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Volumn 42, Issue 2, 2001, Pages 796-817

The equivalence of the class of Rivlin-Sawyers equations and a class of stochastic models for polymer stress

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EID: 0035529627     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1332783     Document Type: Article
Times cited : (4)

References (56)
  • 1
    • 0015248194 scopus 로고
    • Nonlinear continuum mechanics of viscoelastic fluids
    • R.S. Rivlin and K.N. Sawyers, "Nonlinear continuum mechanics of viscoelastic fluids," Annu. Rev. Fluid Mech. 3, 117-146 (1971).
    • (1971) Annu. Rev. Fluid Mech. , vol.3 , pp. 117-146
    • Rivlin, R.S.1    Sawyers, K.N.2
  • 3
    • 0007428295 scopus 로고
    • College of Aeronautics, Cranfield, Note No. 134
    • A. Kaye, College of Aeronautics, Cranfield, Note No. 134, 1962.
    • (1962)
    • Kaye, A.1
  • 4
    • 0000864574 scopus 로고
    • A network theory of flow birefringence and stress in concentrated polymer solutions
    • A.S. Lodge, "A network theory of flow birefringence and stress in concentrated polymer solutions," Trans. Faraday Soc. 52, 120-130 (1956).
    • (1956) Trans. Faraday Soc. , vol.52 , pp. 120-130
    • Lodge, A.S.1
  • 5
    • 0000285734 scopus 로고
    • Constitutive equations from molecular network theories for polymer solutions
    • A.S. Lodge, "Constitutive equations from molecular network theories for polymer solutions," Rheol. Acta 7, 379-392 (1968).
    • (1968) Rheol. Acta , vol.7 , pp. 379-392
    • Lodge, A.S.1
  • 6
    • 0042212048 scopus 로고
    • Dynamics of concentrated polymer systems. 1. Brownian motion in the equilibrium state
    • M. Doi and S.F. Edwards, "Dynamics of concentrated polymer systems. 1. Brownian motion in the equilibrium state," J. Chem. Soc., Faraday Trans. 2 74, 1789-1801 (1978).
    • (1978) J. Chem. Soc., Faraday Trans. 2 , vol.74 , pp. 1789-1801
    • Doi, M.1    Edwards, S.F.2
  • 7
    • 37049109677 scopus 로고
    • Dynamics of concentrated polymer systems. 2. Molecular motion under flow
    • M. Doi and S.F. Edwards, "Dynamics of concentrated polymer systems. 2. Molecular motion under flow," J. Chem. Soc., Faraday Trans. 2 74, 1802-1817 (1978).
    • (1978) J. Chem. Soc., Faraday Trans. 2 , vol.74 , pp. 1802-1817
    • Doi, M.1    Edwards, S.F.2
  • 8
    • 22244487037 scopus 로고
    • Dynamics of concentrated polymer systems. 3. The constitutive equation
    • M. Doi and S.F. Edwards, "Dynamics of concentrated polymer systems. 3. The constitutive equation," J. Chem. Soc., Faraday Trans. 2 74, 1818-1832 (1978).
    • (1978) J. Chem. Soc., Faraday Trans. 2 , vol.74 , pp. 1818-1832
    • Doi, M.1    Edwards, S.F.2
  • 9
    • 37049112742 scopus 로고
    • Dynamics of concentrated polymer systems. 4. Rheological properties
    • M. Doi and S.F. Edwards, "Dynamics of concentrated polymer systems. 4. Rheological properties," J. Chem. Soc., Faraday Trans. 2 75, 38-54 (1979).
    • (1979) J. Chem. Soc., Faraday Trans. 2 , vol.75 , pp. 38-54
    • Doi, M.1    Edwards, S.F.2
  • 10
    • 36749106886 scopus 로고
    • A kinetic theory for polymer melts. 1. The equation for the single-link orientational distribution function
    • C.F. Curtiss and R.B. Bird, "A kinetic theory for polymer melts. 1. The equation for the single-link orientational distribution function," J. Chem. Phys. 74, 2016-2025 (1981).
