A tutorial on Bayesian inference to identify material parameters in solid mechanics

peer reviewedThe aim of this contribution is to explain in a straightforward manner how Bayesian inference can be used to identify material parameters of material models for solids. Bayesian approaches have already been used for this purpose, but most of the literature is not necessarily easy to understand for those new to the field. The reason for this is that most literature focuses either on complex statistical and machine learning concepts and/or on relatively complex mechanical models. In order to introduce the approach as gently as possible, we only focus on stress-strain measurements coming from uniaxial tensile tests and we only treat elastic and elastoplastic material models. Furthermore, the stress-strain measurements are created artificially in order to allow a one-to-one comparison between the true parameter values and the identified parameter distributions.Hussein Rappel, Lars A.A. Beex and St ephane P.A. Bordas would like to acknowledge the nancial support from the University of Luxembourg. St ephane P.A. Bordas also thanks the European Research Council Starting Independent Research Grant (ERC Stg grant agreement No. 279578) entitled "Towards real time multiscale simulation of cutting in nonlinear materials with applications to surgical simulation and computer guided surgery". Jack S. Hale is supported by the National Research Fund, Luxembourg, and cofunded under the Marie Curie Actions of the European Commission (FP7-COFUND Grant No. 6693582)