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Abstract.Thismonographformulatesandsolvesselect-
edissues(formingasubstantivewhole)ofthetheoryof
linearelasticityandrheologyofthermosettingpolymers
andunidirectionalmonotropicfibre-reinforcedthermoset
matrix(UFRT)composites.Theadvancedanalyticalmodell-
ingincludesthefollowingissues:thequasi-exacthomo-
genizationtheoryofUFRTcomposites(necessaryforthe
viscoelasticmodellingofUFRTcompositesbytheelastic-
viscoelasticcorrespondenceprinciple);theinverseproblem
inthehomogenizationtheoryofUFRTcomposites(forpre-
dictingtheelasticconstantsofmonotropicfibres);the
elasticandrheologicalconstitutivemodellingofther-
mosettingpolymersandUFRTcomposites(standardand
inverse,uncoupledandcoupledconstitutiveequations,
mutuallytransformable);experimentalvalidationofanew
rheologicalmodelforthermosets,basedontheMittag-
Lefflerfractionalexponentialgenericfunction;andnumeri-
calvalidationofanewrheologicalmodelforUFRTcom-
posites,basedonasingleMittag-Lefflerfractionalexpo-
nentialgenericfunction(commonforthepolymermatrix
andthecomposite).Boththethermosettingpolymersand
UFRTcompositesaredescribedbytheminimumnumbers
oftheviscoelasticconstantsdeterminedfromwell-con-
ditionedalgorithms.Themonographalsopresentsexten-
sivetesting,identification,validationandcognitivestudies,
including:experimentalidentificationoftheelasticand
viscoelasticconstantsofrepresentativeresins;numerical
identificationoftheelasticandviscoelasticconstantsofre-
presentativeUFRTcomposites,basedonthequasi-exact
homogenizationtheory,theuncoupledrheologicalcon-
stitutiveequations,andtheelastic-viscoelasticcorres-
pondenceprinciple;andsimulationsofselectedrheologi-
calprocessesintherepresentativeresinandrepresentative
UFRTcomposites.TheproprietarysoftwareinPascaland
theMicrosoftExcelspreadsheetwereusedforthecalcula-
tions.Theformulations,analyticalsolutionsandnumerical
analysesofalltheissuesareoriginalanduniqueworldwide.
