CONTINUUM MECHANICS -- CONTINUUM MECHANICS -- CONTENTS -- PREFACE -- Chapter 1 MANIFOLDS ON CONTINUUM MECHANICS -- ABSTRACT -- 1. INTRODUCTION TO DIFFERENTIAL GEOMETRY -- 1.1 Manifolds and Tensors on Manifolds -- 1 Definitions for Covector Space, Dot Product, and Adjoint Operator -- 2 Definition for Inverse Operator, and Inverse Adjoint Operator -- 3 Definition for Tensor Product and Tensor Space -- 4 Definition for Tensors -- 5 Definition for Trace and Double-Dot Product -- 6 Definition for Bases of Covector Spaces -- 7 Definition for Manifold -- 8 Definition for Differentiable Manifold -- 9 Definition for Tangent Vector and Tangent Space on Manifold -- 10 Definition for Tangent Bundle on Manifold -- 11 Definition for Current and Initial Reference Placements -- 12 Definition for Inner Product and Transpose Operator -- 1.2 Rotation Manifold -- 13 Definition for Rotation Vector in Euclidean SpaceE3 -- 14 Definition for Rotation Operator in Euclidean Space E3 -- 15 Definition for Complement Rotation Vector -- 1.2.1 Lie Group and Lie Algebra -- 16 Definition for Group -- 17 Definition for Special Orthogonal Group SO(3) -- 18 Definition for Lie Group -- 19 Definition for Lie Algebra -- 20 Definition for Lie Algebra Adjoint Transformation -- 21 Determination for Lie Brackets -- 22 Definition for Lie Algebra Homomorphism and Isomorphism -- 1.2.2 Compound Rotation -- 23 Definition for Material Description of Compound Rotation -- 24 Definition for Spatial Description of Compound Rotation -- 25 Definition for Material Tangent Space11 of Rotation -- 26 Definition for Spatial Tangent Space12 of Rotation -- 1.2.3 Isomorphisms and Tangential Transformations -- 27 Definition for Virtual Rotation Tensor and Virtual Rotation Vector -- 28 Definition for Material Vector Space of Rotation -- 29 Definition for Spatial Vector Space of Rotation.

1.2.4 Angular Velocities, Accelerations and Curvatures -- 30 Definition for Material Angular Velocity -- 31 Definition for Angular Accelerations -- 32 Definition for Curvatures -- 1.3 Constraint Point-Manifolds -- 33 Definition for (Holonomic) Point-Constraints -- 34 Definition for (Holonomic) Constraint Point-Manifold -- 35 Definition for Tangent Point-Bundle -- 36 Definition for Tangent Point-Space -- 1.4 Constraint Field-Manifolds -- 37 Definition for Fréchet Derivative and Differential -- 38 Definition for Gâteaux Differentia -- 39 Definition for Constraint Field-Manifold -- 40 Definition for Tangent Field-Bundle -- 41 Definition for Tangent Field-Space -- 42 Definition for Velocity Field-Space -- 1.5 Variation, Lie Derivative and Lie Variation -- 43 Definition for Variation Operator -- 44 Theorem -- 45 Definition for Pull-Back Operator -- 46 Definition for Push-Forward Operator -- 47 Definition for Lie Derivative -- 48 Definition for Lie Variation -- 2. VIRTUAL WORK FORMS -- 49 Definition for Virtual Work on Constraint Point-Manifold -- 50 Definition for Virtual Work on Field-Manifold -- 51 Principle of Virtual Work -- 2.1 Weak Balance Equations for Continuum -- 52 Definition for the First Piola-Kirchhoff Stress Tensor -- 53 Definitions for Gradient and Divergence -- 2.2 Constitutive Relations -- 2.3 On Symmetry of Second Variation -- 3. PARAMETRIZATION OF CONSTRAINT MANIFOLD -- 4. CONCLUSIONS -- REFERENCES -- Chapter 2 ANALYSIS OF SHELL STRUCTURES APPLYING TRIANGULAR FINITE ELEMENTS -- ABSTRACT -- 1. INTRODUCTION -- 2. DISPLACEMENT FORMULATION-BASED FLAT TRIANGULAR SHELL ELEMENTS -- 3. DISPLACEMENT FORMULATION-BASED CURVED TRIANGULAR SHELL ELEMENTS -- 4. SHELL ELEMENTS BASED ON DISCRETE KIRCHHOFF THEORY -- 5. MIXED/HYBRID AND ASSUMED NATURAL STRAIN FORMULATION-BASED ELEMENTS -- 5.1. First Phase Developments -- 5.2. Second Phase Developments.

