Statistical Modeling the Process of Porosity-Based Ductile Damage*

Deterministic forecast utilizing continuum-based physical damage models generally lack in representing the statistics of structural evolution during material deformation and damage field forming conditions. A macro-scale damage model, which accounts for elastic compressibility, material deformation rate-dependence and micro-inertial effects, will be presented. An elasto-viscoplastic single-crystal model will be presented which accounts for the motion asymmetry of screw dislocations in Ta. Results of polycrystal calculations using synthetic microstructure models built upon the specific Ta material used for this study will be presented. Non-Gaussian distributions of micro-scale response variables are consistently observed. A statistical reduced-order modeling framework is presented to provide a probabilistic forecast of the statistical stress conditions initiating ductile damage with uncertainty quantification. A simple causality-based sparse model identification algorithm, including essential physical constraints, is utilized to discover the governing equations of these statistical moments. The probability density function (PDF) of material state variables reconstructed from the solution based on the statistical moment equations serves as an approximation to the original PDF. Information measurement is utilized to understand the above approximation, assess the strength of the non-Gaussianity, and quantify the probabilistic forecast skill of extreme events.