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Thepreface
ThemainsubjectdiscussedintheVII-thvolumeoftheseries(TheMono-
graphsofDepartmentofStrengthofMaterials,Theoryofelasticityand
Plasticity)isthehyperelasticitytheoryanditsmodifications.Inthefirst
threechaptersthebasicnotionsofbothcontinuummechanicsandhypere-
lasticityareoutlined.Theconstitutiveequationsfororthotropic,trans-
vereselyisotropicandisotropichyperelasticmaterialsarederived.The
calssicmodelsofhyperelasticmaterialsinroducedintheliteratureareana-
lyzed.Theaimhereistoputthemainemphasisonthestored-energyfunc-
tionsthatfulfilltherequirementofpolyconvexity.Thenextthreechapters
concerntheisotropichyperelasticityincludingtheincompressiblemateri-
als,withapplicationtotheelastomersandthesoftbiologicaltissues.The
stored-energyfunctionswhichsatisfythebasictheoreticalrequirementsand
allowforagoodcurvefittingqualitywereselectedfromthegroupof54dif-
ferentmodelformulations.
Thelastfourchaptersconcernthepossiblemodificationsofthehypere-
lasticitytheory.Theconstitutiverelationsofmaterialswithdamagearede-
scribed.Thesemodelsresultinamaterialresponsewhichisindependentof
boththedeformationrateandtheunrecoberablestrains.Theyareableto
capturesuchbehaviorsastheenergydissipationandtheMullinseffectof
thefirstkind,whichareexhibitedbytheelastomericmaterials.Inbothcas-
esthestretch-nominalstressrelationisdifferentforloadingandunloading.
Thequasi-linearviscoelasticitytheory(QLV),alsoknownasthevisco-
hyperelasticity,isdiscussed.Theformulationofthetheory,itsfiniteelement
(FE)implementationandthedeterminationofmaterialparametervalues
aredescribed.AusersubroutineUMAT(UserMATerial)isattachedandal-
lowsonetousetheQLVmodelintheFEsystemABAQUS.
StanisławJemioło,CyprianSuchocki
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