Understanding Viscoelasticity
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1 Understanding Viscoelasticity Basics of Rheology Bearbeitet von Nhan Phan-Thien 1st ed Corr. 2nd printing Buch. XIII, 164 S. Hardcover ISBN Format (B x L): 15,5 x 23,5 cm Gewicht: 910 g Weitere Fachgebiete > Technik > Werkstoffkunde, Mechanische Technologie > Elastizität, Plastizität, Rheologie schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.
2 Contents 1. Tensor Notation CartesianFrameofReference PositionVector FrameRotation Orthogonal Matrix RotationMatrix Tensors Zero-OrderTensors First-OrderTensor OuterProducts Second-OrderTensors Third-OrderTensors TransposeOperation Decomposition SomeCommonVectors GradientofaScalar SomeCommonTensors TensorandLinearVectorFunction Claim DyadicNotation TensorOperations Substitution Contraction Transpose ProductsofTwoTwo-Tensors Invariants InvariantofaVector InvariantsofaTensor Decompositions EigenvalueandEigenvector SquareRootTheorem PolarDecompositionTheorem Cayley HamiltonTheorem... 13
3 X Contents 1.8 DerivativeOperations Derivativeofdet(A) Derivativeoftr(A) Derivative of tr(a 2 ) GradientofaField Field CartesianFrame Non-CartesianFrames Spherical Coordinates IntegralTheorems GaussDivergenceTheorem StokesCurlTheorem LeibnizFormula Problems Rheological Properties Viscosity Shear-RateDependentViscosity NormalStressDifferences WeissenbergRod-ClimbingEffect DieSwell FlowDownanInclinedChannel TransientResponses Small Strain Oscillatory Flow StressOvershoot StressRelaxation RelaxationModulus Recoil ElongationalFlows ElongationalViscosity Viscoelastic Instabilities Kinematics and Equations of Balance Kinematics ReferenceConfiguration Velocity and Acceleration Fields MaterialDerivative DeformationGradientandStrainTensors DeformationGradient Cauchy GreenStrainTensor RelativeStrainTensors PathLines Oscillatory Shear Flow Rivlin EricksenTensors SmallStrain... 48
4 Contents XI 3.5 EquationsofBalance ReynoldsTransportTheorem ConservationofMass ConservationofMomentum ConservationofEnergy Problems Constitutive Equation SomeWell-KnownConstitutiveEquations PerfectGas InviscidFluid Fourier slaw HookeanSolid NewtonianFluid Non-NewtonianFluid WeissenbergandDeborahNumbers DeborahNumber WeissenbergNumber Some Guidelines in Constitutive Modelling OldroydApproach PrincipleofMaterialObjectivity ObjectivityoftheStress FrameIndifference PrincipleofLocalAction PrincipleofDeterminism IntegrityBases IsotropicScalar-ValuedFunctions IsotropicVector-ValuedFunctions IsotropicTensor-ValuedFunctions SymmetryRestrictions UnimodularMatrix SymmetryGroup IsotropicMaterials IsotropicElasticMaterials TheSimpleMaterial SimpleFluid IncompressibleSimpleFluid FadingMemory OrderFluids UnsteadyMotion VelocityFieldinaSecond-OrderFluid Green RivlinExpansion Problems... 80
5 XII Contents 5. Inelastic Models and Linear Viscoelasticity InelasticFluids CarreauModel Power-lawModel LinearViscoelasticity SimpleShearFlow StepStrain RelaxationSpectrum CorrespondencePrinciple Quasi-StaticApproximation CircularCouetteFlow MechanicalAnalogs Problems Steady Viscometric Flows Kinematics SteadyParallelFlow Rectilinear flow AxialFannedFlow HelicalFlow HelicoidalFlow StressesinSteadyViscometricFlows ControllableandPartiallyControllableFlows Problems Polymer Solutions CharacteristicsofaPolymerChain Random-WalkModel ForcesonaChain Fluctuation-DissipationTheorem LangevinEquation Equi-PartitionofEnergy Fluctuation-DissipationTheorem DiffusivityStokes EinsteinRelation Fokker PlanckEquation Smoothed-OutBrownianForce StressTensor KramersForm ElasticDumbbellModel LangevinEquations AverageMotion StrongandWeakFlows Upper-ConvectedMaxwellModel Oldroyd-BModel
6 Contents XIII 7.6 MainFeaturesoftheOldroyd-BModel SimpleFlows MultipleRelaxationTimeUCMModel Problems Suspensions BulkSuspensionProperties Dilute Suspension of Spheroids Epilogue Problems References Index
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