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Anomalous stability behavior of a properly invariant constitutive equation which generalises fractional derivative models

Identifieur interne : 006B95 ( PascalFrancis/Curation ); précédent : 006B94; suivant : 006B96

Anomalous stability behavior of a properly invariant constitutive equation which generalises fractional derivative models

Auteurs : L. I. Palade [France] ; P. Attane [France] ; R. R. Huilgol [Australie] ; B. Mena [Mexique]

Source :

RBID : Pascal:99-0103782

Descripteurs français

English descriptors

Abstract

Viscoelastic materials like amorphous polymers or organic glasses show a complex relaxation behavior in the softening dispersion region, i.e. from glass transition to the α relaxation zone. It is known that a uni-dimensional Maxwell model, modified within the conceptual framework of fractional calculus, has been found to predict experimental data in this range of temperatures. After developing a fully objective constitutive relation for an incompressible fluid, it is shown here that the fractional derivative Maxwell model results from the linearization of this objective equation about the state of rest, when some assumptions about the memory kernels are made. Next, it is demonstrated that the three dimensional, linearized version of the frame indifferent equation exhibits anomalous stability characteristics, namely that the rest state is neither stable nor unstable under exponential disturbances. Also, the material cannot support purely harmonic excitations either. Consequently, it appears that fractional derivative constitutive equations may be used to study a very limited category of flows in rheology rather than the whole spectrum.
pA  
A01 01  1    @0 0020-7225
A02 01      @0 IJESAN
A03   1    @0 Int. j. eng. sci.
A05       @2 37
A06       @2 3
A08 01  1  ENG  @1 Anomalous stability behavior of a properly invariant constitutive equation which generalises fractional derivative models
A11 01  1    @1 PALADE (L. I.)
A11 02  1    @1 ATTANE (P.)
A11 03  1    @1 HUILGOL (R. R.)
A11 04  1    @1 MENA (B.)
A14 01      @1 Laboratoire de Rhéologie, B.P. - 53 Domaine Universitaire @2 38041, Grenoble @3 FRA @Z 1 aut. @Z 2 aut.
A14 02      @1 Department of Mathematics and Statistics, Flinders University of South Australia, G.P.O. Box 2100 @2 Adelaide, S. A. 5001 @3 AUS @Z 3 aut.
A14 03      @1 Instituto de Investigaciones en Materiales, Departmento de Polimeros, U.N.A.M., Apartado Postal 70-360 @2 Coyoacan 04510, Mexico, D.F. @3 MEX @Z 4 aut.
A20       @1 315-329
A21       @1 1999
A23 01      @0 ENG
A43 01      @1 INIST @2 10407 @5 354000073674450030
A44       @0 0000 @1 © 1999 INIST-CNRS. All rights reserved.
A45       @0 38 ref.
A47 01  1    @0 99-0103782
A60       @1 P
A61       @0 A
A64   1    @0 International journal of engineering science
A66 01      @0 GBR
C01 01    ENG  @0 Viscoelastic materials like amorphous polymers or organic glasses show a complex relaxation behavior in the softening dispersion region, i.e. from glass transition to the α relaxation zone. It is known that a uni-dimensional Maxwell model, modified within the conceptual framework of fractional calculus, has been found to predict experimental data in this range of temperatures. After developing a fully objective constitutive relation for an incompressible fluid, it is shown here that the fractional derivative Maxwell model results from the linearization of this objective equation about the state of rest, when some