메뉴 건너뛰기




Volumn 6, Issue 1, 2015, Pages

George William Scott Blair - the pioneer of fractional calculus in rheology

Author keywords

Fractional calculus; Hereditary solid mechanics; Relaxation; Rheology; Scott Blair's fractional model

Indexed keywords


EID: 85055244198     PISSN: None     EISSN: 20380909     Source Type: Journal    
DOI: 10.1685/journal.caim.481     Document Type: Article
Times cited : (43)

References (67)
  • 2
    • 33645294787 scopus 로고    scopus 로고
    • Origins of Rheology: A Short Historical Excursion
    • D. Doraiswamy, Origins of Rheology: a Short Historical Excursion. http://www.rheology.org/sor/publications/rheology-b/jan02 /origin-of-rheology.pdf, Rheology Bulletin, vol. 71, no. 1, 2002.
    • (2002) Rheology Bulletin , vol.71 , Issue.1
    • Doraiswamy, D.1
  • 3
    • 0038941484 scopus 로고    scopus 로고
    • The influence of the proximity of a solid wall on the consistency of viscous and plastic materials
    • 1212-1215/973-981,1930/1931/1935
    • R. Schofield and G. S. Blair, The influence of the proximity of a solid wall on the consistency of viscous and plastic materials, J. Phys. Chem., vol. 34/35/39, pp. 248-262/1212-1215/973-981, 1930/1931/1935.
    • J. Phys. Chem , vol.34-39 , Issue.35 , pp. 248-262
    • Schofield, R.1    Blair, G.S.2
  • 4
    • 0040705706 scopus 로고
    • The relationship between viscosity, elasticity and plastic strenght of a soft materials as illustrated by some mechanical properties of flour dough. - III
    • R. Schofield and G. S. Blair, The relationship between viscosity, elasticity and plastic strenght of a soft materials as illustrated by some mechanical properties of flour dough. - III, Proc. Roy. Soc. A, vol. 141, pp. 72-85, 1933.
    • (1933) Proc. Roy. Soc. A , vol.141 , pp. 72-85
    • Schofield, R.1    Blair, G.S.2
  • 7
    • 50349117552 scopus 로고
    • The role of psychophysics in rheology
    • G. S. Blair, The role of psychophysics in rheology, J. Colloid Sci., vol. 2, no. 1, pp. 21-32, 1947.
    • (1947) J. Colloid Sci , vol.2 , Issue.1 , pp. 21-32
    • Blair, G.S.1
  • 9
    • 84879355584 scopus 로고
    • Sur les lois de l'équilibre et du mouvement des cor-pes solides élastique
    • 375-393
    • C. Navier, Sur les lois de l'équilibre et du mouvement des cor-pes solides élastique, Bull. Soc. Philomath./Memoire Acad. Sci., vol. 75/7, pp. 177-183/375-393, 1823/1827.
    • (1823) Bull. Soc. Philomath./Memoire Acad. Sci , vol.75 , Issue.7 , pp. 177-183
    • Navier, C.1
  • 11
    • 0002444828 scopus 로고
    • On the dynamical theory of gases
    • 185-217
    • J. Maxwell, On the dynamical theory of gases, Phil. Mag., vol. 35, pp. 129-146; 185-217, 1868.
    • (1868) Phil. Mag , vol.35 , pp. 129-146
    • Maxwell, J.1
  • 12
    • 2542489387 scopus 로고
    • Strength of amorphous and crystallizing rubber polymers (in Russian)
    • A. Alexandrov and J. Lazurkin, Strength of amorphous and crystallizing rubber polymers (in Russian), Doklady Akad Nauk SSSR, vol. 45, pp. 291-294, 1944.
    • (1944) Doklady Akad Nauk SSSR , vol.45 , pp. 291-294
    • Alexandrov, A.1    Lazurkin, J.2
  • 14
    • 6144238041 scopus 로고
    • The classification of rheological properties of industrial materials in the light of power-law relations between stress, strain, and time
    • G. S. Blair and F. Coppen, The classification of rheological properties of industrial materials in the light of power-law relations between stress, strain, and time, J. Sci. Instr., vol. 19, pp. 88-93, 1942.
    • (1942) J. Sci. Instr , vol.19 , pp. 88-93
    • Blair, G.S.1    Coppen, F.2
  • 16
    • 0012841008 scopus 로고
    • Sur une forme perfectionnée de la théorie de la relaxation
    • S. Zaremba, Sur une forme perfectionnée de la théorie de la relaxation, Bull. Acad. Sci. Cracow, pp. 594-614, 1903.
