| 1 |
Introduction, The Continuous Medium |
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| 2 |
Tensor Analysis, Introduction |
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| 3 |
Contraction and Quotient Law, The Permutation Symbol (or Alternator or Alternating Symbol) |
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| 4 |
Gradient, Divergence, and Curl |
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| 5 |
The Gradient Theorem |
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| 6 |
The Divergence Theorem of Gauss |
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| 7 |
Dyads and Dyadics |
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| 8 |
Isotropic Tensors |
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| 9 |
Stress Analysis, Introduction, Stress Vector |
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| 10 |
Stress Vector on Coordinate Planes |
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| 11 |
Cauchy’s Formula |
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| 12 |
Principal Stresses and Principal Axes |
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| 13 |
Force and Moment Equations of Equilibrium |
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| 14 |
Stress Deviator Tensor, Maximum Shearing Stress |
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| 15 |
Analysis of Kinematics in a Continuum, Introduction |
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| 16 |
Eulerian Time Derivative |
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| 17 |
Strain Tensor and Rate of Strain Tensor |
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| 18 |
Stretch Ratio, Rotation Tensor, Stretch Tensors |
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| 19 |
Velocity Gradients, Rate of Deformation, Vorticity |
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| 20 |
The Euler-Expansion Formula |
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| 21 |
The Jacobian and the Continuity Equations |
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| 22 |
Balance Laws of a Continuum: Reynolds Transport Theorem |
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| 23 |
The Law of Balance of Mass |
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| 24 |
The Law of Balance of Linear Momentum |
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| 25 |
The Law of Balance of Angular Momentum |
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| 26 |
The Law of Balance of Energy |
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| 27 |
Application to Solids : Constitutive Law |
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| 28 |
Lagrangian Form of the Energy Equations |
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| 29 |
Constitutive Laws of Materials |
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