Introduction to Elasticity and Fluid Dynamics - Elective (PHY 440.5)

Venue: TBA

Class Timings: TBA

First Meeting: TBA

Course Syllabus: 

Elasticity

  • Continuum mechanics: Deformation gradient, polar decompositions, measures of strain, strain tensor
  • Special cases: Small and large strain, large rotations, large displacements
  • Constitutive laws: Stress-strain relations, Young’s modulus, Poisson ratio 
  • 1D problems: Bending of beams, energetics, Euler elastica, buckling, rod theory, contact forces 
  • Elastodynamics: Wave propagation, half-plane problems, solution strategies
  • Energetics: Variational principles, energy functional, hyperelastic materials

Fluid Dynamics
  • Overview: Continuum formulation, limitations, mathematical preliminaries
  • Kinematics: Lagrangian and Eulerian perspectives, streamlines, streaklines, pathlines, stream function, vorticity, velocity gradients etc.
  • Transport theorem: Stress tensor, symmetries, equilibrium, Reynolds transport theorem, conservation laws, Navier’s equation
  • Navier-Stokes: Constitutive laws, NS equations, Scaling, Reynolds number
  • Special cases: Unidirectional flows, Stokes 1st and 2nd problem, Lubrication
  • Euler equations: Ideal flow, Boundary conditions, Bernoulli's equation, Potential flow, solution strategies, Ideas of boundary layers
  • Stokes equations: Reduction, Properties, Flow past a sphere, Flow past a cylinder, Stokes paradox
  • Hydrodynamic stability: Overview of stability analysis, Kelvin-Helmholtz, Rayleigh-Taylor instabilities.

Textbooks: 

  • Landau and Lifshitz, Theory of elasticity (3rd edition) 
  • William S. Slaughter, The Linearized Theory of Elasticity (Springer)
  • Audoly and Pomeau, Elasticity and Geometry (Oxford)
  • D. J. Acheson, Elementary Fluid Dynamics (Oxford)
  • Kundu, Cohen, and Rowling, Fluid Mechanics (Academic Press)
  • S. Childress, An Introduction to Theoretical Fluid Mechanics (Courant)
  • Batchelor, An Introduction to Fluid Dynamics, (Cambridge)

Course Evaluation: Problem sets (40%), Class participation and notes (20%), Final Exam (40%)

Course Outcome:
  •  Students will learn about the theoretical formalism of elasticity theory and fluid dynamics.
  •  They will also learn about practical applications of the theory to real life phenomena and to experiments.
  •  Develop  problem solving skills  using different techniques, both analytic and numerical





Credit Score: 4