Digital volume correlation

There is a significant need to development measurement techniques in experimental mechanics. Computers, image processing, and inexpensive digital cameras have made digital image correlation (DIC) a common tool in the laboratory. A three-dimensional extension of DIC has been developed called digital volume correlation (DVC). The technique uses high-resolution computed tomography (muCT) images of materials with internal architecture discernible with X-rays to measure displacements and calculate strains. The intrinsic pattern generated by imaging the material architecture is used as the signal for correlation. Correlation is performed on many small subvolumes within the volume of a sample to obtain a discrete displacement vector field. Strains are calculated by locally fitting a deformation tensor to a group of displacement vectors.Two different correlation coefficients have been used: sum of squares and normalized cross-correlation. The correlation coefficients are minimized using a coarse-fine approach. The coarse search is a brute force method to get within a few voxels then the fine search uses gradient based optimization methods (Levenberg-Marquardt or BFGS) to find the minimum. The problem has been formulated with only translational degrees of freedom as well as with both translation and rotational degrees of freedom. Finite rotations were parameterized using a modified version of the angle-axis representation. Both an open celled aluminum foam material and trabecular bone have been successfully used as samples.Repeat unload experiments to characterize the measurement precision have shown that the displacement errors are normally distributed with a standard deviation of 0.035 voxels. Artificial rotation experiments have shown that even small rotations (1 deg) introduce significant errors when rotations are not included in the minimization. Comparisons between DVC measured strains and continuum finite element models of aluminum foam samples show good overall agreement with differences in areas of high strain gradients. DVC indicates spatially where failure is occurring, so that local collapse can be located, then raw muCT image volumes can be used to show the details of the architectural failure mechanisms.