ABSTRACT
If a volume of matter undergoes large motion and finite deformation during evolution, then kinematics of motion, deformation, definition of strains and their measures differ significantly from infinitesimal theories, for example linear theory of elasticity for solid matter. The type of description (Lagrangian or Eulerian) and type of measures (covariant and contravariant) play a significant role in deriving the mathematical descriptions of the kinematics of motion and deformation as well as possible definitions and measures of strains and stresses. In this chapter we consider mathematical details of these various aspects of deforming matter experiencing finite motion and finite deformation.