    • (1981) J. Chem. Phys. , vol.74 , pp. 2016-2025
    • Curtiss, C.F.1    Bird, R.B.2
  • 11
    • 36749118002 scopus 로고
    • A kinetic theory for polymer melts. 2. The stress tensor and the rheological equation of state
    • C.F. Curtiss and R.B. Bird, "A kinetic theory for polymer melts. 2. The stress tensor and the rheological equation of state," J. Chem. Phys. 74, 2026-2033 (1981).
    • (1981) J. Chem. Phys. , vol.74 , pp. 2026-2033
    • Curtiss, C.F.1    Bird, R.B.2
  • 12
    • 0027608224 scopus 로고
    • Calculation of viscoelastic flow using molecular models: The CONNFFESSIT approach
    • M. Laso and H.C. Öttinger, "Calculation of viscoelastic flow using molecular models: the CONNFFESSIT approach," J. Non-Newtonian Fluid Mech. 47, 1-20 (1993).
    • (1993) J. Non-newtonian Fluid Mech. , vol.47 , pp. 1-20
    • Laso, M.1    Öttinger, H.C.2
  • 13
    • 0029292076 scopus 로고
    • The CONNFFESSIT approach for solving a two-dimensional viscoelastic fluid problem
    • K. Feigl, M. Laso, and H.C. Öttinger, "The CONNFFESSIT approach for solving a two-dimensional viscoelastic fluid problem," Macromolecules 28, 3261-3274 (1995).
    • (1995) Macromolecules , vol.28 , pp. 3261-3274
    • Feigl, K.1    Laso, M.2    Öttinger, H.C.3
  • 14
    • 0030131322 scopus 로고    scopus 로고
    • Application of kinetic theory models in spatiotemporal flows for polymer solutions, liquid crystals, and polymer melts using the CONNFFESSIT approach
    • C.C. Hua and J.D. Schieber, "Application of kinetic theory models in spatiotemporal flows for polymer solutions, liquid crystals, and polymer melts using the CONNFFESSIT approach," Chem. Eng. Sci. 51, 1473-1485 (1996).
    • (1996) Chem. Eng. Sci. , vol.51 , pp. 1473-1485
    • Hua, C.C.1    Schieber, J.D.2
  • 15
    • 0000137599 scopus 로고    scopus 로고
    • Viscoelastic flow through fibrous media using the CONNFFESSIT approach
    • C.C. Hua and J.D. Schieber, "Viscoelastic flow through fibrous media using the CONNFFESSIT approach," J. Rheol. 42, 477-491 (1998).
    • (1998) J. Rheol. , vol.42 , pp. 477-491
    • Hua, C.C.1    Schieber, J.D.2
  • 16
    • 0031128185 scopus 로고    scopus 로고
    • Two-dimensional, time-dependent viscoelastic calculations using CONNFFESSIT
    • M. Laso, M. Picasso, and H.C. Öttinger, "Two-dimensional, time-dependent viscoelastic calculations using CONNFFESSIT," AIChE J. 43, 877-892 (1997).
    • (1997) AIChE J. , vol.43 , pp. 877-892
    • Laso, M.1    Picasso, M.2    Öttinger, H.C.3
  • 17
    • 0031097299 scopus 로고    scopus 로고
    • Combined Brownian dynamics and spectral method simulations of the recovery of polymeric fluids after shear flow
    • T.W. Bell, G.H. Nyland, M.D. Graham, and J.J. de Pablo, "Combined Brownian dynamics and spectral method simulations of the recovery of polymeric fluids after shear flow," Macromolecules 30, 1806-1812 (1997).
