Recent improvements in experimental and computational techniques in material characterization have led to a vast amount of data on the microstructure and deformation of heterogeneous media. This information is traditionally arrayed in pixels, on grids. The massive extent of data in this form renders identifying key features difficult, and the cost of digital storage expensive. Our following research highlights introduce ways of efficient representation, construction, and analysis of such data.
Fig. 6. Strain maps calculated using an original image (left), and using its DCT representation, with the sizes of 20% (central map) and 5% (right map) of the of the original image.
Fig. 1. Axial strain fields obtained during uniaxial tension of nitinol sheets, at representative deformation states. The left and right images of each panel correspond to the original strain maps, and their truncated wavelet counterparts using 3% of the number of pixels, respectively.
Fig. 2. The local transformation at an intermediate state of deformation. The left and right columns correspond to the original field and its truncated wavelet expansion using 10% of number of original terms, respectively. The first and second rows correspond to the axial and transverse strain, respectively.
Fig. 3. The macroscopic stress–strain relation. The continuous and dashed curves correspond to the exact and the wavelet-approximation schemes, respectively.
Fig. 4. Wavelet activation map. Black marks denote the active wavelets in wavelet space. White regions are associated with wavelets which are never active.
Fig. 5. Macroscopic stress–strain relation of the spatial regions of active (dashed curves) and non-active wavelets (dash-dot curves). The stress–strain relation of the whole domain is given as a reference (continuous curve).
 Gal Shmuel, Adam Thor Thorgeirsson, Kaushik Bhattacharya (2014), Wavelet Analysis of Microscale Strains, Acta Mat., 76, 118-126.
We thank Samantha daly for providing us the experimental data, Andrew Richards for helpful discussions, and Jin Yang for his work on the DIC method. The research was carried out in Prof. Bhattacharya's group.