Strain Measurement in an Aluminium Foam by Means of Digital Image Correlation - Visual Computing: Scientific Visualization and Imaging Systems - page 140

Fig. 7.8 Distribution of the x strain obtained from the optical measurement at four stages of
crushing: a 10 mm; b 20 mm; c 30 mm; d 40 mm

them can be calculated via the well known strain-displacement matrix B. Since
B is usually defined with the natural coordinates (n, g), a mapping is required to
the physical coordinate (x, y); this is accomplished with the usual shape functions
of finite elements. In conclusion, the strains e are calculated as:

e ¼ Bu ð 7 : 5 Þ

A peculiarity of the considered case is that the foam undergoes very large strains.
This has the detrimental consequence on the measurement technique that the fea-
tures of the speckle can change to a great extent; thus, correlating the deformed to
the undeformed shape can be difficult or even impossible. Again, as reported at the
end of Sect 7.4.1 regarding the search of the subset as undeformed rectangle, the
remedy is considering several images during the evolution of the phenomenon and
correlating each image to the previous one instead of the initial one.
The procedures for tracking the markers and calculating the strains, performing
all the related calculations, have been implemented in MATLAB . Figure 7.6
shows, at four different stages of crushing (10, 20, 30, 40 mm), the markers
superposed to the images of the deformed specimen. Figures 7.7 and 7.8 show,
respectively, the distribution of the longitudinal (y) and transverse (x) strains,