    • (1997) Macromolecules , vol.30 , pp. 1806-1812
    • Bell, T.W.1    Nyland, G.H.2    Graham, M.D.3    De Pablo, J.J.4
  • 18
    • 0033567201 scopus 로고    scopus 로고
    • Variance reduced methods for CONNFFESSIT-like simulations
    • J. Bonvin and M. Picasso, "Variance reduced methods for CONNFFESSIT-like simulations," J. Non-Newtonian Fluid Mech. 84, 191-215 (1999).
    • (1999) J. Non-Newtonian Fluid Mech. , vol.84 , pp. 191-215
    • Bonvin, J.1    Picasso, M.2
  • 20
    • 0031476607 scopus 로고    scopus 로고
    • Brownian configuration fields: A new method for simulating viscoelastic fluid flow
    • B. van den Brule, T. van Heel, and M. Hulsen, "Brownian configuration fields: A new method for simulating viscoelastic fluid flow," Macromol. Symp. 121, 205-217 (1997).
    • (1997) Macromol. Symp. , vol.121 , pp. 205-217
    • Van Den Brule, B.1    Van Heel, T.2    Hulsen, M.3
  • 22
  • 23
    • 0034215791 scopus 로고    scopus 로고
    • Generalization of the deformation field method to simulate advanced reptation models in complex flow
    • E.A.J.F. Peters, A.P.G. van Heel, M.A. Hulsen, and B.H.A.A. van den Brule, "Generalization of the deformation field method to simulate advanced reptation models in complex flow," J. Rheol. 44, 811-829 (2000).
    • (2000) J. Rheol. , vol.44 , pp. 811-829
    • Peters, E.A.J.F.1    Van Heel, A.P.G.2    Hulsen, M.A.3    Van Den Brule, B.H.A.A.4
  • 24
    • 0033567301 scopus 로고    scopus 로고
    • Simulation of fibre suspension flows by the Brownian configuration field method
    • X.-J. Fan, N. Phan-Thien, and R. Zheng, "Simulation of fibre suspension flows by the Brownian configuration field method," J. Non-Newtonian Fluid Mech. 84, 257-274 (1999).
    • (1999) J. Non-Newtonian Fluid Mech. , vol.84 , pp. 257-274
    • Fan, X.-J.1    Phan-Thien, N.2    Zheng, R.3
  • 25
    • 0000951263 scopus 로고    scopus 로고
    • A new class of stochastic simulation models for polymer stress calculation
    • K. Feigl and H.C. Öttinger, "A new class of stochastic simulation models for polymer stress calculation," J. Chem. Phys. 109, 815-826 (1998).
    • (1998) J. Chem. Phys. , vol.109 , pp. 815-826
    • Feigl, K.1    Öttinger, H.C.2
  • 26
    • 0642364614 scopus 로고    scopus 로고
    • Towards realistic rheological models for polymer melt processing
    • K. Feigl and H.C. Öttinger, "Towards realistic rheological models for polymer melt processing," Macromol. Symp. 121, 187-203 (1997).
    • (1997) Macromol. Symp. , vol.121 , pp. 187-203
    • Feigl, K.1    Öttinger, H.C.2
  • 27
    • 0017518270 scopus 로고
    • New constitutive equation derived from network theory
    • N. Phan-Thien and R.I. Tanner, "New constitutive equation derived from network theory," J. Non-Newtonian Fluid Mech. 2, 353-365 (1977).
    • (1977) J. Non-Newtonian Fluid Mech. , vol.2 , pp. 353-365
    • Phan-Thien, N.1    Tanner, R.I.2
  • 28
    • 34250269973 scopus 로고
    • Network theory of polymer melts
    • M.H. Wagner, "Network theory of polymer melts," Rheol. Acta 18, 33-50 (1979).
    • (1979) Rheol. Acta , vol.18 , pp. 33-50
    • Wagner, M.H.1
  • 29
    • 0002569029 scopus 로고
    • A numerical stochastic approach to network theories of polymeric fluids
    • F. Petruccione and P. Biller, "A numerical stochastic approach to network theories of polymeric fluids," J. Chem. Phys. 89, 577-582 (1988).
