The notes and problem sheets mentioned below have been freely available for the past 15 years (since October 2004 until November 2019). They are now available in book format from the publisher.

Course description

• Vectors and Cartesian Tensors
  
  
  • Elementary properties of tensors.
  • Spectral representation theorem. Square-root theorem.
  • Polar decomposition theorem.
  • Vector and tensor calculus. Divergence theorem.
    
    Lecture notes
    Problem Set #1
    Problem Set #2
    Problem Set #3
    

• Kinematics
  
  
  • Mathematical model of a continuum body; Lagrangian and Eulerian descriptions.
    Material time derivatives and useful formulae.
    Deformation gradient and other kinematical measures of deformation.
    
  • Velocity gradient; stretching and spin tensors.
  • Transport formulae.
    
    Lecture notes
    Problem Set #4
    Problem Set #5
    

• Balance Laws: Global and Local Forms
  
  
  • Principle of mass conservation.
  • Principle of conservation of linear momentum.
  • Principle of conservation of angular momentum.
  • Cauchy's stress theorem.
  • Stress tensors (Piola-Kirchhoff and Cauchy).
    
    Lecture notes
    Problem Set #6
    Problem Set #7
    

• Constitutive Assumptions
  
  
  • Principle of material frame-indifference.
    Objectivity and simple materials.
  • Material symmetry; isotropy and anisotropy.
    Representation theorems for isotropic functions.
  • Hyperelastic materials; strain-energy functions.
  • Derivatives with respect to tensors.
  • Internal constraints.
  • Examples of constitutive laws.
    
    Lecture notes
    Problem Set #8
    Additional problems