| Lecture 1 |
Introduction to Real Numbers, Vector Space and Euclidean Space |
| Lecture 2 |
3D-Euclidean Space, Linearly Independent Vectors and Basis Vectors |
| Lecture 3 |
Index Notation, Einstein Convention and Cross-product of Vectors |
| Lecture 4 |
Scalar Triple Product and Tensors |
| Lecture 5 |
Tensor Algebra - I (Tensor Product) |
| Lecture 6 |
Tensor Algebra - II (Transpose and Trace of a Tensor, Symmetric and Skew-symmetric Tensor) |
| Lecture 7 |
Tensor Algebra - III (Inverse, Determinant, Co-factor of a Tensor) |
| Lecture 8 |
Invariants of a Tensor |
| Lecture 9 |
Eigenvalues and Eigenvectors of a Tensor |
Quiz-1 |
Fall 2020
|
| Lecture 10 |
Tensor Transformations |
| Lecture 11 |
Tensor Calculus |
| Lecture 12 |
Integral Theorems, Polar Decomposition of Tensor |
| Lecture 13 |
Concept of Continuum Body, Configuration, Motion |
| Lecture 14 |
Lagrangian and Eulerian Description, Displacement, Velocity and Acceleration Field |
| Lecture 15 |
Spatial Time Derivative, Material Time Derivative |
| Lecture 16 |
Deformation of Material Line Element (Concept of Deformation Gradient), Displacement Gradient Tensor |
| Lecture 17 |
Deformation of a Volume Element, Area Element, Stretch, Right Cauchy Green Deformation tensor |
Quiz-2 |
Fall 2020
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| Lecture 18 |
Left Cauchy Green Deformation Tensor |
| Lecture 19 |
Lagrangian and Eulerian Strain Tensor |
| Lecture 20 |
Strain Tensor for Infinitesimal Deformation, Spatial Velocity Gradient |
| Lecture 21 |
Examples of Uniform Deformation, Simple Shear, Plane Strain, Pure Torsion, Pure Bending |
| Lecture 22 |
Concept of Traction Vector, Cauchy’s Stress Theorem |
| Lecture 23 |
Piola Kirchoff Stress Tensor, Stress Components |
| Lecture 24 |
Normal and Shear Stress on a Plane, Maximum and Minimum Normal and Shear Stress |
| Lecture 25 |
Examples of States of Stress, Deviator and Spherical Stress States |
| Lecture 26 |
Balance Laws, Closed and Open System, Conservation of Mass |
Quiz-3 |
Fall 2020
|
| Lecture 27 |
Conservation of Mass for Closed System |
| Lecture 28 |
Conservation of Mass for Open System, Reynold’s Transport Theorem |
| Lecture 29 |
Conservation of Momentum, Local Form of Momentum Balance |
| Lecture 30 |
Other Form of Stress Measures, Conservation of Energy |
| Lecture 31 |
Mechanical Energy in Spatial, Material Description |
| Lecture 32 |
Constitutive Laws for Various Fluids, Solids |
| Lecture 33 |
Strong Restrictions on Constitutive Equations |
| Lecture 34 |
Concept of Frame Indifference, Objectivity |
| Lecture 35 |
Conditions for Objectivity, Transformations of Kinematical Quantities |
Quiz-4 |
Fall 2020
|
| Lecture 36 |
Transformations of Stress Tensors, Objectivity Restrictions on Response Functions |
| Lecture 37 |
Linearized Elasticity - I (Introduction and Linearized Kinematics) |
| Lecture 38 |
Linearized Elasticity - II (Linearized Kinetics and Balance Laws) |
| Lecture 39 |
Linearized Elasticity - III (Anisotropic, Orthotropic, Transversely Isotropic and Isotropic Materials) |
End-term Examination |
Fall 2020
|