ME622A

INTRODUCTION TO CONTINUUM MECHANICS

Credits:

 

 

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

References:

  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