Constitutive behavior modeling and fractional derivatives

[1]  S. Hellinckx.  Mechanical behaviour of isotactic polypropylenes in the lower and the upper glass transitions ranges , 1997 .

[2]  H. Winter,et al.  Relaxation Patterns of Nearly Critical Gels , 1996 .

[3]  N. Heymans.  Hierarchical models for viscoelasticity: dynamic behaviour in the linear range , 1996 .

[4]  C. Friedrich,et al.  Rheological analysis of triblock copolymer-microemulsion networks , 1996 .

[5]  L. Palade,et al.  A modified fractional model to describe the entire viscoelastic behavior of polybutadienes from flow to glassy regime , 1996 .

[6]  R. Metzler,et al.  Generalized viscoelastic models: their fractional equations with solutions , 1995 .

[7]  J. Weese,et al.  Determination of relaxation time spectra by analytical inversion using a linear viscoelastic model with fractional derivatives , 1995 .

[8]  R. Metzler,et al.  Relaxation in filled polymers: A fractional calculus approach , 1995 .

[9]  C. Friedrich.  Linear viscoelastic behavior of branched polybutadiene: A fractional calculus approach , 1995 .

[10]  H. Schiessel,et al.  FRACTAL ASPECTS IN POLYMER SCIENCE , 1995 .

[11]  H. Schiessel,et al.  Mesoscopic Pictures of the Sol-Gel Transition: Ladder Models and Fractal Networks , 1995 .

[12]  C. Friedrich,et al.  Linear viscoelastic behaviour of complex polymeric materials: a fractional mode representation , 1994 .

[13]  Francesco Mainardi,et al.  Fractional relaxation in anelastic solids , 1994 .

[14]  J. Stastna,et al.  Fractional complex modulus manifested in asphalts , 1994 .

[15]  W. Glöckle,et al.  Fractional relaxation and the time-temperature superposition principle , 1994 .

[16]  N. Heymans,et al.  Fractal rheological models and fractional differential equations for viscoelastic behavior , 1994 .

[17]  Helmut Schiessel,et al.  Hierarchical analogues to fractional relaxation equations , 1993 .

[18]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[19]  C. Friedrich.  Mechanical stress relaxation in polymers: fractional integral model versus fractional differential model , 1993 .

[20]  Massimiliano Giona,et al.  Fractional diffusion equation and relaxation in complex viscoelastic materials , 1992 .

[21]  C. Friedrich.  Rheological material functions for associating comb-shaped or H-shaped polymers A fractional calculus approach , 1992 .

[22]  C. Friedrich,et al.  Generalized Cole-Cole behavior and its rheological relevance , 1992 .

[23]  J. Bauwens.  Two nearly equivalent approaches for describing the non-linear creep behavior of glassy polymers , 1992 .

[24]  T. Nonnenmacher,et al.  Fractional integral operators and Fox functions in the theory of viscoelasticity , 1991 .

[25]  W. Glöckle,et al.  A fractional model for mechanical stress relaxation , 1991 .

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

[27]  C. Friedrich,et al.  Evolution of time constants during sol-gel transition , 1989 .

[28]  C. Friedrich,et al.  Extension of a Model for Crosslinking Polymer at the Gel Point , 1988 .

[29]  T. Dorfmüller,et al.  Molecular Dynamics and Relaxation Phenomena in Glasses , 1987 .

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

[31]  A. Méhauté,et al.  Scaling properties and kinetics: Williams-Watts relaxations , 1985 .

[32]  W. E. Vanarsdale.  Fractional Rates of Deformation , 1985 .

[33]  Friedrich,et al.  Patterns of relaxation in disordered materials. , 1985, Physical review. B, Condensed matter.

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

[35]  Lynn Rogers,et al.  Operators and Fractional Derivatives for Viscoelastic Constitutive Equations , 1983 .

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

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

[38]  W. Smit,et al.  Rheological models containing fractional derivatives , 1970 .

[39]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[40]  A. Erdélyi,et al.  Higher Transcendental Functions , 1954 .

[41]  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.

[42]  R. C. L. BOSWORTH,et al.  A Definition of Plasticity , 1946, Nature.

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

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

[45]  A. Gemant,et al.  XLV. On fractional differentials , 1938 .

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

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

[48]  H. Schiessel,et al.  Dynamics in disordered systems , 1994 .

[49]  S. Havlin,et al.  Fractals and Disordered Systems , 1991 .

[50]  N. Tschoegl.  The Phenomenological Theory of Linear Viscoelastic Behavior , 1989 .

[51]  Richard G. Palmer,et al.  Relaxation in complex systems , 1987 .

[52]  Hanswalter Giesekus,et al.  Progress and Trends in Rheology II , 1982 .

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

[54]  Graham Williams.  Molecular aspects of multiple dielectric relaxation processes in solid polymers , 1979 .

[55]  Graham Williams,et al.  Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function , 1970 .

[56]  P. R. Pinnock,et al.  The mechanical properties of solid polymers , 1966 .

[57]  A. Tobolsky,et al.  Elastoviscous properties of polyisobutylene (and other amorphous polymers) from stress–relaxation studies. IX. A summary of results , 1956 .

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

[59]  F. Kohlrausch,et al.  Ueber die elastische Nachwirkung bei der Torsion , 1863 .