assumptions about the memory kernels are made. Next, it is demonstrated that the three dimensional, linearized version of the frame indifferent equation exhibits anomalous stability characteristics, namely that the rest state is neither stable nor unstable under exponential disturbances. Also, the material cannot support purely harmonic excitations either. Consequently, it appears that fractional derivative constitutive equations may be used to study a very limited category of flows in rheology rather than the whole spectrum.
C02 01  X    @0 001B40F30J
C02 02  3    @0 001B80C50F
C02 03  X    @0 001D10A05A1
C03 01  X  FRE  @0 Viscoélasticité @5 01
C03 01  X  ENG  @0 Viscoelasticity @5 01
C03 01  X  GER  @0 Viskoelastizitaet @5 01
C03 01  X  SPA  @0 Viscoelasticidad @5 01
C03 02  X  FRE  @0 Rhéologie @5 02
C03 02  X  ENG  @0 Rheology @5 02
C03 02  X  GER  @0 Rheologie @5 02
C03 02  X  SPA  @0 Reología @5 02
C03 03  X  FRE  @0 Verre organique @5 05
C03 03  X  ENG  @0 Organic glass @5 05
C03 03  X  SPA  @0 Vidrio orgánico @5 05
C03 04  X  FRE  @0 Polymère amorphe @5 06
C03 04  X  ENG  @0 Amorphous polymer @5 06
C03 04  X  SPA  @0 Polímero amorfo @5 06
C03 05  X  FRE  @0 Transition vitreuse @5 07
C03 05  X  ENG  @0 Glass transition @5 07
C03 05  X  SPA  @0 Transición vítrea @5 07
C03 06  X  FRE  @0 Modélisation @5 14
C03 06  X  ENG  @0 Modeling @5 14
C03 06  X  SPA  @0 Modelización @5 14
C03 07  X  FRE  @0 Equation constitutive @5 15
C03 07  X  ENG  @0 Constitutive equation @5 15
C03 07  X  SPA  @0 Ecuación constitutiva @5 15
C03 08  X  FRE  @0 Dérivée fractionnaire @5 16
C03 08  X  ENG  @0 Fractional derivative @5 16
C03 08  X  SPA  @0 Derivada fracionario @5 16
C03 09  X  FRE  @0 Effet mémoire @5 17
C03 09  X  ENG  @0 Memory effect @5 17
C03 09  X  SPA  @0 Efecto memoria @5 17
C03 10  X  FRE  @0 Modèle 3 dimensions @5 18
C03 10  X  ENG  @0 Three dimensional model @5 18
C03 10  X  SPA  @0 Modelo 3 dimensiones @5 18
C03 11  X  FRE  @0 Indifférence matérielle @5 19
C03 11  X  ENG  @0 Material frame indifference @5 19
C03 11  X  SPA  @0 Indiferencia material @5 19
C03 12  X  FRE  @0 Etude expérimentale @5 20
C03 12  X  ENG  @0 Experimental study @5 20
C03 12  X  GER  @0 Experimentelle Untersuchung @5 20
C03 12  X  SPA  @0 Estudio experimental @5 20
C03 13  X  FRE  @0 4635 @2 PAC @4 INC @5 56
C03 14  X  FRE  @0 8350F @2 PAC @4 INC @5 57
N21       @1 060

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Le document en format XML

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<s5>17</s5>
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<s5>17</s5>
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<s5>18</s5>
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<s5>18</s5>
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</fC03>
<fC03 i1="12" i2="X" l="ENG">
<s0>Experimental study</s0>
<s5>20</s5>
</fC03>
<fC03 i1="12" i2="X" l="GER">
<s0>Experimentelle Untersuchung</s0>
<s5>20</s5>
</fC03>
<fC03 i1="12" i2="X" l="SPA">
<s0>Estudio experimental</s0>
<s5>20</s5>
</fC03>
<fC03 i1="13" i2="X" l="FRE">
<s0>4635</s0>
<s2>PAC</s2>
<s4>INC</s4>
<s5>56</s5>
</fC03>
<fC03 i1="14" i2="X" l="FRE">
<s0>8350F</s0>
<s2>PAC</s2>
<s4>INC</s4>
<s5>57</s5>
</fC03>
<fN21>
<s1>060</s1>
</fN21>
</pA>
</standard>
</inist>
</record>

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   |texte=   Anomalous stability behavior of a properly invariant constitutive equation which generalises fractional derivative models
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