A relative methodology for the uncertainty quantification of material model calibration using a DIC-levelled FEMU and a heterogeneous test

Non-homogeneous mechanical tests are experiments that present strain heterogeneity regarding the observed different strain states. These came to replace the conventional approaches for mechanical characterization and constitutive model parameter identification. Using Digital Image Correlation (DIC) and the Finite Element Model Updating (FEMU) method, it is possible to calibrate a constitutive model with this type of test. Yet, it is of upmost importance to estimate the errors and uncertainties of these identifications in order to obtain accurate simulations. The DIC procedure alone presents a vast number of sources of error that were already evaluated in [1]. Also, the material parameter identification itself deals with error propagation since it generally compares experimental data measured using optical techniques with numerical data [2]. When using optical cameras to measure the displacement fields, the image noise can be related to displacement uncertainties and the latter to material parameter fluctuations [3]. The FEMU approach is largely used to identify parameters, but the majority of the studies do not account for uncertainty measurements in parameter identification [4,5].The present work aims at evaluating the uncertainties in material parameter identification using a heterogeneous strain test. The general probabilistic and non-probabilistic approaches to quantify errors require large computational efforts that are drastically increased when dealing with model calibration. Thus, an expedited method is essential. Considering the FEMU approach as an optimisation problem and when using a virtual experiment, the global minimum is known, then it is possible to use the KKT conditions [6] for a fast and relative error estimation. The regarded identification approach is a FEMU with a DIC-levelling technique [7], which was already employed with a heterogeneous test in [8]. This technique compares both the experimental and numerical data, similarly, minimising the errors between the two. The mechanical test that feeds the FEMU approach is a strain heterogeneous test proposed in [9], which was originated using shape optimisation. The material under analysis was modelled with the Swift law and Yld2000-2d yield function. These constitutive models are also the target of the uncertainty quantification of the calibration.