    • (1988) J. Chem. Phys. , vol.89 , pp. 577-582
    • Petruccione, F.1    Biller, P.2
  • 30
    • 0001458931 scopus 로고
    • Rheological properties of network models with configuration-dependent creation and loss rates
    • F. Petruccione and P. Biller, "Rheological properties of network models with configuration-dependent creation and loss rates," Rheol. Acta 27, 557-560 (1988).
    • (1988) Rheol. Acta , vol.27 , pp. 557-560
    • Petruccione, F.1    Biller, P.2
  • 31
    • 0007378630 scopus 로고
    • Continuous-time simulation of transient polymer network models
    • P. Biller and F. Petruccione, "Continuous-time simulation of transient polymer network models," J. Chem. Phys. 92, 6322-6326 (1990).
    • (1990) J. Chem. Phys. , vol.92 , pp. 6322-6326
    • Biller, P.1    Petruccione, F.2
  • 32
    • 84986850907 scopus 로고
    • Continuous-time simulation of transient polymer networks: Rheological properties
    • P. Biller and F. Petruccione, "Continuous-time simulation of transient polymer networks: Rheological properties," Macromol. Symp. 45, 169-175 (1991).
    • (1991) Macromol. Symp. , vol.45 , pp. 169-175
    • Biller, P.1    Petruccione, F.2
  • 33
    • 0000130329 scopus 로고
    • Modified reptation model
    • H.C. Öttinger, "Modified reptation model," Phys. Rev. E 50, 4891-4895 (1994).
    • (1994) Phys. Rev. E , vol.50 , pp. 4891-4895
    • Öttinger, H.C.1
  • 34
    • 0004074550 scopus 로고
    • International Series of Monographs on Physics Clarendon, Oxford
    • M. Doi and S.F. Edwards, The Theory of Polymer Dynamics, International Series of Monographs on Physics (Clarendon, Oxford, 1986).
    • (1986) The Theory of Polymer Dynamics
    • Doi, M.1    Edwards, S.F.2
  • 35
    • 0020749830 scopus 로고
    • Explanation for the 3.4-power law for the viscosity of polymeric liquids on the basis of the tube model
    • M. Doi, "Explanation for the 3.4-power law for the viscosity of polymeric liquids on the basis of the tube model," J. Polym. Sci., Polym. Phys. Ed. 21, 667-684 (1983).
    • (1983) J. Polym. Sci., Polym. Phys. Ed. , vol.21 , pp. 667-684
    • Doi, M.1
  • 36
    • 0001318229 scopus 로고    scopus 로고
    • Segment connectivity, chain-length breathing, segmental stretch, and constraint release in reptation models. I. Theory and single-step strain predictions
    • C.C. Hua and J.D. Schieber, "Segment connectivity, chain-length breathing, segmental stretch, and constraint release in reptation models. I. Theory and single-step strain predictions," J. Chem. Phys. 109, 10018-10027 (1998).
    • (1998) J. Chem. Phys. , vol.109 , pp. 10018-10027
    • Hua, C.C.1    Schieber, J.D.2
  • 37
    • 0001318230 scopus 로고    scopus 로고
    • Segment connectivity, chain-length breathing, segmental stretch, and constraint release in reptation models. II. Double-step strain predictions
    • C.C. Hua, J.D. Schieber, and D.C. Venerus, "Segment connectivity, chain-length breathing, segmental stretch, and constraint release in reptation models. II. Double-step strain predictions," J. Chem. Phys. 109, 10028-10032 (1998).
