메뉴 건너뛰기




Volumn 42, Issue 6, 2003, Pages 500-515

Rheological constitutive equation of solids: A link between models based on irreversible thermodynamics and on fractional order derivative equations

Author keywords

Fractal dynamics rheology; Fractional calculus; Irreversible thermodynamics; Relaxation phenomena; Viscoelasticity

Indexed keywords

FRACTAL ANALYSIS; MATHEMATICAL ANALYSIS; MODEL; RHEOLOGY; THERMODYNAMICS; VISCOELASTICITY;

EID: 0345530048     PISSN: 00354511     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00397-003-0305-z     Document Type: Article
Times cited : (21)

References (66)
  • 1
    • 0035202530 scopus 로고    scopus 로고
    • The DNLR approach and relaxation phenomena. Part II. Application: Volume recovery of PV Ac. Comparison between the DNLR approach and some other modelings
    • Aharoune A, Marceron-Balland P, Cunat C (2001) The DNLR approach and relaxation phenomena. Part II. Application: volume recovery of PV Ac. Comparison between the DNLR approach and some other modelings. Mech Time-Depend Mater 5:345-377
    • (2001) Mech Time-Depend Mater , vol.5 , pp. 345-377
    • Aharoune, A.1    Marceron-Balland, P.2    Cunat, C.3
  • 2
    • 0021850738 scopus 로고
    • A prediction of heat generation in a thermo-viscoplastic uniaxial bar
    • Allen DH (1985) A prediction of heat generation in a thermo-viscoplastic uniaxial bar. Int J Solids Struct 21(4):325-342
    • (1985) Int J Solids Struct , vol.21 , Issue.4 , pp. 325-342
    • Allen, D.H.1
  • 3
    • 0033137544 scopus 로고    scopus 로고
    • Thermodynamic modeling of creep mechanical behaviour by non linear relaxation
    • Ayadi Z, Marceon P, Schmitt JF, Cunat C (1999) Thermodynamic modeling of creep mechanical behaviour by non linear relaxation. Eur Phys J AP 6:229-235
    • (1999) Eur Phys J AP , vol.6 , pp. 229-235
    • Ayadi, Z.1    Marceon, P.2    Schmitt, J.F.3    Cunat, C.4
  • 4
    • 0024748763 scopus 로고
    • Power law and fractional calculus model of viscoelasticity
    • Bagley RL (1989) Power law and fractional calculus model of viscoelasticity. AIAA J 27(10):1412-1417
    • (1989) AIAA J , vol.27 , Issue.10 , pp. 1412-1417
    • Bagley, R.L.1
  • 5
    • 0025842580 scopus 로고
    • The thermorheologically complex material
    • Bagley RL (1991) The thermorheologically complex material. Int J Eng Sci 29(7):797-806
    • (1991) Int J Eng Sci , vol.29 , Issue.7 , pp. 797-806
    • Bagley, R.L.1
  • 6
    • 0022660581 scopus 로고
    • On the fractional calculus model of viscoelastic behavior
    • Bagley RL, Torvik PJ (1986) On the fractional calculus model of viscoelastic behavior. J Rheol 30(1):133-155
    • (1986) J Rheol , vol.30 , Issue.1 , pp. 133-155
    • Bagley, R.L.1    Torvik, P.J.2
  • 7
    • 0031131244 scopus 로고    scopus 로고
    • Physics of fracture and mechanics of self-affine cracks
    • Balankin AS (1997) Physics of fracture and mechanics of self-affine cracks. Eng Fracture Mech 57:135-203
    • (1997) Eng Fracture Mech , vol.57 , pp. 135-203
    • Balankin, A.S.1
  • 8
    • 0004544811 scopus 로고
    • Dielectric relaxation via the Montroll-Weiss random walk of defect
    • Shlesinger MF, Weiss GH (eds) Elsevier Sciences
    • Bendler JT, Shlesinger MF (1985) Dielectric relaxation via the Montroll-Weiss random walk of defect. In: Shlesinger MF, Weiss GH (eds) The wonderful world of stochastics, a tribute to E.W. Montroll. Elsevier Sciences, pp 33-46
    • (1985) The Wonderful World of Stochastics, a Tribute to E.W. Montroll , pp. 33-46
    • Bendler, J.T.1    Shlesinger, M.F.2
  • 9
    • 0344788032 scopus 로고
    • A first passage time problem for random walk occupancy
