3L-0T-0L-0D (9 Credits)


Course Content:

The purpose of the course is to expose the students to the basic elements of continuum mechanics in a sufficiently rigorous manner. After attending this course, the students should be able to appreciate a wide variety of advanced courses in solid and fluid mechanics

Lecturewise Breakup (based on 50min per lecture)(total lecture 40)

I. Introduction: (1 Lectures)

II. Mathematical Preliminaries: (6 Lectures)

  • Vector and tensor calculus.

  • Tensor analysis, derivatives of functions with respect to tensors

  • Fields, div, grad, curl

  • Divergence theorem, transport theorem

III. Kinematics: (6 Lectures)

  • Configurations of a body, displacement, velocity, motion

  • Deformation gradient, rotation, stretch, strain, strain rate, spin tensor

  • Assumption of small deformation and small strain

IV. Balance laws: (6 Lectures)

  • Balances of mass, linear momentum and angular momentum

  • Contact forces and the concept of stress.

  • Balance of energy and Clausius-Duhem inequalit.

V. Constitutive relation: (12 Lectures)

  • Frame indifference.

  • Material symmetry

  • Kinematic constraints (incompressibility, etc.)

  • Thermodynamical restrictions.

VI. Viscous fluid: (4 Lectures)

  • constitutive relations, non-Newtonian fluid, boundary value problem.

VII. Finite elasticit: (5 Lectures)

  • Hyperelasticity, isotropy, simple constitutive relations, boundary value problem


  1. Continuum Mechanics, A. J. M. Spencer

  2. Continuum Mechanics, P. Chadwick

  3. An Introduction to Continuum Mechanics, M. E. Gurtin

  4. ntroduction to the Mechanics of a Continuous Medium, L. E. Malvern

  5. Continuum Mechanics, C. S. Jog