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

The article shows the pioneering role of the British scientist, Professor G.W.Scott Blair, in the creation of the application of fractional modelling in rheology. Discussion of his results is presented. His approach is highly recognized by the rheological society and is adopted and generalized by his successors. Further development of this branch of Science is briefly described in this article too.

[1]  Y. Rabotnov.  Equilibrium of an elastic medium with after-effect , 2014 .

[2]  Marina V. Shitikova,et al.  Two approaches for studying the impact response of viscoelastic engineering systems: An overview , 2013, Comput. Math. Appl..

[3]  José António Tenreiro Machado,et al.  Some pioneers of the applications of fractional calculus , 2013 .

[4]  J. Maxwell,et al.  XV. On the dynamical theory of gases , 1868 .

[5]  G. W. Blair,et al.  Limitations of the Newtonian time scale in relation to non-equilibrium rheological states and a theory of quasi-properties , 1947, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[6]  The rheological law underlying the nutting equation , 1951 .

[7]  William Thomson,et al.  Mathematical and physical papers , 1880 .

[8]  J. Martinez-vega,et al.  The effect of physical ageing on the relaxation time spectrum of amorphous polymers: the fractional calculus approach , 1999 .

[9]  G. W. Blair.  Analytical and Integrative Aspects of the Stress-Strain-Time Problem , 1944 .

[10]  A. Gemant.  Frictional Phenomena. I , 1941 .

[11]  G. W. Blair,et al.  The Classification of the Rheological Properties of Industrial Materials in the light of Power-Law Relations between Stress, Strain and Time , 1942 .

[12]  Igor M. Sokolov,et al.  Physics of Fractal Operators , 2003 .

[13]  G. W. Blair,et al.  The Subjective Judgment of the Elastic and Plastic Properties of Soft Bodies; the , 1939 .

[14]  Michael Stiassnie,et al.  On the application of fractional calculus for the formulation of viscoelastic models , 1979 .

[15]  M. Caputo,et al.  A new dissipation model based on memory mechanism , 1971 .

[16]  B. Kibble,et al.  A Study of Five-Dimensional Small Black Rings and Closed String Tachyon Potential , 2007 .

[17]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[18]  J. Maxwell,et al.  The Dynamical Theory of Gases , 1905, Nature.

[19]  R. Bagley,et al.  On the Fractional Calculus Model of Viscoelastic Behavior , 1986 .

[20]  I. Podlubny.  Fractional differential equations , 1998 .

[21]  R. Metzler,et al.  Fractional model equation for anomalous diffusion , 1994 .

[22]  P. Nutting.  Deformation in relation to time, pressure and temperature , 1946 .

[23]  A. Gemant.  Frictional Phenomena. VIII , 1942 .

[24]  A. G.,et al.  Mathematical and Physical Papers , 1912, Nature.

[25]  M. Caputo.  Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[26]  S. Zaremba,et al.  Sur une forme perfectionee de la theorie de la relaxation , 1903 .

[27]  Franz-Josef Ulm,et al.  Indentation analysis of fractional viscoelastic solids , 2009 .

[28]  H H Macey,et al.  Survey of General and Applied Rheology , 1950 .

[29]  H. Poincaré.  La valeur de la science , 1905 .

[30]  PSYCHORHEOLOGY: LINKS BETWEEN THE PAST AND THE PRESENT† , 1974 .

[31]  G. W. Blair,et al.  The Relationship between Viscosity, Elasticity and Plastic Strength of a Soft Material as Illustrated by Some Mechanical Properties of Flour Dough. III , 1933 .

[32]  G. W. Blair.  The role of psychophysics in rheology , 1947 .

[33]  R. Koeller.  Polynomial operators, stieltjes convolution, and fractional calculus in hereditary mechanics , 1986 .

[34]  P. G. Nutting,et al.  A new general law of deformation , 1921 .

[35]  James Clerk Maxwell.  On the Dynamical Theory of Gases , 2003 .

[36]  R. Gorenflo,et al.  Time-fractional derivatives in relaxation processes: a tutorial survey , 2008, 0801.4914.

[37]  C. Friedrich.  Relaxation and retardation functions of the Maxwell model with fractional derivatives , 1991 .

[38]  A. Gemant,et al.  A Method of Analyzing Experimental Results Obtained from Elasto‐Viscous Bodies , 1936 .

[39]  P. Nutting.  A general stress-strain-time formula , 1943 .

[40]  V. Uchaikin.  Fractional Derivatives for Physicists and Engineers , 2013 .

[41]  H. Schiessel,et al.  Applications to Problems in Polymer Physics and Rheology , 2000 .

[42]  G. McKinley,et al.  Power-law rheology in the bulk and at the interface: quasi-properties and fractional constitutive equations , 2013, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[43]  George A. Gescheider,et al.  Psychophysics: The Fundamentals , 1997 .

[44]  R. Koeller.  A Theory Relating Creep and Relaxation for Linear Materials With Memory , 2010 .

[45]  Iu.N. Rabotnov.  Elements of hereditary solid mechanics , 1980 .

[46]  E. C. Bingham,et al.  The Origins of Rheology : A Short Historical Excursion , 2002 .

[47]  R. Bagley,et al.  A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity , 1983 .

[48]  M. T. Cicero.  FRACTIONAL CALCULUS AND WAVES IN LINEAR VISCOELASTICITY , 2012 .

[49]  Joseph John Thomson Joh Henry Poynting.  A Textbook of Physics , 2008 .

[50]  G. W. Blair,et al.  The Influence of the Proximity of a Solid Wall on the Consistency of Viscous and Plastic Materials. III , 1929 .

[51]  G. W. Blair,et al.  Significance of Power-Law Relations in Rheology , 1945, Nature.

[52]  G. W. Scott Blair,et al.  The Subjective Conception of the Firmness of Soft Materials , 1942 .

[53]  F. Mainardi,et al.  Creep, relaxation and viscosity properties for basic fractional models in rheology , 2011, 1110.3400.

[54]  G. W. Scott Blair,et al.  The Estimation of Firmness in Soft Materials , 1943 .

[55]  I. Podlubny,et al.  Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives , 2005, math-ph/0512028.

[56]  G. W. Scott Blair,et al.  THE SUBJECTIVE JUDGEMENT OF THE ELASTIC AND PLASTIC PROPERTIES OF SOFT BODIES , 1940 .

[57]  G. Gescheider.  Psychophysics: The Fundamentals , 1997 .

[58]  E. C. Bingham.  Fluidity And Plasticity , 1922 .

[59]  J. Klafter,et al.  The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics , 2004 .

[60]  G. W. Blair,et al.  Report on the principles of rheological nomenclature , 1949 .

[61]  R. Gorenflo,et al.  Mittag-Leffler Functions, Related Topics and Applications , 2014, Springer Monographs in Mathematics.

[62]  A. Aleksandrov,et al.  Strength of Amorphous and of Crystallizing Rubberlike Polymers , 1946 .

[63]  Franz-Josef Ulm,et al.  Viscoelastic solutions for conical indentation , 2006 .

[64]  G. W. Scott Blair,et al.  VI. An application of the theory of quasi-properties to the treatment of anomalous strain-stress relations , 1949 .

[65]  Francesco Mainardi,et al.  Linear models of dissipation in anelastic solids , 1971 .

[66]  V. Postnikov,et al.  Integral representations of εγ-functions and their application to problems in linear viscoelasticity , 1971 .

[67]  R. Koeller.  Applications of Fractional Calculus to the Theory of Viscoelasticity , 1984 .