    • Bendler JT, Shlesinger MF (1988) A first passage time problem for random walk occupancy. J Stat Phys 53:1069-1087
    • (1988) J Stat Phys , vol.53 , pp. 1069-1087
    • Bendler, J.T.1    Shlesinger, M.F.2
  • 11
    • 0036028181 scopus 로고    scopus 로고
    • A fractional calculus approach to the description of stress and strain localization in fractal media
    • Carpinteri A, Cornetti P (2002) A fractional calculus approach to the description of stress and strain localization in fractal media. Chaos Solitons Fractals 13:85-94
    • (2002) Chaos Solitons Fractals , vol.13 , pp. 85-94
    • Carpinteri, A.1    Cornetti, P.2
  • 12
    • 0345218901 scopus 로고    scopus 로고
    • Analyse expérimentale et modélisation numérique des couplages thermomécaniques dans les matériaux solides
    • Chrysochoos A, Peyroux R (1998) Analyse expérimentale et modélisation numérique des couplages thermomécaniques dans les matériaux solides. Rev Gén Therm 37:582-606
    • (1998) Rev Gén Therm , vol.37 , pp. 582-606
    • Chrysochoos, A.1    Peyroux, R.2
  • 13
    • 36849104050 scopus 로고
    • Thermodynamics with internal state variables
    • Coleman BD, Gurtin ME (1967) Thermodynamics with internal state variables. J Chem Phys 47:597-613
    • (1967) J Chem Phys , vol.47 , pp. 597-613
    • Coleman, B.D.1    Gurtin, M.E.2
  • 15
    • 0006843022 scopus 로고
    • Thermodynamic treatment of relaxation in frozen-in systems. "University" of the distribution law for relaxation times
    • 425-429
    • Cunat C (1988) Thermodynamic treatment of relaxation in frozen-in systems. "University" of the distribution law for relaxation times. Z Phys Chem Neue Folge 157:419-423, 425-429
    • (1988) Z Phys Chem Neue Folge , vol.157 , pp. 419-423
    • Cunat, C.1
  • 16
    • 0026413704 scopus 로고
    • A thermodynamical theory of relaxation based on distribution of non linear processes
    • 196-199
    • Cunat C (1991) A thermodynamical theory of relaxation based on distribution of non linear processes. J Non-Cryst Solids 131-133, 196-199
    • (1991) J Non-Cryst Solids , pp. 131-133
    • Cunat, C.1
  • 17
    • 0035079155 scopus 로고    scopus 로고
    • The DNLR approach and relaxation phenomena. Part I. Historical account and DNLR formalism
    • Cunat C (2001) The DNLR approach and relaxation phenomena. Part I. Historical account and DNLR formalism. Mech Time-Depend Mater 5:39-65
    • (2001) Mech Time-Depend Mater , vol.5 , pp. 39-65
    • Cunat, C.1
  • 20
    • 0041169153 scopus 로고
    • An experimental study of the heat generated during torsional oscillations
    • Dillon OW (1962) An experimental study of the heat generated during torsional oscillations. J Mech Phys Solids 10:224-235
    • (1962) J Mech Phys Solids , vol.10 , pp. 224-235
    • Dillon, O.W.1
  • 21
    • 0033097283 scopus 로고    scopus 로고
    • Damping described by fading memory analysis and application to fractional derivative models
    • Enelund M, Olsson P (1999) Damping described by fading memory analysis and application to fractional derivative models, Int J Solids Struct 36:939-970
    • (1999) Int J Solids Struct , vol.36 , pp. 939-970
    • Enelund, M.1    Olsson, P.2
  • 22
    • 0035082509 scopus 로고    scopus 로고
    • Modeling of the mechanical behavior of a nickel alloy by using a time-dependent thermodynamic approach to relaxation of continuous media
    • Faccio-Toussaint E, Ayadi Z, Pilvin P, Cunat C (2001) Modeling of the mechanical behavior of a nickel alloy by using a time-dependent thermodynamic approach to relaxation of continuous media. Mech Time-Depend Mater 5:1-25
    • (2001) Mech Time-Depend Mater , vol.5 , pp. 1-25
