viscoelastic behaviour of aqueous detergent solutions. J Non-Newton Fluid Mech 28:171-182
174. Shiraishi Y, Narazaki N, Kikutani T (2001) The application of an integral type constitutive equation to numerical flow analyses of viscoelastic fluid in unsteady flow. Polym Eng Sci 41(10):1695-1704
175. Sodeifian G, Haghtalab A (2004) Discrete relaxation spectrum and K-BKZ constitutive equation for PVC, NBR and their blends. Appl Rheol 14:180-189
176. Sofou S, Muliawan EB, Hatzikiriakos SG, Mitsoulis E (2008) Rheological characterization and constitutive modeling of bread dough. Rheol Acta 47:369-381
177. Soskey PR, Winter HH (1984) Large step shear strain experiments with parallel-disk rotational rheometers. J Rheol 28(5):625-645
178. Soskey PR, Winter HH (1985) Equibiaxial extension of two polymer melts: polystyrene and low density polyethylene. J Rheol 29(5):493-517
179. Stadler FJ, Auhl D, Münstedt H (2008) Influence of the molecular structure of polyolefins on the damping function in shear. Macromolecules 41:3720-3726
180. Stephenson SE (1980) Biaxial extensional flow of polymer melts and its realization in a newly developed rheometer. PhD Thesis ETH No. 6664
181. Sugimoto M, Suzuki Y, Hyun K, Ahn KH, Ushioda T, Nishioka A, Taniguchi T, Koyama K (2006) Melt rheology of long-chain-branched polypropylenes. Rheol Acta 46(1):33-44
182. Sui C, McKenna GB (2007) Nonlinear viscoelastic properties of branched polyethylene in reversing flows. J Rheol 51(3):341-365
183. Sui C, McKenna GB, Puskas JE (2007) Nonlinear viscoelastic response of dendritic (arborescent) polyisobutylenes in single- and reversing double-step shearing flows. J Rheol 51(6):1143-1169
184. Sun J, Phan-Thien N, Tanner RI (1996) Extrudate swell through an orifice die. Rheol Acta 35:1-12
185. Takahashi M, Isaki T, Takigawa T, Masuda T (1993) Measurement of biaxial and uniaxial extensional flow behaviour of polymer melts at constant strain rates. J Rheol 37(5):827-846
186. Takahashi T, Toda H, Minagawa K, Takimoto J, Iwakura K, Koyama K (1995) Nonlinear stress properties of poly(syterene-block-butadiene-block-styrene) melt under elongational and shear deformation. J Appl Polym Sci 56:411-417
187. Takahashi T, Takimoto J, Koyama K (1998) Elongational viscosities of random and block copolymer melts. J Appl Polym Sci 69:1765-1774
188. Takahashi T, Takimoto J, Koyama K (1999) Uniaxial elongational viscosity of various molten polymer composites. Polym Compos 20(3):357-366
189. Tanner RI (1988) From A to (BK)Z in constitutive relations. J Rheol 32(7):673-702
190. Tanner RI (2006) On the congruence of some network and pom-pom models. Korean-Australia Rheol J 18(1):9-14
191. Tobolsky AV, Andrews RD (1945) Systems manifesting superposed elastic and viscous behavior. J Chem Phys 13:3-27
192. Tsenoglou CJ, Voyiatzis E, Gotsis AD (2006) Simple constitutive modelling of nonlinear viscoelasticity under general extension. J Non-Newton Fluid Mech 138:33-43
193. Urakawa O, Takahashi M, Masuda T, Ebrahimi NG (1995) Damping functions and chain relaxation in uniaxial and biaxial extensions: Comparison with the Doi-Edwards theory. Macromolecules 28:7196-7201
194. Urayama K, Kawamura T, Kohjiya S (2001) Multiaxial deformations of end-linked poly(dimethylsiloxane) networks. 2. Experimental tests of molecular entanglement models of rubber elasticity. Macromolecules 34:8261-8269
195. Valencia C, Sánchez MC, Ciruelos A, Latorre A, Madiedo JM, Gallegos C (2003) Non-linear viscoelasticity modeling of tomato paste products. Food Res Int 36:911-919
196. Vasquez PA, McKinley GH, Cook LP (2007) A network scission model for wormlike micellar solutions I. Model formulation and viscometric flow predictions. J Non-Newton Fluid Mech 144:122-139
197. Vega DA, Milner ST (2007) Shear damping function measurements for branched polymers. J Polym Sci Part B Polym Phys 45:3117-3136
198. Venerus DC (2005) A critical evaluation of step strain flows of entangled linear polymer liquids. J Rheol 49(1):277-295
199. Venerus DC, Kahvand H (1994) Doi-Edwards theory evaluation in double-step strain flows. J Polym Sci B Polym Phys 32:1531-1542
200. Venerus DC, Nair R (2006) Stress relaxation dynamics of an entangled polystyrene solution following step strain flow. J Rheol 50(1):59-75
