• Computational Continuum Mechanics, 3rd Edition (4)
• Contents (6)
• Preface (10)
• 1 Introduction (14)
  • 1.1 Matrices (15)
  • 1.2 Vectors (19)
  • 1.3 Summation Convention (24)
  • 1.4 Cartesian Tensors (25)
  • 1.5 Polar Decomposition Theorem (34)
  • 1.6 D’Alembert’s Principle (36)
  • 1.7 Virtual Work Principle (42)
  • 1.8 Approximation Methods (45)
  • 1.9 Discrete Equations (47)
  • 1.10 Momentum, Work, and Energy (50)
  • 1.11 Parameter Change and Coordinate Transformation (52)
  • Problems (57)
• 2 Kinematics (60)
  • 2.1 Motion Description (61)
  • 2.2 Strain Components (68)
  • 2.3 Other Deformation Measures (73)
  • 2.4 Decomposition of Displacement (75)
  • 2.5 Velocity and Acceleration (77)
  • 2.6 Coordinate Transformation (81)
  • 2.7 Objectivity (87)
  • 2.8 Change of Volume and Area (90)
  • 2.9 Continuity Equation (94)
  • 2.10 Reynolds’ Transport Theorem (95)
  • 2.11 Examples of Deformation (97)
  • 2.12 Geometry Concepts (105)
  • Problems (107)
• 3 Forces and Stresses (110)
  • 3.1 Equilibrium of Forces (110)
  • 3.2 Transformation of Stresses (113)
  • 3.3 Equations of Equilibrium (113)
  • 3.4 Symmetry of the Cauchy Stress Tensor (115)
  • 3.5 Virtual Work of the Forces (116)
  • 3.6 Deviatoric Stresses (126)
  • 3.7 Stress Objectivity (128)
  • 3.8 Energy Balance (132)
  • Problems (133)
• 4 Constitutive Equations (136)
  • 4.1 Generalized Hooke’s Law (137)
  • 4.2 Anisotropic Linearly Elastic Materials (139)
  • 4.3 Material Symmetry (140)
  • 4.4 Homogeneous Isotropic Material (142)
  • 4.5 Principal Strain Invariants (149)
  • 4.6 Special Material Models for Large Deformations (150)
  • 4.7 Linear Viscoelasticity (154)
  • 4.8 Nonlinear Viscoelasticity (168)
  • 4.9 A Simple Viscoelastic Model for Isotropic Materials (174)
  • 4.10 Fluid Constitutive Equations (175)
  • 4.11 Navier–Stokes Equations (177)
  • Problems (177)
• 5 Finite Element Formulation: Large-Deformation, Large-Rotation Problem (180)
  • 5.1 Displacement Field (182)
  • 5.2 Element Connectivity (189)
  • 5.3 Inertia and Elastic Forces (191)
  • 5.4 Equations of Motion (193)
  • 5.5 Numerical Evaluation of The Elastic Forces (201)
  • 5.6 Finite Elements and Geometry (206)
  • 5.7 Two-Dimensional Euler–Bernoulli Beam Element (212)
  • 5.8 Two-Dimensional Shear Deformable Beam Element (216)
  • 5.9 Three-Dimensional Cable Element (218)
  • 5.10 Three-Dimensional Beam Element (219)
  • 5.11 Thin-Plate Element (221)
  • 5.12 Higher-Order Plate Element (223)
  • 5.13 Brick Element (224)
  • 5.14 Element Performance (225)
  • 5.15 Other Finite Element Formulations (229)
  • 5.16 Updated Lagrangian and Eulerian Formulations (231)
  • 5.17 Concluding Remarks (234)
  • Problems (236)
• 6 Finite Element Formulation: Small-Deformation, Large-Rotation Problem (238)
  • 6.1 Background (239)
  • 6.2 Rotation and Angular Velocity (242)
  • 6.3 Floating Frame of Reference (FFR) (247)
  • 6.4 Intermediate Element Coordinate System (249)
  • 6.5 Connectivity and Reference Conditions (251)
  • 6.6 Kinematic Equations (256)
  • 6.7 Formulation of The Inertia Forces (258)
  • 6.8 Elastic Forces (261)
  • 6.9 Equations of Motion (263)
  • 6.10 Coordinate Reduction (264)
  • 6.11 Integration of Finite Element and Multibody System Algorithms (266)
  • Problems (271)
• 7 Computational Geometry and Finite Element Analysis (274)
  • 7.1 Geometry and Finite Element Method (275)
  • 7.2 ANCF Geometry (277)
  • 7.3 Bezier Geometry (279)
  • 7.4 B-Spline Curve Representation (280)
  • 7.5 Conversion of B-Spline Geometry to ANCF Geometry (284)
  • 7.6 ANCF and B-Spline Surfaces (286)
  • 7.7 Structural and Nonstructural Discontinuities (288)
  • Problems (290)
• 8 Plasticity Formulations (292)
  • 8.1 One-Dimensional Problem (294)
  • 8.2 Loading and Unloading Conditions (295)
  • 8.3 Solution of the Plasticity Equations (296)
  • 8.4 Generalization of The Plasticity Theory: Small Strains (304)
  • 8.5 J2 Flow Theory with Isotropic/Kinematic Hardening (311)
  • 8.6 Nonlinear Formulation for Hyperelastic–Plastic Materials (325)
  • 8.7 Hyperelastic–Plastic J2 Flow Theory (335)
  • Problems (339)
• References (342)
• Index (352)