Uncertainty quantification for for strain softening models of brittle media.

We present an approach for assessing the impact of epistemic uncertainty arising in damage theory models brittle fracture. The incomplete information about the distribution of the yield stress in the material is modeled by a random damage field. Parameters of this random field are often inferred from experimental data. We focus on estimating the impact of the data induced uncertainty on selected quantities of interest and develop bounds on errors for those quantities of interest. The presented method is demonstrated computationally in the expanding ring test problem.