    • (1903) Bull. Acad. Sci. Cracow , pp. 594-614
    • Zaremba, S.1
  • 20
    • 84981379427 scopus 로고
    • Psychoreology: Links between the past and present
    • G. S. Blair, Psychoreology: links between the past and present, Journal of Texture Studies, vol. 5, pp. 3-12, 1974.
    • (1974) Journal of Texture Studies , vol.5 , pp. 3-12
    • Blair, G.S.1
  • 21
    • 0000266650 scopus 로고
    • A new general law of deformation
    • P. Nutting, A new general law of deformation, J. Frankline Inst., vol. 191, pp. 679-685, 1921.
    • (1921) J. Frankline Inst , vol.191 , pp. 679-685
    • Nutting, P.1
  • 22
    • 0343020693 scopus 로고
    • A general stress-strain-time formula
    • P. Nutting, A general stress-strain-time formula, J. Frankline Inst., vol. 235, pp. 513-524, 1943.
    • (1943) J. Frankline Inst , vol.235 , pp. 513-524
    • Nutting, P.1
  • 23
    • 0001504447 scopus 로고
    • Deformation in relation to time, pressure and temperature
    • P. Nutting, Deformation in relation to time, pressure and temperature, J. Frankline Inst., vol. 242, pp. 449-458, 1946.
    • (1946) J. Frankline Inst , vol.242 , pp. 449-458
    • Nutting, P.1
  • 25
    • 36849132306 scopus 로고
    • Frictional phenomena: VIII
    • A. Gemant, Frictional phenomena: VIII, J. Appl. Phys., vol. 13, pp. 210-221, 1942.
    • (1942) J. Appl. Phys , vol.13 , pp. 210-221
    • Gemant, A.1
  • 26
    • 0345218900 scopus 로고
    • A method of analyzing experimental results obtained from elastiviscous bodies
    • A. Gemant, A method of analyzing experimental results obtained from elastiviscous bodies, Physics, vol. 7, pp. 311-317, 1936.
    • (1936) Physics , vol.7 , pp. 311-317
    • Gemant, A.1
  • 27
    • 0001552054 scopus 로고
    • On fractional differentials
    • A. Gemant, On fractional differentials, Phil. Mag. (Ser. 7), vol. 25, pp. 540-549, 1938.
    • (1938) Phil. Mag. (Ser. 7) , vol.25 , pp. 540-549
    • Gemant, A.1
  • 28
    • 22244470069 scopus 로고
    • Limitation of the Newtonian time scale in relation to non-equilibrium rheological states and a theory of quasi-properties
    • collaboration with J.E. Caffyn
    • G. S. Blair and B. C. Veinoglou, in collaboration with J.E. Caffyn, Limitation of the Newtonian time scale in relation to non-equilibrium rheological states and a theory of quasi-properties, Proc. Roy. Soc. A, vol. 189, pp. 69-87, 1947.
    • (1947) Proc. Roy. Soc. A , vol.189 , pp. 69-87
    • Blair, G.S.1    Veinoglou, B.C.2
  • 29
    • 0011155172 scopus 로고
    • The subjective judgement of the elastic and plastic properties of soft bodies: The differential thresholds for viscosities and compression moduli
    • G. S. Blair and F. Coppen, The subjective judgement of the elastic and plastic properties of soft bodies: the differential thresholds for viscosities and compression moduli, Proc. Roy. Soc. B, vol. 128, pp. 109-125, 1939.
    • (1939) Proc. Roy. Soc. B , vol.128 , pp. 109-125
    • Blair, G.S.1    Coppen, F.2
  • 30
    • 0009921050 scopus 로고
    • The subjective judgement of the elastic and plastic properties of the soft bodies
    • G. S. Blair and F. Coppen, The subjective judgement of the elastic and plastic properties of the soft bodies, British J. Psychol., vol. 31, no. 1, pp. 61-79, 1940.
    • (1940) British J. Psychol , vol.31 , Issue.1 , pp. 61-79
    • Blair, G.S.1    Coppen, F.2
  • 31
    • 84872317714 scopus 로고
    • The subjective conception of the firmness of the soft materials
    • G. S. Blair and F. Coppen, The subjective conception of the firmness of the soft materials, Amer. J. Psychol., vol. 55, pp. 215-229, 1942.
