Basic models supporting Experimental Mechanics of deformations, geometrical representations, connections among different techniques

Techniques that process experimental displacement information have become prevalent tools of Experimental Mechanics. This paper introduces basic models describing the kinematics of the two-dimensional continuum and connects models with graphical representations illustrating the derived mathematical expressions. These elements of differential geometry are used to describe the different techniques. Techniques are divided in two groups: (i) techniques that operate with projected displacements like moiré, holography and speckle techniques and (ii) techniques that determine relative displacement vectors like digital image correlation and harmonic phase analysis. Fundamental ideas concerning how each of these techniques extracts displacements and displacement derivatives are presented. Comparisons between techniques are given indicating the consequences of particular selected processes and implications of some of the particular choices. A qualitative evaluation among techniques is an extremely difficult task because the selection of a given approach depends on a very large number of issues such as the particular problem to be investigated and even includes familiarity with processing software. It is possible to conclude that in some cases for a given signal, using well coded processing software, results are similar regardless of the particular selected method