On the validation of solid mechanics models using optical measurements and data decomposition

Abstract

Engineering simulation has a significant role in the process of design and analysis of most engineered products at all scales and is used to provide elegant, lightweight , optimized designs. A major step in achieving high confidence in computational models with good predictive capabilities is model validation. It is normal practice to validate simulation models by comparing their numerical results to experimental data. However, current validation practices tend to focus on identifying hot-spots in the data and checking that the experimental and modeling results have a satisfactory agreement in these critical zones. Often the comparison is restricted to a single or a few points where the maximum stress / strain is predicted by the model. The objective of the present paper is to demonstrate a step-by-step approach for performing model validation by combining fullfield optical measurement methodologies with computational simulation techniques. Two important issues of the validation procedure are discussed, i.e. effective techniques to perform data compression using the principles of orthogonal decomposition, as well as methodologies to quantify the quality of simulations and make decisions about model validity. An I-beam with open holes under three-point bending loading is selected as an exemplar of the methodology. Orthogonal decomposition by Zernike shape descriptors is performed to compress large amounts of numerical and experimental data in selected regions of interest (ROI) by reducing its dimensionality while preserving information; and different comparison techniques including traditional error norms, a linear comparison methodology and a concordance coefficient correlation are used in order to make decisions about the validity of the simulation.

Infrared thermography for void mapping of a graphene/epoxy composite and its full‐field thermal simulation

“…The validation of computational mechanics models can be achieved by employing the CEN/CWA (CEN Workshop Agreement) 16799 standard . The methodology integrates sophisticated full‐field comparison techniques along with the quantification of measurement uncertainties into a rigorous and effective validation technique, which decides on the acceptance or not of a computational mechanics simulation model . This technique comprises FE analysis, full‐field experimental results, data reconstruction and compression using image analysis techniques, and, finally, a decision on the validation of the model based on the comparison of the difference between the numerical and experimental results and the experimental uncertainties.…”

“…14 The methodology integrates sophisticated full-field comparison techniques along with the quantification of measurement uncertainties into a rigorous and effective validation technique, which decides on the acceptance or not of a computational mechanics simulation model. 15 This technique comprises FE analysis, full-field experimental results, data reconstruction and compression using image analysis techniques, and, finally, a decision on the validation of the model based on the comparison of the difference between the numerical and experimental results and the experimental uncertainties. According to the CEN standard, any data field I(x,y) can be fully described by a vector containing a small number (a few decades) of orthogonal moments (Zernike, Tchebycheff, Krawtchouk, etc).…”

Uncertainty quantification in DIC with Kriging regression

“…It is worth noting that the strain fields shown in Figure 13 and 14 are linearly interpolated from the original discrete strain data (16×64) only for the purpose of visualisation. In order to quantify the similarity between post-processing results and analytical results, an image decomposition technique based on Tchebichef polynomials [39,40] was used to represent each dataset and the concordance correlation coefficient [41] employed to compare the resultant moments. Specifically, 400 Tchebichef moments were used and the corresponding concordance correlation coefficients are listed in Table 2 where it is seen that Kriging regression with error estimation shows superior correlation with the analytical solution than does the subset-based DIC method.…”

High Temperature Vibratory Response of Hastelloy-X: Stereo-DIC Measurements and Image Decomposition Analysis

“…Data from both experiment (red) and simulation (blue) have been included as well as at room (dark colors) and high (bright colors) temperature. The exclusion of low value coefficients following the approach of Lampeas et al [19] simplifies the figure without excluding any significant information. The shape represented by the kernels is shown along the top of the figure. A comparison of the height of the bars in each chart provides information both about the changes in behavior from room to high temperature (left pair for experiment or right pair for simulation) and about the degree to which the simulation represents the experiment (right pair relative to left pair).…”