Visual representation of the kinematics of the continuum

Abstract

The purpose of this paper is to present some experimentally determined properties of the continuum. The development starts with the illustration of deformed shapes, or metamorphoses, and the introduction of the concept of displacement. From there on, the development follows the classic mechanics-of-continuum presentation, spatial and time derivatives of displacement, strains, stresses and rigid rotations. To unify the presentation, all considerations are applied to the case of a circular ring subjected to diametral compression. Particular advantage is taken of grids, moiré, brittle-coatings and photoelasticity methods to obtain the physical representations of the properties. The following loci are considered: isokinetics, isothetics, isogonics, isoclinics of displacement, displacement trajectories, loci of partial derivative, isogyros, isotenics, isochromatics, isoclinics of strain and stress, isostatics, isopachics, isobars, isostrophics and isoentatics. The understanding of the properties of these fields helps in the visualization of the mechanics of the continuum, in general, and may prove to be particularly useful in the fields of plasticity and finite strain.