High resolution measurement of internal full-field displacements and strains using global spectral digital volume correlation

• A global digital volume correlation approach is developed based on Fourier basis functions, leading to a computationally efficient algorithm using Fast Fourier Transform.
• Displacements and strains with high degrees of freedom can be sought without significantly increasing the computational complexity.
• Artificial experiment on randomly generated composites with spherical and non-aligned ellipsoidal particles proves its capability in capturing strain in the particles.
• Artificial experiment on an imaginary cracked sample shows its stability at high resolutions.

Thanks to its ability to non-destructively access internal strains in materials, Digital Volume Correlation (DVC) is gaining growing interest from both experimental and theoretical mechanics communities. One important issue in the implementation of DVC is the considerable computational costs associated with the huge amount of data, which hinders the applications of the technique, especially for high-resolution displacement and strain measurements. In this paper, we propose an accurate global DVC approach based on a Fourier decomposition for the kinematic basis of the sought displacement field. The approach, referred to as IS-DVC, leads to an algorithm whose computational complexity is not considerably increased by increasing the number of Degrees of Freedom (DOF) of the kinematic basis, thus being computationally efficient using the Fast Fourier Transform (FFT). Artificial experiments have been used to evaluate the uncertainties of IS-DVC at high resolutions. Especially, displacement fields of 3D composites with spherical and non-aligned ellipsoidal particles at small scales were reconstructed. Resulting measurements revealed close similarities in terms of strain heterogeneities throughout the volume with the benchmark strains. Furthermore, it was shown that, in the presence of a discontinuity, the measurement uncertainties are not significantly affected, except for regions surrounding the discontinuity, hence validating the robustness of the reconstructed displacement field at a large number of DOF.