    • (1998) J. Chem. Phys. , vol.109 , pp. 10028-10032
    • Hua, C.C.1    Schieber, J.D.2    Venerus, D.C.3
  • 38
    • 0001739528 scopus 로고    scopus 로고
    • Segment connectivity, chain-length breathing, segmental stretch, and constraint release in reptation models. III. Shear flows
    • C.C. Hua, J.D. Schieber, and D.C. Venerus, "Segment connectivity, chain-length breathing, segmental stretch, and constraint release in reptation models. III. Shear flows," J. Rheol. 43, 701-717 (1999).
    • (1999) J. Rheol. , vol.43 , pp. 701-717
    • Hua, C.C.1    Schieber, J.D.2    Venerus, D.C.3
  • 39
    • 0030083167 scopus 로고    scopus 로고
    • Dynamics of entanglements: A nonlinear model consistent with the Cox-Merz rule
    • G. Marrucci, "Dynamics of entanglements: A nonlinear model consistent with the Cox-Merz rule," J. Non-Newtonian Fluid Mech. 62, 279-289 (1996).
    • (1996) J. Non-Newtonian Fluid Mech. , vol.62 , pp. 279-289
    • Marrucci, G.1
  • 40
    • 0030201393 scopus 로고    scopus 로고
    • On compatibility of the Cox-Merz rule with the model of Doi and Edwards
    • G. Ianniruberto and G. Marrucci, "On compatibility of the Cox-Merz rule with the model of Doi and Edwards," J. Non-Newtonian Fluid Mech. 65, 241-246 (1996).
    • (1996) J. Non-Newtonian Fluid Mech. , vol.65 , pp. 241-246
    • Ianniruberto, G.1    Marrucci, G.2
  • 41
    • 0032480701 scopus 로고    scopus 로고
    • A molecular theory for fast flows of entangled polymers
    • D.W. Mead, R. Larson, and M. Doi, "A molecular theory for fast flows of entangled polymers," Macromolecules 31, 7895-7914 (1998).
    • (1998) Macromolecules , vol.31 , pp. 7895-7914
    • Mead, D.W.1    Larson, R.2    Doi, M.3
  • 43
    • 0002835364 scopus 로고
    • The stress relaxation of molten PMMA at large deformations and its theoretical interpretation
    • G. Marrucci and B. de Cindio, "The stress relaxation of molten PMMA at large deformations and its theoretical interpretation," Rheol. Acta 19, 68-75 (1980).
    • (1980) Rheol. Acta , vol.19 , pp. 68-75
    • Marrucci, G.1    De Cindio, B.2
  • 44
    • 0001380092 scopus 로고
    • Nonlinear viscoelasticity of concentrated polymeric liquids
    • G. Marrucci and J.J. Hermans, "Nonlinear viscoelasticity of concentrated polymeric liquids," Macromolecules 13, 380-387 (1980).
    • (1980) Macromolecules , vol.13 , pp. 380-387
    • Marrucci, G.1    Hermans, J.J.2
  • 45
    • 3743153894 scopus 로고
    • Nonlinear strain measures for general biaxial extension of polymer melts
    • M.H. Wagner and J. Schaeffer, "Nonlinear strain measures for general biaxial extension of polymer melts," J. Rheol. 36, 1-26 (1992).
    • (1992) J. Rheol. , vol.36 , pp. 1-26
    • Wagner, M.H.1    Schaeffer, J.2
  • 46
    • 0032216101 scopus 로고    scopus 로고
    • Stress tensor and stress-optical law in entangled polymers
    • G. Ianniruberto and G. Marrucci, "Stress tensor and stress-optical law in entangled polymers," J. Non-Newtonian Fluid Mech. 79, 225-234 (1998).
    • (1998) J. Non-Newtonian Fluid Mech. , vol.79 , pp. 225-234
    • Ianniruberto, G.1    Marrucci, G.2
  • 47
    • 0033133817 scopus 로고    scopus 로고
    • Open problems in tube models for concentrated polymers
    • G. Marrucci and G. Ianniruberto, "Open problems in tube models for concentrated polymers," J. Non-Newtonian Fluid Mech. 82, 275-286 (1999).