201. Venerus DC, Vrentas CM, Vrentas JS (1990) Step strain deformations for viscoelastic fluids: Experiment. J Rheol 34(5):657-683
202. Venerus DC, Tariq SA, Bernstein B (1993) On the use of stress growth data to determine strain-dependent material functions for factorable K-BKZ equations. J Non-Newton Fluid Mech 49:299-315
203. Venerus DC, Brown EF, Burghardt WR (1998) The nonlinear response of a polydisperse polymer solution to step strain deformations. Macromolecules 31:9206-9212
204. Vinogradov GV, Malkin AYa (1980) Rheology of polymers. Mir Publishers URSS
205. Vrentas CM, Graessley WW (1981) Relaxation of shear and normal stress components in step-strain experiments. J Non-Newton Fluid Mech 9:339-355
206. Vrentas CM, Graessley WW (1982) Study of shear stress relaxation in well-characterized polymer liquids. J Rheol 26(4):359-371
207. Vrentas JS, Vrentas CM (1993) Strain-coupling effects in extensional flows. J Appl Polym Sci 49:733-740
208. Vrentas JS, Venerus DC, Vrentas CM (1991a) Step-strain deformations for viscoelastic fluids: Formulation of a strain-coupling constitutive equation. J Polym Sci B Polym Phys 29:537-545
209. Vrentas JS, Vrentas CM, Venerus DC (1991b) Evaluation of the Wagner irreversible constitutive equation. Rheol Acta 30:175-179
210. Wagner MH (1976a) Analysis of stress-growth data for simple extension of a low-density branched polyethylene melt. Rheol Acta 15:133-135
211. Wagner MH (1976b) Analysis of time-dependent non-linear stress-growth data for shear and elongational flow of a low-density branched polyethylene melt. Rheol Acta 15:136-142
212. Wagner MH (1978) A constitutive analysis of uniaxial elongational flow data of a low-density polyethylene melt. J Non-Newton Fluid Mech 4:39-55
213. Wagner MH (1979) Zur Netzwerktheorie von Polymer-Schmelzen. Rheol Acta 18:33-50
214. Wagner MH (1990) The nonlinear strain measure of polyisobutylene melt in general biaxial flow and its comparison to the Doi-Edwards model. Rheo Acta 29:594-603
215. Wagner MH (1992) The slip-link model: A constitutive equation for general biaxial extension of polymer melts. Makromol Chem Macromol Symp 56:13-24
216. Wagner MH (1994a) Analysis of small angle neutron scattering data on poly(dimethylsiloxane) network unfolding. Macromolecules 27:5223-5226
217. Wagner MH (1994b) The origin of the C 2 term in rubber elasticity. J Rheol 38(3):655-679
218. Wagner MH, Demarmels A (1990) A constitutive analysis of extensional flows of polyisobutylene. J Rheol 34(6):943-958
219. Wagner MH, Ehrecke P (1998) Dynamics of polymer melts in reversing shear flows. J Non-Newton Fluid Mech 76:183-197
220. Wagner MH, Meissner J (1980) Network disentanglement and time-dependent flow behaviour of polymer melts. Makromol Chem 181:1533-1550
221. Wagner MH, Rolón-Garrido VH (2008) Verification of branch point withdrawal in elongational flow of pom-pom polystyrene melt. J Rheol 52(5):1049-1068
222. Wagner MH, Schaeffer J (1992) Nonlinear measures for general biaxial extension of polymer melts. J Rheol 36(1):1-26
223. Wagner MH, Schaeffer J (1993) Rubbers and polymer melts: Universal aspects of nonlinear stress-strain relations. J Rheol 37(4):643-661
224. Wagner MH, Schaeffer J (1994) Assessment of nonlinear strain measures for extensional and shearing flows of polymer melts. Rheol Acta 33:506-516
225. Wagner MH, Stephenson SE (1979a) The spike-strain test for polymeric liquids and its relevance for irreversible destruction of network connectivity by deformation. Rheol Acta 18:463-468
226. Wagner MH, Stephenson SE (1979b) The irreversibility assumption of network disentanglement in flowing polymer melts and its effects on elastic recoil predictions. J Rheol 23(4):489-504
227. Wagner MH, Raible T, Meissner J (1979) Tensile stress overshoot in uniaxial extension of a LDPE melt. Rheol Acta 18:427-428
228. Wagner MH, Ehrecke P, Hachmann P, Meissner J (1998) A Constitutive analysis of uniaxial, equibiaxial and planar extension of a commercial linear high-density polyethylene melt. J Rheol 42(3):621-638
229. Wagner MH, Bastian H, Hachmann P, Meissner J, Kurzbeck S, Münstedt H, Langouche F (2000) The strain-hardening behaviour of linear and long-chain branched polyolefin melts in extensional flows. Rheol Acta 39:97-109
