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