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Preface
compositeisdescribedbyfiveindependentelasticconstantsandfourviscoelastic
constants,wherebytwoviscoelasticconstantsarecommontothethermosetma-
trixandthecomposite.
Themonographdevelopsselectedproblemsinmechanicsofthermosetsand
UFRTcomposites,intheauthors’approach,relatedtotheauthors’methodolo-
gyofelasticandrheologicalmodelling.Chapter1presentsacriticalreviewof
knowledgeinrheologyofthermosettingpolymersandUFRTcomposites,includ-
ingpublicationsbyotherresearchersandthosebytheauthors.Againstthisback-
ground,thescopeofthemonographispresented.Chapter2describesthethermo-
setandcompositematerialsappliedfortheexperimentalandnumericalstudies,
i.e.identification,validation,andcognitivestudies.
Chapter3developselasticandrheologicalmodellingofthermosets,preceded
byasummaryofthematerialandmechanicalassumptions.Theconsiderations
wereconductedusingmatrixcalculus,takingintoaccountthefullstressandstrain
states.Coupledstandardconstitutiveequationsofthermosetelasticityweretrans-
formedtoanuncoupledform,whichwerethengeneralizedtotheformdescribing
viscoelasticshearstrainsandelasticbulkstrains.Constitutiveequationsofelastic-
ityandviscoelasticitywereformulatedineightpossibleforms,i.e.coupledand
uncoupled,standardandinverse,elasticandrheologicalequations.Theuseofthe
genericfunctionintheformofaMittag-Lefflerfractionalexponentialfunction
waspositivelyvalidatedexperimentally.
ForelasticandrheologicalmodellingofUFRTcompositeswithheterogeneous
microstructure,aquasi-exacthomogenizationtheorybasedontheelasticitytheo-
ryofisotropicandmonotropicmediaisneeded.Suchtheory,basedonanalytical
solutionsoftheselectedtasksofthetheoryoflinearelasticity,isformulatedin
Chapter4formonotropicfibresandpositivelyvalidatedexperimentallyonthe
enhancedreliabilityUFRTcomposites.
Chapter5presentsanadditionalelasticproblem,namelytheinverseproblem
inUFRTcompositehomogenizationtheory.Theanalyticalsolutionsdescribing
theelasticconstantsofmonotropicfibreshavebeenshowntobewell-conditioned.
Chapter6isthemostimportantchapterinthismonograph.Itcontainsfor-
mulationandresultsofanalyticalmodellingofUFRTcomposites,intheelastic
andrheologicalterms,usingthematrixcalculus.ThefirstSubchaptersummarizes
theassumptionsmadeinrheologicalmodelling.Standardconstitutiveequations
ofelasticityofthehomogenizedUFRTcompositeweredecoupledusinganew
conceptofquasi-shearandquasi-bulkstrains(uniqueworldwide).Theseequa-
tionsallowedstandardconstitutiveequationsofviscoelasticityofthecomposite
tobeformulatedbygeneralizingtheviscoelasticityconstitutiveequationsofthe
polymermatrix(uniqueworldwide).Thehomogenizedcompositewasdescribed
byasinglegenericfunctionconsistentwiththegenericfunctionofthepolymer
matrix,andbyfiveviscoelasticityconstants.Constitutiveequationsofelasticity