    • (1942) Amer. J. Psychol , vol.55 , pp. 215-229
    • Blair, G.S.1    Coppen, F.2
  • 32
    • 0038797294 scopus 로고
    • The estimation of firmness in soft materials
    • G. S. Blair and F. Coppen, The estimation of firmness in soft materials, Amer. J. Psychol., vol. 56, pp. 234-246, 1943.
    • (1943) Amer. J. Psychol , vol.56 , pp. 234-246
    • Blair, G.S.1    Coppen, F.2
  • 33
    • 0006981852 scopus 로고
    • The rheological law underlying the Nuting equation
    • G. S. Blair and M. Reiner, The rheological law underlying the Nuting equation, Appl. Sci. Res., vol. A 2, pp. 225-234, 1950.
    • (1950) Appl. Sci. Res , vol.A 2 , pp. 225-234
    • Blair, G.S.1    Reiner, M.2
  • 34
    • 33750042937 scopus 로고
    • Analytical and integrative aspects of the stress-strain-time problem
    • G. S. Blair, Analytical and integrative aspects of the stress-strain-time problem, J. Sci. Instruments, vol. 21, no. 5, pp. 80-84, 1944.
    • (1944) J. Sci. Instruments , vol.21 , Issue.5 , pp. 80-84
    • Blair, G.S.1
  • 35
    • 85069692014 scopus 로고
    • Significance of power-law relations in rheology
    • G. S. Blair and J. Caffyn, Significance of power-law relations in rheology, Nature, vol. 155, pp. 171-172, 1945.
    • (1945) Nature , vol.155 , pp. 171-172
    • Blair, G.S.1    Caffyn, J.2
  • 36
    • 0018505722 scopus 로고
    • On the application of fractional calculus on the formulation of viscoelastic models
    • M. Stiassnie, On the application of fractional calculus on the formulation of viscoelastic models, Appl. Math. Modelling, vol. 3, pp. 300-302, 1979.
    • (1979) Appl. Math. Modelling , vol.3 , pp. 300-302
    • Stiassnie, M.1
  • 38
    • 0010127267 scopus 로고
    • An application of the theory of quasi-properties to the treatment of anomalous srain-stress relations
    • G. S. Blair and J. Caffyn, An application of the theory of quasi-properties to the treatment of anomalous srain-stress relations, Phil. Magazine, pp. 80-94, 1949.
    • (1949) Phil. Magazine , pp. 80-94
    • Blair, G.S.1    Caffyn, J.2
  • 39
    • 0022700808 scopus 로고
    • Polynomial operators, Stieltjes convolution, and fractional calculus in hereditary mechanics
    • R. Koeller, Polynomial operators, Stieltjes convolution, and fractional calculus in hereditary mechanics, Acta Mechanica, vol. 58, pp. 251-264, 1986.
    • (1986) Acta Mechanica , vol.58 , pp. 251-264
    • Koeller, R.1
  • 40
    • 17844388644 scopus 로고
    • Generalization of linear laws of deformation and its application to problems with internal friction (in Russian)
    • A. Gerasimov, Generalization of linear laws of deformation and its application to problems with internal friction (in Russian), Prik- ladnaya Matematika i Mekhanika, vol. 12, pp. 251-260, 1948.
    • (1948) Prik- Ladnaya Matematika i Mekhanika , vol.12 , pp. 251-260
    • Gerasimov, A.1
  • 42
    • 0010093317 scopus 로고
    • On the law of deformation of highly plastic polymeric bodies (in Russian)
    • G. Slonimsky, On the law of deformation of highly plastic polymeric bodies (in Russian), Dokl. Akad. Nauk SSSR, vol. 110, no. 2, pp. 343-346, 1961.
    • (1961) Dokl. Akad. Nauk SSSR , vol.110 , Issue.2 , pp. 343-346
    • Slonimsky, G.1
  • 43
    • 0002403135 scopus 로고
    • Equilibrium of an elastic medium with after effect (in Russian)
    • Y. Rabotnov, Equilibrium of an elastic medium with after effect (in Russian), Prikladnaya Matematika i Mekhanika, vol. 12, no. 1, pp. 53-62, 1948.
    • (1948) Prikladnaya Matematika i Mekhanika , vol.12 , Issue.1 , pp. 53-62
    • Rabotnov, Y.1
  • 45
    • 0021292814 scopus 로고
    • Application of fractional calculus to the theory of vis-coelasticity
    • R. Koeller, Application of fractional calculus to the theory of vis-coelasticity, ASME J. Appl. Mech., vol. 51, pp. 299-307, 1984.
