Description
Taylor & Francis Ltd Advanced Mechanics Of Continua 2015 Edition by Karan S. Surana
Explore the Computational Methods and Mathematical Models That Are Possible through Continuum Mechanics FormulationsMathematically demanding, but also rigorous, precise, and written using very clear language, Advanced Mechanics of Continua provides a thorough understanding of continuum mechanics. This book explores the foundation of continuum mechanics and constitutive theories of materials using understandable notations. It does not stick to one specific form, but instead provides a mix of notations that while in many instances are different than those used in current practice, are a natural choice for the information that they represent. The book places special emphasis on both matrix and vector notations, and presents material using these notations whenever possible.The author explores the development of mathematical descriptions and constitutive theories for deforming solids, fluids, and polymeric fluids-both compressible and incompressible with clear distinction between Lagrangian and Eulerian descriptions as well as co- and contravariant bases. He also establishes the tensorial nature of strain measures and influence of rotation of frames on various measures, illustrates the physical meaning of the components of strains, presents the polar decomposition of deformation, and provides the definitions and measures of stress.Comprised of 16 chapters, this text covers: Einstein's notationIndex notationsMatrix and vector notationsBasic definitions and conceptsMathematical preliminariesTensor calculus and transformations using co- and contra-variant basesDifferential calculus of tensorsDevelopment of mathematical descriptions and constitutive theoriesAdvanced Mechanics of Continua prepares graduate students for fundamental and basic research work in engineering and sciences, provides detailed and consistent derivations with clarity, and can be used for self-study. IntroductionConcepts and Mathematical PreliminariesIntroductionSummation ConventionDummy Index and Dummy VariablesFree IndicesVector and Matrix NotationIndex Notation and Kronecker DeltaPermutation TensorOperations Using Vector, Matrix, and Einstein's NotationChange of Reference Frame, Transformations, TensorsSome Useful RelationsSummary Kinematics of Motion, Deformation and Their MeasuresDescription of MotionLagrangian and Eulerian DescriptionsMaterial Particle Displacements Continuous Deformation and Restrictions on the MotionMaterial Derivative Acceleration of a Material ParticlesCoordinate Systems and BasesCovariant BasisContravariant BasisAlternate Way to Visualize Co- and Contra-Variant BasesJacobian of DeformationChange of Description, Co- and Contra-Variant MeasuresNotations For Covariant and Contravariant MeasuresDeformation, Measures of Length and Change in LengthCovariant and Contravariant Measures of StrainChanges in Strain Measures Due To Rigid Rotation of FramesInvariants of Strain TensorsExpanded Form of Strain TensorsPhysical Meaning of StrainsPolar Decomposition: Rotation and Stretch TensorsDeformation of Areas and VolumesSummaryDefinitions and Measures of StressesCauchy Stress Tensor Contravariant and Covariant Stress TensorsGeneral Remarks Summary of Stresses and Considerations in Their DerivationsGeneral ConsiderationsSummary of Stress MeasuresConjugate Strain MeasuresRelations between Stress Measures and Useful RelationsSummaryRate of Deformation, Strain Rate, and SpinTensorsRate of DeformationDecomposition of [ L], the Spatial Velocity Gradient TensorInterpretation of the Components of [D]Rate of Change or Material Derivative of Strain TensorsPhysical Meaning of Spin Tensor [ W ]Vorticity Vector and VorticityMaterial Derivative of Determinant of JMaterial Derivative of VolumeRate of Change of Area: Material Derivative of AreaStress And Strain Measures for Convected Time DerivativesConvected Time DerivativesConjugate Convected Time Derivatives of Stress And Strain TensorsSummaryConservation and Balance Laws in Eulerian DescriptionIntroductionMass DensityConservation Of Mass: Continuity EquationTransport Theorem Conservation Of Mass: Continuity EquationBalance of Linear MomentaKinetics of Continuous Media: Balance of Angular Momenta First Law of ThermodynamicsSecond Law of ThermodynamicsA Summary of Mathematical ModelsSummaryConservation and Balance Laws In Lagrangian DescriptionIntroductionMathematical Model for Deforming Matter in Lagrangian DescriptionConservation Of Mass: Continuity Equation Balance of Linear MomentaBalance of Angular MomentaFirst Law of ThermodynamicsSecond law of thermodynamics in terms of Second law of thermodynamics in terms of Summary of Mathematical ModelsFirst and Second Laws for Thermoelastic SolidsSummaryGeneral Considerations in the Constitutive TheoriesIntroductionAxioms of Constitutive TheoryObjectiveSolid MatterFluidsPreliminary Considerations in the Constitutive TheoriesGeneral Approach of Deriving Constitutive TheoriesSummaryOrdered Rate Constitutive Theories for Thermoelastic SolidsIntroductionEntropy inequality in : Lagrangian descriptionConstitutive Theories for Thermoelastic SolidsConstitutive Theories Using Generators and InvariantsStrain energy density : Lagrangian descriptionStress in terms of Green strain based on : LagrangianStress in terms of Cauchy strain based on : LagrangianConstitutive Theories for the Heat Vector: LagrangianAlternate Derivations: Strain In Terms Of StressAlternate Derivations: Heat Vector In Terms Of StressSummary Thermoviscoelastic Solids without MemoryIntroductionConstitutive Theories Using Helmholtz Free Energy DensityConstitutive Theories Using Gibbs PotentialComparisons of constitutive theories using and Thermoviscoelastic Solids with MemoryIntroductionConstitutive Theories Using Helmholtz Free Energy DensityConstitutive Theories Using Gibbs PotentialComparisons of constitutive theories using and Ordered Rate Constitutive Theories for ThermofluidsIntroductionSecond Law of Thermodynamics: Entropy InequalityDependent Variables and Their Arguments Development of Constitutive Theory for Thermo FluidsRate Constitutive Theory of Order NRate Constitutive Theory of Order TwoRate Constitutive Theory of Order OneGeneralized Newtonian and Newtonian FluidsIncompressible Ordered Thermo Fluids of Orders N, 2 And 1Incompressible Generalized Newtonian, Newtonian Fluids Conjugate Measures, Validity of Rate Constitutive Theories SummaryOrdered Rate Constitutive Theories for PolymersIntroduction Second Law of Thermodynamics: Entropy InequalityDependent Variables and Their ArgumentsDevelopment of Constitutive Theory for PolymersRate Constitutive Theory of Orders `M' and `N' Rate Constitutive Theory of Orders M=1 and N=1Rate Constitutive Theory of Orders M=1 and N=2Constitutive Theories for Incompressible PolymersNumerical Studies Using Giesekus Constitutive Model Ordered Rate Constitutive Theories for Hypoelastic SolidsIntroductionSecond Law of Thermodynamics: Entropy InequalityDependent Variables and Their ArgumentsDevelopment of Constitutive Theory for Hypo-Elastic SolidsRate Constitutive Theory of Order `N'Rate Constitutive Theory of Order TwoRate Constitutive Theory of Order OneCompressible Generalized Hypo-Elastic Solids of Order One Incompressible Ordered Hypo-Elastic SolidsIncompressible Generalized Hypo-Elastic Solids: Order One SummaryMathematical Models with Thermodynamic RelationsIntroductionThermodynamic Pressure: Compressible MatterMechanical Pressure: Incompressible MatterSpecific Internal Energy Variable Transport Properties or Material CoefficientsFinal Form of the Mathematical ModelsSummaryPrinciple of Virtual WorkIntroductionHamilton's Principle in Continuum MechanicsEuler-Lagrange Equation: Lagrangian DescriptionEuler-Lagrange Equation: Eulerian DescriptionSummary and RemarksAppendices