PrefacetotheThirdEdition
PrefacetotheFirstEdition
Introduction.
1.1Theobjectiveofthiscourse
1.2Applicationstoscienceandtechnology
1.3Whatismechanics?
1.4Aprototypeofacontinuum:Theclassicaldefinition
1.5Ourdefinitionofacontinuum
1.6Theconceptofstressinourdefinitionofacontinuum
1.7Abstractcopyofarealcontinuum
1.8Whatiscontinuummechanicsabout?
1.9Axiomsofcontinuummechanics
1.10Abiologicalexampleofahierarchyofcontinuadependingonthesizeoftheobjectinvolvedinascientificinquiry
1.11Elementarytopicthroughwhichbasicideasevolved
2VectorsandTensors
2.1Vectors
2.2Vectorequations
2.3Thesummationconvention
2.4Translationandrotationofcoordinates
2.5Coordinatetransformationingeneral
2.6Analyticaldefinitionsofscalars,vectors,andCartesiantensors
2.7Thesignificanceoftensorequations
2.8Notationsforvectorsandtensors:Boldfaceorindices?
2.9Quotientrule
2.10Partialderivatives
3Stress
3.1Theideaofstress
3.2Thelawsofmotion
3.3Cauchy'sformula
3.4Equationsofequilibrium
3.5Changeofstresscomponentsintransformationofcoordinates
3.6Stresscomponentsinorthogonalcurvilinearcoordinates
3.7Stressboundaryconditions
4PrincipalStressesandPrincipalAxes
4.1Introduction
4.2Planestateofstress
4.3Mohr'scircleforplanestress
4.4Mohr'scirclesforthree-dimensionalstressstates
4.5Principalstresses
4.6Shearingstresses
4.7Stress-deviationtensor
4.8Lam6'sstressellipsoid
5AnalysisofDeformation
5.1Deformation
5.2Thestrain
5.3Straincomponentsintermsofdisplacements
5.4Geometricinterpretationofinfinitesimalstraincomponents
5.5Infinitesimalrotation
5.6Finitestraincomponents
5.7Principalstrains:Mohr'scircle
5.8Infinitesimalstraincomponentsinpolarcoordinates
5.9Directderivationofthestrain-displacementrelationsinpolarcoordinates
5.10Otherstrainmeasures
6VelocityField.andCompatibilityConditions
6.1Velocityfields
6.2Thecompatibilitycondition
6.3Compatibilityofstraincomponentsinthreedimensions
7ConstitutiveEquations
7.1Specificationofthepropertiesofmaterials
7.2Thenonviscousfluid
7.3Newtonianfluid
7.4Hookeanelasticsolid
7.5Effectoftemperature
7.6Materialswithmorecomplexmechanicalbehavior
8Isotropy..
8.1Theconceptofmaterialisotropy
8.2Isotropictensor
8.3Isotropictensorsofrank3
8.4Isotropictensorsofrank4
8.5Isotropicmaterials
8.6Coincidenceofprincipalaxesofstressandofstrain
8.7Othermethodsofcharacterizingisotropy
8.8Canwerecognizeamaterial'sisotropyfromthemicrostructure?
9MechanicalPropertiesofRealFluidsandSolids
9.1Fluids
9.2Viscosity
9.3Plasticityofmetals
9.4Materialswithnonlinearelasticity
9.5Nonlinearstress-strainrelationshipsofrubberandbiologicaltissues
9.6Linearviscoelasticbodies
9.7Quasi-linearviscoelasticityofbiologicaltissues
9.8Non-Newtonianfluids
9.9Viscoplasticmaterials
9.10Sol-geltransformationandthixotropy
DerivationofFieldEquations
10.1Gauss'stheorem
10.2Materialdescriptionofthemotionofacontinuum
10.3Spatialdescriptionofthemotionofacontinuum
10.4Thematerialderivativeofavolumeintegral
10.5Theequationofcontinuity
10.6Theequationsofmotion
10.7Momentofmomentum
10.8Thebalanceofenergy
10.9Theequationsofmotionandcontinuityinpolarcoordinates
FieldEquationsandBoundaryConditionsinFluidMechanics
11.1TheNavier-Stokesequations
11.2Boundaryconditionsatasolid-fluidinterface
11.3Surfacetensionandtheboundaryconditionsataninterfacebetweentwofluids
11.4DynamicsimilarityandReynoldsnumber
11.5Laminarflowinahorizontalchannelortube
11.6Boundarylayer
11.7Laminarboundarylayeroveraflatplate
11.8Nonviscousfluid
11.9Vorticityandcirculation
11.10Irrotationalflow
11.11Compressiblenonviscousfluids
11.12Subsonicandsupersonicflow
11.13Applicationstobiology
SomeSimpleProblemsinElasticity
12.1Basicequationsofelasticityforhomogeneous,isotropicbodies
12.2Planeelasticwaves
12.3Simplifications
12.4Torsionofacircularcylindricalshaft
12.5Beams
12.6Biomechanics
Stress,Strain,andActiveRemodelingofStructures
13.1Introduction
13.2Howtodiscoverthezero-stressstateofmaterialinasolidbody
13.3Remodelingthezero-stressstateofastructure:Abiologicalexampleofactiveremodelingduetochangeinstress
13.4Changeofzero-stressstatewithtemperature:Materialsthat"remember''theirshapes
13.5Morphologicalandstructuralremodelingofbloodvesselduetoachangeinbloodpressure
13.6Remodelingofmechanicalproperties...
13.7Stressanalysiswiththezero-stressstatetakenintoaccount
13.8Stress-growthrelationship
Index
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