    • (1984) ASME J. Appl. Mech , vol.51 , pp. 299-307
    • Koeller, R.1
  • 46
    • 77955262712 scopus 로고    scopus 로고
    • A theory relating creep and relaxation for linear materials with memory
    • R. Koeller, A theory relating creep and relaxation for linear materials with memory, ASME J. Appl. Mech., vol. 77, pp. 031008/1-9, 2010.
    • (2010) ASME J. Appl. Mech , vol.77 , pp. 0310081-0310089
    • Koeller, R.1
  • 47
    • 0015052227 scopus 로고
    • Integral represaentation of eY -functions and their application to linear viscoelasticity
    • S. Meshkov, G. Pachevskaya, V. Postnikov, and Y. Rossikhin, Integral represaentation of eY -functions and their application to linear viscoelasticity, Int. J. Eng. Sci., vol. 9, pp. 387-398, 1971.
    • (1971) Int. J. Eng. Sci , vol.9 , pp. 387-398
    • Meshkov, S.1    Pachevskaya, G.2    Postnikov, V.3    Rossikhin, Y.4
  • 48
    • 77954346342 scopus 로고    scopus 로고
    • Comparative analysis of viscoelastic models involving fractional derivatives of different orders
    • Y. Rossikhin and M. Shitikova, Comparative analysis of viscoelastic models involving fractional derivatives of different orders, Fract. Calc. Appl. Anal., vol. 10, no. 2, pp. 111-121, 2007.
    • (2007) Fract. Calc. Appl. Anal , vol.10 , Issue.2 , pp. 111-121
    • Rossikhin, Y.1    Shitikova, M.2
  • 49
    • 84881477554 scopus 로고    scopus 로고
    • Two approaches for studying the impact response of viscoelastic engineering systems: An overview
    • Y. Rossikhin and M. Shitikova, Two approaches for studying the impact response of viscoelastic engineering systems: an overview, Comp. Math. Appl., vol. 66, pp. 755-773, 2013.
    • (2013) Comp. Math. Appl , vol.66 , pp. 755-773
    • Rossikhin, Y.1    Shitikova, M.2
  • 50
    • 84977255207 scopus 로고
    • Linear models of dissipation whose q is almost frequency independent, part II
    • M. Caputo, Linear models of dissipation whose q is almost frequency independent, part II, Geophys. J. R. Astr. Soc., vol. 13, pp. 529-539, 1967.
    • (1967) Geophys. J. R. Astr. Soc , vol.13 , pp. 529-539
    • Caputo, M.1
  • 51
    • 77956144191 scopus 로고    scopus 로고
    • [Reprinted in Fract. Calc. Appl. Anal., vol. 11, pp. 4-14, 2008].
    • (2008) Fract. Calc. Appl. Anal , vol.11 , pp. 4-14
  • 52
    • 0000930143 scopus 로고
    • A new dissipation model based on memory mechanism
    • M. Caputo and F. Mainardi, A new dissipation model based on memory mechanism, Pure and Applied Geophysics, vol. 91, pp. 134-147, 1971.
    • (1971) Pure and Applied Geophysics , vol.91 , pp. 134-147
    • Caputo, M.1    Mainardi, F.2
  • 53
    • 0020765202 scopus 로고
    • A theoretical basis for the application of fractional calculus to viscoelasticity
    • R. Bagley and P. Torvik, A theoretical basis for the application of fractional calculus to viscoelasticity, J. Rheology, vol. 27, pp. 201- 210, 1983.
    • (1983) J. Rheology , vol.27 , pp. 201-210
    • Bagley, R.1    Torvik, P.2
  • 54
    • 0022660581 scopus 로고
    • On the fractional calculus model of vis- coelastic behavior
    • R. Bagley and P. Torvik, On the fractional calculus model of vis- coelastic behavior, J. Rheology, vol. 30, pp. 133-155, 1986.
    • (1986) J. Rheology , vol.30 , pp. 133-155
    • Bagley, R.1    Torvik, P.2
  • 55
    • 51649182765 scopus 로고
    • Linear models of dissipation in anelas-tic solids
    • M. Caputo and F. Mainardi, Linear models of dissipation in anelas-tic solids, Riv. Nuovo Cimento, Ser. II, vol. 1, pp. 161-198, 1971.
