- Vectors and Cartesian Tensors
- 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
Page created by Ciprian D.Coman
Last updated: December 2007