Continuum Mechanics (ME613)

Course Contents and Assessment

S. No. Description Download link
1 Course contents Syllabus
2 Grading methodology Assessment Criteria

Lectures Schedule, Topics and Assignments/Papers

Lecture. No. Lecture Topic
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


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


Fall 2020
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


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


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