5.2.1. Elements with Non-Optimal Properties -- 5.2.2. Elements with Optimal Properties -- 5.2.3. Mixed Formulation and Derivation of Optimal Shell Elements -- 5.2.3.1. Hellinger-Reissner Variational Principle -- 5.2.3.2. Discretized Functional and Equilibrium Equation -- 5.2.3.3 Element Geometry -- 5.2.3.4 Displacement and Strain Interpolations -- 5.2.3.5. Hybrid Strain Based Element Stiffness Matrices -- 5.2.3.6. Element Stiffness Matrices Incoporating Ddof -- 5.2.4. Representative Computed Results -- 5.2.4.1 Spherical Ring Loaded with its Own Weight -- 5.2.4.2 Pinched Cylinder -- 5.2.4.3 Hemispherical Shell -- 6. SPLINE FUNCTION-BASED FLAT TRIANGULAR SHELL ELEMENTS -- 7. CONCLUDING REMARKS -- APPENDIX A. DISPLACEMENT AND ROTATION FIELDS -- REFERENCES -- Chapter 3 TRANSPORT CONTROL OF FLUID AND SOLUTES IN MICROCHANNELS USING AC FIELD AND SEMICONDUCTOR DIODES -- ABSTRACT -- INTRODUCTION -- GOVERNING EQUATIONS FOR FLUID AND ANALYTE FLOW IN MICROCHANNELS -- SEMICONDUCTOR DIODE PUMPS AND MIXERS POWERED BY ALTERNATE CURRENT ELECTRIC FIELD -- CONCLUSIONS -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter 4 CONTINUUM DESCRIPTION OF FLOW-LIKE LANDSLIDE DYNAMICS -- ABSTRACT -- INTRODUCTION -- CHARACTERISTICS OF FLOW-LIKE LANDSLIDES -- OBJECTIVES FOR CONTINUUM MODEL DEVELOPMENT -- CONTINUUM MECHANICS FORMULATION -- BOUNDARY CONDITIONS -- DEPTH INTEGRATION -- FURTHER APPROXIMATIONS -- DISCRETIZATION -- RASH3D DESCRIPTION -- NUMERICAL IMPLEMENTATION -- Finite Volume Method -- Triangular Mesh Selection -- Kinetic Scheme -- Source Term: Bottom Slope -- Source Term: Friction Slope -- Rheological Laws -- MODEL EVALUATION -- THE MESH-DEPENDENCY PROBLEM -- MOTION ACROSS COMPLEX 3D MORPHOLOGY -- Deflected Run out Experiment -- Val Pola Rock Avalanche (Italy, 1987) -- CALIBRATION OF RHEOLOGICAL PARAMETERS -- The Thurwieser Rock Avalanche (Italy, 2004).

