Shape descriptors and mapping methods for full-field comparison of experimental to simulation data

Validation of computational solid mechanics simulations requires full-field comparison methodologies between numerical and experimental results. The continuous Zernike and Chebyshev moment descriptors are applied to decompose data obtained from numerical simulations and experimental measurements, in order to reduce the high amount of ‘raw’ data to a fairly modest number of features and facilitate their comparisons. As Zernike moments are defined over a unit disk space, a geometric transformation (mapping) of rectangular to circular domain is necessary, before Zernike decomposition is applied to non-circular geometry. Four different mapping techniques are examined and their decomposition/ reconstruction efficiency is assessed. A deep mathematical investigation to the reasons of the different performance of the four methods has been performed, comprising the effects of image mapping distortion and the numerical integration accuracy. Special attention is given to the Schwarz–Christoffel conformal mapping, which in most cases is proven to be highly efficient in image description when combined to Zernike moment descriptors. In cases of rectangular structures, it is demonstrated that despite the fact that Zernike moments are defined on a circular domain, they can be more effective even from Chebyshev moments, which are defined on rectangular domains, provided that appropriate mapping techniques have been applied

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

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, light-weight, 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-bystep approach for performing model validation by combining full-field 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

A hybrid framework for nonlinear dynamic simulations including full-field optical measurements and image decomposition algorithms

Innovative designs of transport vehicles need to be validated in order to demonstrate reliability and provide confidence. It is normal practice to study the mechanical response of the structural elements by comparing numerical results obtained from finite element simulation models with results obtained from experiment. In this frame, the use of wholefield optical techniques has been proven successful in the validation of deformation, strain, or vibration modes. The strength of full-field optical techniques is that the entire displacement field can be acquired. The objective of this article is to integrate full-field optical measurement methodologies with state-of-the-art computational simulation techniques for nonlinear transient dynamic events. In this frame, composite car bonnet frame structures of dimensions about 1.8 m 30.8 m are considered. They have been tested in low-velocity mass-drop impact loading with impact energies ranging from 20 to 200 J. In parallel, simulation models of the car bonnet frame have been developed using layered shell elements. The Zernike shape descriptor approach was used to decompose numerical and experimental data into moments for comparison purposes. A very good agreement between numerical and experimental results was observed. Therefore, integration of numerical analysis with full-field optical measurements along with sophisticated comparison techniques can increase design reliability