Basic Equations

The continuum mechanics summarized here is based on References. 1 2 3

Three basic choices need to be made in the development of a large deformation semi discretization scheme:
  • Mesh description
  • Kinematic description, that is, how the deformation is measured
  • Kinetic description, that is, how the stresses are measured

Usually, the kinematic description implies the kinetic description as kinetic and kinematic measures should be energetically conjugated.

To go further in to the theory, two sets of coordinates are introduced:
  • Spatial or Eulerian coordinates
  • Material or Lagrangian coordinates

1 Belytschko T. and Hughes T.J.R., “Computational Methods for Transient Analysis”, North-Holland, 1983.
2 Belytschko T., Wing Kam Liu, and Moran B., “Finite Elements for Nonlinear Continua and Structures”, John Wiley, 1999.
3 Geradin M., “Structural Dynamics ”, Masson, 1993.