230. Wagner MH, Rubio P, Bastian H (2001) The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release. J Rheol 45(6):1387-1412
231. Wagner MH, Yamaguchi M, Takahashi M (2003) Quantitative assessment of strain hardening of low-density polyethylene melts by the molecular stress function model. J Rheol 47(3):779-793
232. Wagner MH, Hepperle J, Münstedt H (2004) Relating rheology and molecular structure of model branched polystyrene melts by molecular stress function theory. J Rheol 48(3):489-503
233. Wagner MH, Rolón-Garrido VH, Nielsen JK, Rasmussen HK, Hassager O (2008) A constitutive analysis of transient and steady-state elongational viscosities of bidisperse polystyrene blends. J Rheol 52(1):67-86
234. Wang CF, Kokini JL (1995) Simulation of the nonlinear rheological properties of gluten dough using the Wagner constitutive model. J Rheol 39(6):1465-1482
235. Watanabe H, Matsumiya Y (2005) Rheology of diblock copolymer micellar dispersions having soft cores. Macromolecules 38:3808-3819
236. Watanabe H, Sato T, Osaki K, Yao ML (1996) Relaxation of spherical micellar systems of styrene-isoprene diblock copolymers. 2. Nonlinear stress relaxation behavior. Macromolecules 29:3890-3897
237. Watanabe H, Yao ML, Sato T, Osaki K (1997) Non-newtonian flow behaviour of diblock copolymer micelles: Shear-thinning in a nonentangling matrix. Macromolecules 30:5905-5912
238. Watanabe H, Sato T, Osaki K, Aoki Y, Li L, Kakiuchi M, Yao ML (1998a) Rheological images of poly(vinyl chloride) gels. 4. Nonlinear behavior in a critical gel state. Macromolecules 31:4198-4204
239. Watanabe H, Osaki K, Matsumoto M, Bossev DP, McNamee CE, Nakahara M, Yao ML (1998b) Nonlinear rheology of threadlike micelles of tetraethylammonium perfluorooctyl sulfonate. Rheol Acta 37:470-485
240. Watanabe H, Yao ML, Osaki K, Shikata T, Niwa H, Morishima Y (1999) Nonlinear rheology of concentrated spherical silica suspensions: 3. Concentration dependence. Rheol Acta 38:2-13
241. Watanabe H, Matsumiya Y, Ishida S, Takigawa T, Yamamoto T, Vlassopoulos D, Roovers J (2005) Nonlinear rheology of multiarm star chains. Macromolecules 38:7404-7415
242. Waton G, Michels B, Steyer A, Schosseler F (2004) Shear-induced demixing and shear-banding instabilities in dilute triblock copolymer solutions. Macromolecules 37:2313-2321
243. Wekumbura C, Stastna J, Zanzotto L (2005) Stress growth coefficient in polymer modified asphalt. Mater Struct 38:755-760
244. Winter HH (1978) On the network models of molten polymers: Loss of junctions due to stretching of material planes. Rheol Acta 17:589-594
245. Yamaguchi M, Takahashi M (2001) Rheological properties of low-density polyethylenes produced by tubular and vessel processes. Polymer 42:8663-8670
246. Yamamoto T, Ohta Y, Takigawa T, Masuda T (2002) Stress relaxation of multi-arm star polystyrenes in the molten state. Nihon Reoroji Gakkaishi 30(3):129-132
247. Yin G, Solomon MJ (2008) Soft glassy rheology model applied to stress relaxation of a thermoreversible colloidal gel. J Rheol 52(3):785-800
248. Zapas LJ, Phillips JC (1971) Simple shearing flows in polyisobutylene solutions. J Res Natl Bur Stand 75A:33-40
249. Zdilar AM, Tanner RI (1992) The recoil of rigid PVC. Rheol Acta 31:44-54
250. Zdilar AM, Tanner RI (1993) Erratum. Rheol Acta 32:114
251. Zdilar AM, Tanner RI (1994) Role of structure in rigid PVC recoil. J Rheol 38(4):909-920
252. Zeng XS, Takahashi M, Yamane H, Takigawa T, Masuda T (1999a) Dynamic viscoelasticity of ionomers based on ethylene-co-methacrylic acid copolymer in the melt state. J Soc Rheol Japan 27(1):53-57
253. Zeng XS, Takahashi M, Yamane H, Masuda T (1999b) Stress relaxation under large step strain for ionomers based on ethylene-co-methacrylic acid copolymer in the melt state. J Soc Rheol Japan 27(1):59-62
254. Zheng Q, Wang W, Yu Q, Yu J, He L, Tan H (2006) Nonlinear viscoelastic behaviour of styrene-[ethylene-ethylene-propylene)]-styrene block copolymer. J Polym Sci B Polym Phys 44:1309-1319
255. Zhou L, Vasquez PA, Cook LP, McKinley GH (2008) Modeling the inhomogeneous response and formation of shear bands in steady and transient flows of entangled liquids. J Rheol 52(2):591-623