Stochastic Upscaling via Linear Bayesian Updating

In this work we present an upscaling technique for multi-scale computations based on a stochastic model calibration technique. We consider a coarse scale continuum material model described in the framework of generalised standard materials. The model parameters are considered uncertain in this approach, and are approximated using random variables. The update or calibration of these random variables is performed in a Bayesian framework where the information from a deterministic fine scale model computation is used as observation. The proposed approach is independent w.r.t. the choice of models on coarse and fine scales. Simple numerical examples are shown to demonstrate the ability of the proposed approach to calibrate coarse-scale elastic and inelastic material parameters.