An integrated sensitivity‐uncertainty quantification framework for stochastic phase‐field modeling of material damage

Materials accumulate energy around voids and defects under external loading, causing the formation of microcracks. With increasing or repeated loads, those microcracks eventually coalesce to form macrocracks, 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 fractured material and fatigue is treated as a continuous internal field variable to model the effects of microcracks arising from energy accumulation. We formulate a computational‐mathematical 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‐to‐global 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.