LAUSR

Correspondence *Mohsen Zayernouri, Department of Computational Mathematics, Science, and Engineering, Michigan State University, 428 S Shaw Ln, East Lansing, MI, 48824. Email: [email protected] Summary Materials accumulate energy around voids and defects under external loading, causing the formation of micro-cracks. With increasing or repeated loads, those micro-cracks eventually coalesce to form macro-cracks, which in a brittle material can cause catastrophic failure without apparent permanent deformation. At the continuum level, a stochastic phase-field model is employed to simulate failure through introducing damage and fatigue variables. The damage phase-field is introduced as a continuous dynamical variable representing the volumetric portion of fracturedmaterial and fatigue is treated as a continuous internal field variable to model the effects of micro-cracks arising from energy accumulation. We formulate a computationalmathematical framework for quantifying the corresponding model uncertainties and sensitivities in order to unfold and mitigate the salient sources of unpredictability in the model, hence, leading to new possible modeling paradigms. Considering an isothermal isotropic linear elastic material with viscous dissipation under the hypothesis of small deformations, we employed Monte Carlo and Probabilistic Collocation methods to perform the forward uncertainty propagation, in addition to local-toglobal sensitivity analysis. We demonstrate that the model parameters associated with free-energy potentials contribute significantly more to the total model output uncertainties, motivating further investigations for obtaining more predictable model forms, representing the damage diffusion.