Purdue School of Engineering and Technology

Purdue School of Engineering and Technology

Continuum Mechanics

ME 69700 / 3 Cr. (3 Class)

This course will covers the formal, consistent and unified mathematical treatment of the mechanics of continuous solids and fluids.


  • Naive set theory
  • Linear spaces
  • Points, vectors, and tensors in Euclidian space
  • Direct vs. indicial notation
  • Bodies, configurations, motions
  • Mass and mass density
  • The deformation gradient
  • The Jacobian
  • The polar decomposition
  • Lagrange and Almansi strain tensors
  • Velocity gradient and vorticity
  • Superposed rigid body motions and change of reference frame
  • Reynold's transport theorem
  • Conservation of mass
  • Euler's laws
  • Traction vector
  • Stress tensor
  • Localization theorem and local forms of balance laws
  • Stress measures in the reference and current configuration
  • Invariance and relationship to constitutive laws
  • The balance of energy
  • Directional (Gâteux) derivatives
  • Consistent linearization
  • Inviscid fluid
  • Viscous fluid
  • Elastic solids
  • Linear Elastic Solids