    • (1999) J. Non-Newtonian Fluid Mech. , vol.82 , pp. 275-286
    • Marrucci, G.1    Ianniruberto, G.2
  • 48
    • 0000782981 scopus 로고    scopus 로고
    • A thermodynamically admissible reptation model for fast flows of entangled polymers
    • H.C. Öttinger, "A thermodynamically admissible reptation model for fast flows of entangled polymers," J. Rheol. 43, 1461-1493 (1999).
    • (1999) J. Rheol. , vol.43 , pp. 1461-1493
    • Öttinger, H.C.1
  • 49
    • 0034652504 scopus 로고    scopus 로고
    • Thermodynamically admissible reptation models with anisotropic tube cross sections and convective constraint release
    • H.C. Öttinger, "Thermodynamically admissible reptation models with anisotropic tube cross sections and convective constraint release," J. Non-Newtonian Fluid Mech. 89, 165-186 (2000).
    • (2000) J. Non-Newtonian Fluid Mech. , vol.89 , pp. 165-186
    • Öttinger, H.C.1
  • 51
    • 0002577320 scopus 로고
    • Estimates of Laguerre spectral projectors in Sobolev spaces
    • C. Brezinski, L. Gori, and A. Ronveaux J.C. Baltzer AG, Scientific Publishing, IMACS
    • D. Funaro, "Estimates of Laguerre spectral projectors in Sobolev spaces" in Orthogonal Polynomials and their Applications, edited by C. Brezinski, L. Gori, and A. Ronveaux (J.C. Baltzer AG, Scientific Publishing, IMACS, 1991), pp. 263-266.
    • (1991) Orthogonal Polynomials and Their Applications , pp. 263-266
    • Funaro, D.1
  • 52
    • 0025445675 scopus 로고
    • Laguerre spectral approximation of elliptic problems in exterior domains
    • O. Coulaud, D. Funaro, and O. Kavian, "Laguerre spectral approximation of elliptic problems in exterior domains," Comput. Methods Appl. Mech. Eng. 80, 451-458 (1990).
    • (1990) Comput. Methods Appl. Mech. Eng. , vol.80 , pp. 451-458
    • Coulaud, O.1    Funaro, D.2    Kavian, O.3
  • 53
    • 0000964252 scopus 로고
    • Une réhabilitation des méthodes spectrales de type Laguerre
    • Y. Maday, B. Pernaud-Thomas, and H. Vandeven, "Une réhabilitation des méthodes spectrales de type Laguerre," Rech. Aerosp. 6, 353-375 (1985).
    • (1985) Rech. Aerosp. , vol.6 , pp. 353-375
    • Maday, Y.1    Pernaud-Thomas, B.2    Vandeven, H.3
  • 54
    • 67349095304 scopus 로고    scopus 로고
    • Spectral methods
    • P.G. Ciarlet and J.-L. Lions North-Holland, Amsterdam
    • C. Bernardi and Y. Maday, "Spectral methods" in Handbook of Numerical Analysis, edited by P.G. Ciarlet and J.-L. Lions (North-Holland, Amsterdam, 1997), Vol. 5. pp. 209-485.
    • (1997) Handbook of Numerical Analysis , vol.5 , pp. 209-485
    • Bernardi, C.1    Maday, Y.2
  • 55
    • 0000950141 scopus 로고    scopus 로고
    • Spectral element methods
    • P.G. Ciarlet and J.-L. Lions (North-Holland, Amsterdam, to appear)
    • C. Bernardi, Y. Maday, and A.T. Patera, "Spectral element methods" in Handbook of Numerical Analysis, edited by P.G. Ciarlet and J.-L. Lions (North-Holland, Amsterdam, to appear).
    • Handbook of Numerical Analysis
    • Bernardi, C.1    Maday, Y.2    Patera, A.T.3


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