On mappings and deformation processes

This note focuses on kinematics in continuum mechanics and suggests the need for distinguishing between a mapping and a deformation process. As an example, it is shown that the standard discussion of isochoric bending of a cube into sectors of circular tubes is actually an isochoric deformation process that continuously deforms only members of the set of sectors of circular tubes. Specifically, this mapping cannot continuously deform a cube into sectors of circular tubes.