Stochastic Models of Uncertainties in Computational Mechanics

We present an overview concerning the main concepts, formulations and advances, including new results, for the stochastic modeling of uncertainties and random fields in computational mechanics. In a first part, the parametric probabilistic approach, the nonparametric probabilistic approach and the generalized probabilistic approach of uncertainties are presented in the context of linear and nonlinear structural dynamics and in structural acoustics and vibration, including not only the construction of prior probability models but also the identification of posterior probability models. In a second part, a set of recent results is presented and is devoted to the construction of prior probability models and the identification of posterior probability models with an application to the mesoscale modeling of heterogeneous elastic microstructures