New validation metric for solid mechanics models

Abstract

Numerical simulation is essential in mechanical engineering as it predicts the mechanical behaviour of a component when subjected to external forces, helping to improve performance and optimise design. Before utilizing the numerical model's valuable information, its reliability must be verified through a validation process. Validation is usually carried out by comparison with full field experimental measurements of the displacement or strain maps that undergoes the probe sample when subjected to the external forces, mainly with the technique of digital image correlation. The numerical simulation and its predictions are validated if there is an agreement between the model's prediction and the corresponding experimental measurements. In this procedure, comparing the simulated and experimental data requires an image compression process, typically using descriptors based on Zernike moments or any polynomial decomposition. In more recent work, agreement or validation is quantified with a “probabilistic validation metric” (PVM), which is obtained by measuring the normalised differences of these moments. For the PVM, these differences must be below a predetermined and constant threshold obtained from the experimental uncertainty and the reconstruction error of the moments. The threshold effectively captures the behaviour of lower-order moments, but is insensitive to changes in higher-order moments. In this work, a new validation method called “Moment Validation Metric” (MVM) is proposed. It introduces an adaptive threshold that is specific to each moment, considering the impact of the propagation of the uncertainty and the errors in the experimental and simulated measurements of the associated maps. The uncertainty of the maps is propagated to the moments through an accurate calculation procedure of the moments shown in [1]. As a result, moments containing most of the information (with the highest impact) have a smaller threshold, while moments with lower impact tend to have a larger threshold. The proposed validation method detects and quantifies differences in the experimental and simulated maps which are not detected by previous techniques. The MVM, being more accurate, is able to identify these differences more effectively.