    • Faccio-Toussaint, E.1    Ayadi, Z.2    Pilvin, P.3    Cunat, C.4
  • 24
    • 0342619501 scopus 로고    scopus 로고
    • Constitutive behavior modeling and fractional calculus
    • Siginer DA, De-Kee D, Chabra RP (eds) Elsevier, Amsterdam
    • Friedrich C, Schiessel H, Blumen A (1999) Constitutive behavior modeling and fractional calculus. In: Siginer DA, De-Kee D, Chabra RP (eds) Advances in the flow and rheology of non-Newtonian fluids. Elsevier, Amsterdam, pp 429-466
    • (1999) Advances in the Flow and Rheology of Non-Newtonian Fluids , pp. 429-466
    • Friedrich, C.1    Schiessel, H.2    Blumen, A.3
  • 25
    • 0345218900 scopus 로고
    • A method of analyzing experimental results obtained from el-asto-viscous bodies
    • Gemant A (1936) A method of analyzing experimental results obtained from el-asto-viscous bodies. Physics 7:17-31
    • (1936) Physics , vol.7 , pp. 17-31
    • Gemant, A.1
  • 26
    • 0026260899 scopus 로고
    • Fractional integral operators and Fox functions in the theory of viscoelasticity
    • Glöckle WG, Nonnenmacher TF (1991) Fractional integral operators and Fox functions in the theory of viscoelasticity. Macromolecules 24:6426-6434
    • (1991) Macromolecules , vol.24 , pp. 6426-6434
    • Glöckle, W.G.1    Nonnenmacher, T.F.2
  • 28
    • 0001488637 scopus 로고
    • Fractal rheological models and fractional differential equations for viscoelastic behaviour
    • Heymans N, Bawens JC (1994) Fractal rheological models and fractional differential equations for viscoelastic behaviour. Rheol Acta, 33:210-219
    • (1994) Rheol Acta , vol.33 , pp. 210-219
    • Heymans, N.1    Bawens, J.C.2
  • 29
    • 0022779409 scopus 로고
    • The fractal nature of slips in crystals
    • Kleiser T, Bocek MX (1986) The fractal nature of slips in crystals. Z Metallkd 77:582-587
    • (1986) Z Metallkd , vol.77 , pp. 582-587
    • Kleiser, T.1    Bocek, M.X.2
  • 30
    • 0041817044 scopus 로고
    • Thermodynamic theory of elasticity and plasticity
    • Kluitenberg GA (1962) Thermodynamic theory of elasticity and plasticity. Physica 28:217-232
    • (1962) Physica , vol.28 , pp. 217-232
    • Kluitenberg, G.A.1
  • 31
    • 0021440218 scopus 로고
    • Applications of fractional calculus to the theory of viscoelasticity
    • Koeller RC (1984) Applications of fractional calculus to the theory of viscoelasticity. J Appl Mech 51:299-307
    • (1984) J Appl Mech , vol.51 , pp. 299-307
    • Koeller, R.C.1
  • 32
    • 0018491130 scopus 로고
    • Isobaric volume and enthalpy recovery of glasses. A transparent multiparameter theory
    • Kovacs AJ, Aklonis JJ, Hutchinson JM, Ramos AR (1979) Isobaric volume and enthalpy recovery of glasses. A transparent multiparameter theory. J Polym Sci Phys 17:1097
    • (1979) J Polym Sci Phys , vol.17 , pp. 1097
    • Kovacs, A.J.1    Aklonis, J.J.2    Hutchinson, J.M.3    Ramos, A.R.4
  • 35
    • 0025510540 scopus 로고
    • Finite element modeling of frequency-dependent material damping using augmenting thermodynamic field
    • Lesieutre GA, Mingori DL (1990) Finite element modeling of frequency-dependent material damping using augmenting thermodynamic field. J Guidance Control Dynam 13:1040-1050
    • (1990) J Guidance Control Dynam , vol.13 , pp. 1040-1050
    • Lesieutre, G.A.1    Mingori, D.L.2
  • 36
    • 0031285474 scopus 로고    scopus 로고
    • On the thermodynamics of fractional damping elements
    • Lion A (1997) On the thermodynamics of fractional damping elements. Continuum Mech Thermodyn 9:83-96
    • (1997) Continuum Mech Thermodyn , vol.9 , pp. 83-96
    • Lion, A.1
  • 37
    • 0028497784 scopus 로고
    • Fractional relaxation in anelastic solids
