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Programmes → I.M.Sc. in Mathematical Sciences; M.Sc. Mathematics/Applied Mathematics

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Continuum Mechanics

Course Code: AM 586; MM 586  |  Credits: 4  |  Prerequisite: Vector Analysis, Cartesian tensors, Linear algebra, Differential Equations

Syllabus Details

  • Unit I: (Cartesian Tensors and Kinematics) Cartesian tensors. Description of continua and kinematics.
  • Unit II: (Forces and Deformation) Forces in a continuum. The polar decomposition theorem. Continuum deformation.
  • Unit III: (Constitutive Equations) Geometrical restrictions on the form of constitutive equations. Constitutive equations for fluid, elastic and thermo-elastic materials.
  • Unit IV: (Non-Newtonian Fluids) Shear flow solutions of Reiner-Rivlin fluids.
  • Unit V: (Navier-Stokes Equations) Some solutions of the Navier-Stokes equations.
  • Unit VI: (Inviscid Hydrodynamics) General theorems in inviscid hydrodynamics.

Course Learning Objective

  1. Describe motion, deformation and forces in a continuum.
  2. Derive equations of motion and conservation laws for a continuum.
  3. Learn the constitutive equations for solid and fluids.
  4. Solve simple boundary value problems for solids and fluids.
  5. Apply the conservation principles and the constitutive equations.
  1. Hunter, S. C., Mechanics of Continuous Media, Mathematics and its Applications, Ellis Horwood Ltd. / John Wiley & Sons, 1976.
  2. Chadwick, P., Continuum Mechanics: Concise Theory and Problems, 2nd ed., Dover Publications, 1999.
  3. Lai, W. M., Rubin, D. and Krempl, E., Introduction to Continuum Mechanics, 3rd ed., Butterworth-Heinemann, 1993.
  4. Sedov, L. I., A Course in Continuum Mechanics, Wolters-Noordhoff, 1971.
  5. Narasimhan, M. N. L., Principles of Continuum Mechanics, Wiley, 1993.
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