Description
Taylor & Francis Ltd Continuum Mechanics Elasticity Plasticity Viscoelasticity 2006 Edition by Ellis H. Dill
Most books on continuum mechanics focus on elasticity and fluid mechanics. But whether student or practicing professional, modern engineers need a more thorough treatment to understand the behavior of the complex materials and systems in use today. Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity offers a complete tour of the subject that includes not only elasticity and fluid mechanics but also covers plasticity, viscoelasticity, and the continuum model for fatigue and fracture mechanics.In addition to a broader scope, this book also supplies a review of the necessary mathematical tools and results for a self-contained treatment. The author provides finite element formulations of the equations encountered throughout the chapters and uses an approach with just the right amount of mathematical rigor without being too theoretical for practical use. Working systematically from the continuum model for the thermomechanics of materials, coverage moves through linear and nonlinear elasticity using both tensor and matrix notation, plasticity, viscoelasticity, and concludes by introducing the fundamentals of fracture mechanics and fatigue of metals. Requisite mathematical tools appear in the final chapter for easy reference.Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity builds a strong understanding of the principles, equations, and finite element formulations needed to solve real engineering problems. FUNDAMENTALS OF CONTINUUM MECHANICSMaterial ModelsClassical Space-TimeMaterial BodiesStrainRate of StrainCurvilinear Coordinate SystemsConservation of MassBalance of MomentumBalance of EnergyConstitutive EquationsThermodynamic DissipationObjectivity: Invariance for Rigid MotionsColeman-Mizel ModelFluid MechanicsProblems for Chapter 1BibliographyNONLINEAR ELASTICITYThermoelasticityMaterial SymmetriesIsotropic MaterialsIncompressible MaterialsConjugate Measures of Stress and StrainSome Symmetry GroupsRate Formulations for Elastic MaterialsEnergy PrinciplesGeometry of Small DeformationsLinear ElasticitySpecial Constitutive Models for Isotropic MaterialsMechanical Restrictions on the Constitutive RelationsProblems for Chapter 2BibliographyLINEAR ELASTICITYBasic EquationsPlane StrainPlane StressProperties of SolutionsPotential EnergySpecial Matrix NotationThe Finite Element Method of SolutionGeneral Equations for an Assembly of ElementsFinite Element Analysis for Large DeformationsProblems for Chapter 3BibliographyPLASTICITYClassical Theory of PlasticityWork Principlevon Mises-Type Yield CriterionHill Yield Criterion for Orthotropic MaterialsIsotropic HardeningKinematic HardeningCombined Hardening lawsGeneral Equations of PlasticityStrain Formulation of PlasticityFinite Element AnalysisLarge DeformationsThermodynamics of Elastic-Plastic MaterialsProblems for Chapter 4BibliographyVISCOELASTICITYLinear ViscoelasticityEffect of TemperatureNonlinear ViscoelasticityThermodynamics of Materials with Fading MemoryProblems for Chapter 5BibliographyFRACTURE AND FATIGUEFracture CriterionPlane Crack through a SheetFracture ModesCalculation of the Stress Intensity FactorCrack GrowthProblems for Chapter 6BibliographyMATHEMATICAL TOOLS FOR CONTINUUM MECHANICSSets of Real NumbersMatricesVector AnalysisTensorsIsotropic FunctionsAbstract DerivativesSome Basic Mathematical Definitions and TheoremsProblems for Chapter 7BibliographyINDEX