Continuum Mechanics

  1. Kinematics of Deformation
    1. Descriptions of Motion
      1. Reference Configuration
        1. Current Configuration
          1. Material Description
            1. Lagrangian Formulation
              1. Material Coordinates
                1. Particle Tracking
                2. Spatial Description
                  1. Eulerian Formulation
                    1. Spatial Coordinates
                      1. Field Point Description
                      2. Relationship Between Descriptions
                      3. Motion and Deformation Mapping
                        1. Deformation Function
                          1. Displacement Vector
                            1. Deformation Gradient Tensor
                              1. Physical Interpretation
                                1. Jacobian Determinant
                                2. Polar Decomposition
                                  1. Right Stretch Tensor
                                    1. Left Stretch Tensor
                                      1. Rotation Tensor
                                        1. Geometric Interpretation
                                      2. Strain Measures
                                        1. Finite Strain Tensors
                                          1. Green-Lagrange Strain Tensor
                                            1. Euler-Almansi Strain Tensor
                                              1. Other Strain Measures
                                              2. Infinitesimal Strain Theory
                                                1. Small Displacement Gradient
                                                  1. Infinitesimal Strain Tensor
                                                    1. Engineering Strain Components
                                                      1. Geometric Interpretation
                                                      2. Strain Decomposition
                                                        1. Volumetric Strain
                                                          1. Deviatoric Strain
                                                            1. Principal Strains
                                                          2. Velocity and Acceleration
                                                            1. Velocity Field
                                                              1. Acceleration Field
                                                                1. Velocity Gradient Tensor
                                                                  1. Rate of Deformation Tensor
                                                                    1. Spin Tensor
                                                                      1. Vorticity Vector
                                                                      2. Compatibility Conditions
                                                                        1. Saint-Venant Compatibility Equations
                                                                          1. Physical Significance
                                                                            1. Simply Connected Domains
                                                                              1. Multiply Connected Domains

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                                                                            2. Mathematical Foundations

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                                                                            4. Stress Analysis