The Tate's Cairn Debris Flow (Hong Kong, 2005) -- CONCLUSION -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter 5 EXAMINATION OF CRACKS BASED ON CONTINUUM-MECHANICS -- ABSTRACT -- INTRODUCTION -- FUNDAMENTAL CONCEPTS AND NOTATIONS -- DEVELOPMENT OF J-INTEGRAL -- PATH-INDEPENDENCE OF THE J-INTEGRAL -- APPLICABILITY OF SPECIAL ISOPARAMETRIC ELEMENTS -- A. Singular Isoparametric Elements -- B. Isoparametric Transition Elements -- Case 1. Non-Singular Isoparametric Elements -- Case 2. Singular Isoparametric Elements -- NUMERICAL EXAMPLES -- 1. Model -- 2. Model -- 3. Model -- CONVERGENCE OF THE SOLUTION -- CONCLUSION -- REFERENCES -- Chapter 6 REVIEW ON METHODOLOGIES OF PROGRESSIVE FAILURE ANALYSIS OF COMPOSITE LAMINATES -- ABSTRACT -- 1. INTRODUCTION -- 2. FAILURE CRITERIA OF COMPOSITE LAMINATES -- 3. CONTINUUM DAMAGE MECHANICS THEORY -- 4. FINITE ELEMENT IMPLEMENTATION OF PROGRESSIVE FAILURE ANALYSIS -- 5. PROGRESSIVE FAILURE ANALYSIS OF CARBON FIBER/EPOXY COMPOSITE CYLINDRICAL LAMINATES -- 6. CONCLUSION -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter7DIFFERENTIALFORMOFCONTINUUMMECHANICS:OPERATORSANDEQUATIONS -- Abstract -- 1Introduction -- 2DifferentialForms -- 2.1Thedefinitionofdifferentialformsandwedgeproduct -- 2.2Exteriordifferentialoperator -- 2.3Hodgestaroperator -- 2.4Adjointoperator -- 2.5Homotopyoperator -- 2.6Otherusefulformulas -- 3DualMaterialSpace-Time -- 3.1Constitutiveequations:theusefulnessofHodgestaroperator -- 3.2Stressspace-time:theusefulnessofexteriordifferentialoperator -- 3.3Strainspace-time:theusefulnessofhomotopyoperator -- 4NavierEquationandItsAntiexactSolution -- 4.1TheNavierequations -- 4.2Anti-exactsolutionoftheNavierequation -- 5WaveandLaplaceEquationsforDefectsField -- 5.1Waveequations:theusefulnessofadjointoperator -- 5.2Laplaceequation(waveequationfordefectsfield) -- 5.3(3+1)-dimensionalexpressionofwaveequations.

6IncompatibilityEquationsandStressFunctions -- 6.1Incompatibilityequationinstrainspace -- 6.2Incompatibilityequationinstressspaceandstressfunctions -- 7EnergyIntegralandJ-Integral -- 7.1Energyintegral(J-integral)infracturemechanics -- 7.2GeneralizedPeach-Koehlerforce -- 8GeometricalInterpretationofBasicEquations -- 8.1Differentialgeometryintermsofthedifferentialforms -- 8.2Differentialgeometricalexpressionofthedualmaterialspace-time -- 9ElectrodynamicsofContinuainTermsoftheDifferentialForms -- 9.1Linearconstitutiveequations -- 9.2Waveequations -- 9.3Electromagneticfieldanddefectsfield -- 10Discussion -- 10.1Operatorsandequations -- 10.2Otherphysicalfields -- 11Conclusion -- References -- Chapter8STRESSDEPENDENTMORPHOGENESIS:CONTINUUMMECHANICSANDSYSTEMOFTRUSSES -- ABSTRACT -- 1INTRODUCTION -- 2CONTINUUMMECHANICS -- 2.1Kinematics -- 2.2Balanceequations -- 2.2.1Balanceofmass -- 2.2.2Balanceoflinearmomentum -- 2.3Thermodynamics -- 2.3.1Balanceequationsintheabsenceofgrowth -- 2.3.2Thermodynamicsofactiveelongation -- 2.4Equilibriumequationsforunconstraineddeformedconfiguration -- 2.4.1Variationalapproach -- 2.4.2Non-variationalapproach -- 2.5Constraineddeformedconfiguration -- 2.6Stressdependentactivedeformations -- 3MECHANICSOFTRUSSES -- 3.1Trusskinematics -- 3.2Unconstrainedequilibriumequations -- 3.3Stressdependentactivedisplacements -- 4MODELLINGOFCYTOSKELETALELEMENTS -- 4.1Activedeformations -- 4.2Passivedeformations -- 4.3Controlfunction -- 4.4Equilibriumequations -- 4.5Implementation -- 5RESULTS -- 6CONCLUSION -- ASTRAINANDSTRESSMEASURESFORTRUSSES -- REFERENCES -- Chapter9NEAREST-NODESFINITEELEMENTMETHOD -- Abstract -- 1Introduction -- 2Nearest-NodesFiniteElementMethod(NN-FEM) -- 2.1Strategyforconstructingshapefunctions -- 2.2Assemblyofglobalstiffnessmatrix -- 2.3Searchingnearestnodesbyelementadjacency.

2.4Constructionofshapefunctionsforaquadraturepointnearacrack.