    • (1971) Riv. Nuovo Cimento, Ser. II , vol.1 , pp. 161-198
    • Caputo, M.1    Mainardi, F.2
  • 57
    • 0003427295 scopus 로고    scopus 로고
    • Applications to problems in polymer physics and rheology
    • (R. Hilfer, ed.), World Scientific
    • H. Schiessel, C. Friedrich, and A. Blumen, Applications to problems in polymer physics and rheology, in Applications of Fractional Calculus in Physics (R. Hilfer, ed.), pp. 331-376, World Scientific, 2000.
    • (2000) Applications of Fractional Calculus in Physics , pp. 331-376
    • Schiessel, H.1    Friedrich, C.2    Blumen, A.3
  • 59
    • 67649154697 scopus 로고    scopus 로고
    • Time-fractional derivatives in relaxation processes: A tutorial survey
    • F. Mainardi and R. Gorenflo, Time-fractional derivatives in relaxation processes: a tutorial survey, Fract. Calc. Appl. Anal., vol. 10, pp. 269-308, 2007.
    • (2007) Fract. Calc. Appl. Anal , vol.10 , pp. 269-308
    • Mainardi, F.1    Gorenflo, R.2
  • 60
    • 34147203638 scopus 로고
    • Relaxation and retardation functions of the Maxwell model with fractional derivatives
    • C. Friedrich, Relaxation and retardation functions of the Maxwell model with fractional derivatives, Rheol. Acta, vol. 30, pp. 151-158, 1991.
    • (1991) Rheol. Acta , vol.30 , pp. 151-158
    • Friedrich, C.1
  • 61
    • 43949160695 scopus 로고
    • Fractional model equation for anomalous diffusion
    • R. Metzler, W. G. Glöckle, and T. F. Nonnenmacher, Fractional model equation for anomalous diffusion, Physica A, vol. 211, pp. 13-24, 1994.
    • (1994) Physica A , vol.211 , pp. 13-24
    • Metzler, R.1    Glöckle, W.G.2    Nonnenmacher, T.F.3
  • 62
    • 4043151477 scopus 로고    scopus 로고
    • The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics
    • R. Metzler and J. Klafter, The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics, J. Phys. A. Math. Gen., vol. 37, pp. R161-R208, 2004.
    • (2004) J. Phys. A. Math. Gen , vol.37 , pp. R161-R208
    • Metzler, R.1    Klafter, J.2
  • 63
    • 33745869026 scopus 로고    scopus 로고
    • Physical interpretation of initial conditions for fractional differential equations with Rieman-Liouville fractional derivatives
    • N. Heymans and I. Podlubny, Physical interpretation of initial conditions for fractional differential equations with Rieman-Liouville fractional derivatives, Rheol. Acta, vol. 45, pp. 765-771, 2006.
    • (2006) Rheol. Acta , vol.45 , pp. 765-771
    • Heymans, N.1    Podlubny, I.2
  • 64
    • 0032667787 scopus 로고    scopus 로고
    • The effect of physical ageing on the time relaxation spectrum of amorphous polymers: The fractional calculus approach
    • M. Alcoutlabi and J. Martinez-Vega, The effect of physical ageing on the time relaxation spectrum of amorphous polymers: the fractional calculus approach, J. Material Science, vol. 34, pp. 2361- 2369, 1999.
    • (1999) J. Material Science , vol.34 , pp. 2361-2369
    • Alcoutlabi, M.1    Martinez-Vega, J.2
  • 65
    • 33645150455 scopus 로고    scopus 로고
    • Viscoelastic solutions for conical indentation
    • M. Vandamme and F.-J. Ulm, Viscoelastic solutions for conical indentation, Int. J. Solids Struct., vol. 43, pp. 3142-3165, 2006.
    • (2006) Int. J. Solids Struct , vol.43 , pp. 3142-3165
    • Vandamme, M.1    Ulm, F.-J.2
  • 67
    • 84896939823 scopus 로고    scopus 로고
    • Some pioneers of the applications of Fractional Calculus
    • D. Valério, J. T. Machado, and V. Kiryakova, Some pioneers of the applications of Fractional Calculus, Fract. Calc. Appl. Anal., vol. 17, no. 2, pp. 552-578, 2014.
    • (2014) Fract. Calc. Appl. Anal , vol.17 , Issue.2 , pp. 552-578
    • Valério, D.1    Machado, J.T.2    Kiryakova, V.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.