Quantitative Comparisons of Volumetric Datasets From Experiments and Computational Models

Wide-spread availability of low-cost digital sensors has made the acquisition of full-field experimental measurements less challenging, with modern measurement systems, such as X-ray computed tomography, capable of obtaining three-dimensional (3D) data fields. This presents difficulties when comparing computational and corresponding experimental data that often do not share the same, coordinate system or data pitch. This paper presents a method of orthogonally decomposing 3D data arrays into feature vectors using a pre-defined set of basis vectors, which are based on discrete Chebyshev polynomials. This allows one-to-one quantitative comparisons of 3D data fields with the same orientation but differing data pitch and coordinate system, irrespective of the source from which they are acquired. Two case-studies, each involving a pair of finite element (FE) model and experimental datasets, were used in this paper to demonstrate the capability of the method. The first case study represented the internal 3D strain fields in a reinforced-rubber matrix specimen under tensile load, measured using digital volume correlation, whilst the second study involved time-varying, surface displacements of an aerospace panel under resonance, which were measured using digital image correlation. From the two case studies, it was demonstrated that the decomposition method can be successfully employed to perform quantitative validation of 3D FE-predicted data using a validation metric, which was previously developed for two-dimensional data fields.