    • Mainardi F (1994) Fractional relaxation in anelastic solids. J Alloys Compd 211/ 212:534-538
    • (1994) J Alloys Compd , vol.211-212 , pp. 534-538
    • Mainardi, F.1
  • 39
    • 0028602836 scopus 로고
    • Thermodynamics with internal variables. Part I. General concepts
    • Maugin GA, Muschik W (1994) Thermodynamics with internal variables. Part I. General concepts. J Non-Equilib Thermodyn 19:217-249
    • (1994) J Non-Equilib Thermodyn , vol.19 , pp. 217-249
    • Maugin, G.A.1    Muschik, W.2
  • 40
    • 84941389359 scopus 로고
    • Thermodynamik und Relaxationsserscheinungen
    • Meixner J (1949) Thermodynamik und Relaxationsserscheinungen. Z Naturforsch 4a:594-600
    • (1949) Z Naturforsch , vol.4 a , pp. 594-600
    • Meixner, J.1
  • 41
    • 0032136257 scopus 로고    scopus 로고
    • Physical and geometrical interpretation of fractional operators
    • Moshrefi-Torbati M, Hammond JK (1998) Physical and geometrical interpretation of fractional operators. J Franklin Inst 335B(6):1077-1086
    • (1998) J Franklin Inst , vol.335 B , Issue.6 , pp. 1077-1086
    • Moshrefi-Torbati, M.1    Hammond, J.K.2
  • 42
    • 0028547629 scopus 로고
    • Singular fractal functions and mesoscopic effects in mechanics
    • Mosolov A (1994) Singular fractal functions and mesoscopic effects in mechanics. Chaos Solitons Fractals 4:2093-2102
    • (1994) Chaos Solitons Fractals , vol.4 , pp. 2093-2102
    • Mosolov, A.1
  • 43
    • 0004681849 scopus 로고
    • Fractional integral and its physical interpretation
    • Nigmatullin RR (1990) Fractional integral and its physical interpretation. J Theor Math Phys 90(3):242-251
    • (1990) J Theor Math Phys , vol.90 , Issue.3 , pp. 242-251
    • Nigmatullin, R.R.1
  • 44
    • 0002267332 scopus 로고
    • A fractional model for mechanical stress relaxation
    • Nonnenmacher TF, Glöckle WG (1991) A fractional model for mechanical stress relaxation. Philos Mag Lett 64(2):89-93
    • (1991) Philos Mag Lett , vol.64 , Issue.2 , pp. 89-93
    • Nonnenmacher, T.F.1    Glöckle, W.G.2
  • 46
    • 0000266650 scopus 로고
    • A new generalized law of deformation
    • Nutting PG (1921) A new generalized law of deformation. J Franklin Inst 191:679-685
    • (1921) J Franklin Inst , vol.191 , pp. 679-685
    • Nutting, P.G.1
  • 47
    • 0020831071 scopus 로고
    • Analogue instrumentation for processing polarographic data
    • Oldham KB, Zoski CG (1983) Analogue instrumentation for processing polarographic data. J Electroanal Chem 157:27-51
    • (1983) J Electroanal Chem , vol.157 , pp. 27-51
    • Oldham, K.B.1    Zoski, C.G.2
  • 48
    • 36149006492 scopus 로고
    • Reciprocal relations in irreversible processes I
    • Reciprocal relations in irreversible processes II. Phys Rev 38:2265-2279
    • Onsager L (1931) Reciprocal relations in irreversible processes I. Phys Rev 37:405-426; Reciprocal relations in irreversible processes II. Phys Rev 38:2265-2279
    • (1931) Phys Rev , vol.37 , pp. 405-426
    • Onsager, L.1
  • 50
    • 0023859640 scopus 로고
    • General response of viscoelastic systems modeled by fractional operators
    • Padovan J, Guo Y (1988) General response of viscoelastic systems modeled by fractional operators. J Franklin Inst 325:247-275
    • (1988) J Franklin Inst , vol.325 , pp. 247-275
    • Padovan, J.1    Guo, Y.2
  • 52
    • 0345218898 scopus 로고    scopus 로고
    • A nonlinear viscoelastic model based on fluctuating modes
    • Lemaître J (ed) Deformations of Materials. Academic Press
    • Rahouadj R, Cunat C (2001a) A nonlinear viscoelastic model based on fluctuating modes. In: Lemaître J (ed) Handbook of materials behavior models, vol I. Deformations of materials. Academic Press, pp 107-116
