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Course11210691260 lectures

Foundations of Continuum Mechanics

Prof. Gaurav Bhutani · IIT Mandi

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Introduction Video
  2. Tensors Video
  3. Summation Convention (Einstein Notation) Video
  4. Kronecker Delta Video
  5. Tutorial - Week 1 Video

Week 2

  1. Permutation Symbol Video
  2. Vector Operations Video
  3. Tensor Operations Video
  4. More on Indicial notation Video
  5. Tutorial - Week 2 Video

Week 3

  1. Matrices and Determinants Video
  2. Tensor Transformation Video
  3. Tensor Transformation - part 2 Video
  4. Isotropy and Invariance Video
  5. Tutorial - Week 3 Video

Week 4

  1. Principal Values and Directions Video
  2. Principal Values and Directions - part 2 Video
  3. Tensor Calculus - part 1 Video
  4. Tensor Calculus - part 2 Video
  5. Tutorial - Week 4 Video

Week 5

  1. Cauchy Stress Principle Video
  2. Cauchy Stress Formula Video
  3. Cauchy Stress Tensor Video
  4. Local Equilibrium Equations Video
  5. Tutorial - Week 5 Video

Week 6

  1. Stress Transformation and Principal Values Video
  2. Stress Maxima - Lagrange Multiplier Method Video
  3. Mohr's Circles Video
  4. Plane Stress, Deviatoric Stress and Octahedral Shear Stress Video
  5. Tutorial - Week 6 Video

Week 7

  1. Deformation and Configurations Video
  2. Material and Spatial Coordinates Video
  3. Lagrangian and Eulerian Description Video
  4. Material Derivative Video
  5. Tutorial - Week 7 Video

Week 8

  1. Deformation Gradient Tensor Video
  2. Finite Strain Tensors Video
  3. Infinitesimal Deformation Theory Video
  4. Strain Tensor and Plane Strain Video
  5. Tutorial - Week 8 Video

Week 9

  1. Rotations and Compatibility Video
  2. Finite Deformations Video
  3. Velocity Gradient Video
  4. Strain Rate and Rate of Rotation Video
  5. Tutorial - Week 9 Video

Week 10

  1. Material Derivative of Elements Video
  2. Reynolds Transport Theorem and Conservation of Mass Video
  3. Momentum Equations Video
  4. Lagrangian Form of Momentum Equations Video
  5. Energy Equation and Tutorial - Week 10 Video

Week 11

  1. Introduction to Constitutive Modelling Video
  2. Introduction to Constitutive Modelling - part 2 Video
  3. Elasticity Video
  4. Viscous and Viscoelastic Materials Video
  5. Plasticity Video

Week 12

  1. Tutorial - Constitutive Modelling Video
  2. Application - Linear Fluids Video
  3. Navier-Stokes Equation Video
  4. Fluid Flow Problem Video
  5. Summary Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Mandi
Department
Mechanical Engineering
Teacher
Prof. Gaurav Bhutani
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
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