Calibration of material model using mixed-effects models

Abstract : The quantification of model parameter uncertainty is a long-standing issue in model calibration. Classical techniques provide methods to handle some type of uncertainties (e.g. experimental noise or model bias). However, usual calibration techniques are not designed to take into account the variability between the different individuals. This is not a problem if the individual variability is negligible but it is an important issue if the individual variability is signifcant. The mixed-effects models provide a statistical framework to calibrate the parameters of a model taking into account the individual variability. The objective of this paper is to introduce the mixed-effects in material science. The ONERA Damage model (ODM) is considered, first with synthetic data, then with thirteen experimental strain-stress curves of a ceramic matrix composite material. The robustness of the mixed-effects approach regarding the variability and the number of specimen is investigated. Model choices such as the correlation between ODM parameters and other settings are discussed. The ability of mixed-effects models to characterize the material variability and to provide accurate estimates of the parameters associated to each specimen is illustrated.