    • (2001) Handbook of Materials Behavior Models , vol.1 , pp. 107-116
    • Rahouadj, R.1    Cunat, C.2
  • 54
    • 0020805145 scopus 로고
    • Operators and fractional derivatives for viscoelastic constitutive equation
    • Rogers L (1983) Operators and fractional derivatives for viscoelastic constitutive equation. J Rheol 27(4):351-372
    • (1983) J Rheol , vol.27 , Issue.4 , pp. 351-372
    • Rogers, L.1
  • 55
    • 0344252790 scopus 로고
    • The theory of the linear viscoelastic properties of dilute solutions of coiling polymers
    • Rouse PE (1953) The theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J Chem Phys 21(7):1272-1280
    • (1953) J Chem Phys , vol.21 , Issue.7 , pp. 1272-1280
    • Rouse, P.E.1
  • 57
    • 36149037022 scopus 로고
    • Hierarchical analogues to fractional relaxation equations
    • Schiessel H, Blumen A (1993) Hierarchical analogues to fractional relaxation equations. J Phys A Math Gen 26:5057-5069
    • (1993) J Phys A Math Gen , vol.26 , pp. 5057-5069
    • Schiessel, H.1    Blumen, A.2
  • 58
    • 0000902727 scopus 로고
    • Generalized viscoelastic models: Their fractional equations with solutions
    • Schiessel H, Metzler R, Blumen A, Nonnenmacher TF (1995) Generalized viscoelastic models: their fractional equations with solutions. J Phys A Math Gen 28:6567-6584
    • (1995) J Phys A Math Gen , vol.28 , pp. 6567-6584
    • Schiessel, H.1    Metzler, R.2    Blumen, A.3    Nonnenmacher, T.F.4
  • 59
    • 0010127267 scopus 로고
    • An application of the theory of quasi-properties to the treatment of anomalous strain-stress relation
    • Scott-Blair G, Caffyn JE (1949) An application of the theory of quasi-properties to the treatment of anomalous strain-stress relation. Philos Mag 40:80-94
    • (1949) Philos Mag , vol.40 , pp. 80-94
    • Scott-Blair, G.1    Caffyn, J.E.2
  • 60
    • 0002426874 scopus 로고
    • The nature of temporal hierarchies underlying relaxation in disordered systems
    • Pietronero L, Tosatti E (eds) Elsevier Sciences
    • Shlesinger MF, Klafter J (1986) The nature of temporal hierarchies underlying relaxation in disordered systems. In: Pietronero L, Tosatti E (eds) Fractals in physics. Elsevier Sciences
    • (1986) Fractals in Physics
    • Shlesinger, M.F.1    Klafter, J.2
  • 61
    • 0344356229 scopus 로고
    • Fractal-time stochastic processes and dynamic functions of polymeric systems
    • Stastna J, De Kee D, Powley M, Schümmer P, Otten B (1990) Fractal-time stochastic processes and dynamic functions of polymeric systems. Rheol Acta 29:137-144
    • (1990) Rheol Acta , vol.29 , pp. 137-144
    • Stastna, J.1    De Kee, D.2    Powley, M.3    Schümmer, P.4    Otten, B.5
  • 62
    • 49949147382 scopus 로고
    • The temperature generated during torsional oscillations in polyethylene rods
    • Tauchert TR (1967) The temperature generated during torsional oscillations in polyethylene rods. Int J Eng Sci 5:353-365
    • (1967) Int J Eng Sci , vol.5 , pp. 353-365
    • Tauchert, T.R.1
  • 65
    • 85007677053 scopus 로고
    • Structural analysis of viscoelastic materials
    • Williams ML (1964) Structural analysis of viscoelastic materials. AIAA J 2(5):785-808
    • (1964) AIAA J , vol.2 , Issue.5 , pp. 785-808
    • Williams, M.L.1
  • 66
    • 0001545976 scopus 로고    scopus 로고
    • The flow stress of fractal dislocation arrangements
    • Zaiser M, Hähner P (1999) The flow stress of fractal dislocation arrangements. Mater Sci Eng A270:299-307
    • (1999) Mater Sci Eng , vol.A270 , pp. 299-307
    • Zaiser, M.1    Hähner, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.