Data-driven multi-scale modeling, analysis and simulation of material failure

Material failure processes are inherently stochastic and anomalous, occurring across a wide span of length and time scales, from dislocation motion at the micro-scale, to formation of micro-cracks, up to crack propagation and aging mechanisms at the macro-scale and cascading failure at the system-level. Anomalies such as intermittent signals in Acoustic Energy experiments, power-law distribution of the energy spectrum, crackling noise, dislocation avalanches, among other indicators, occur even in standard, ordered, crystalline materials. Modeling and simulation of failure must take into account parametric and model-form uncertainties that propagate across the scales, when seemingly unimportant material properties or loading conditions could cause catastrophic failure at the component level. The pursuit of a unified framework for quantitative and qualitative failure prediction that can bridge the multiple scales while still incorporating the material's underlying stochastic processes is still a challenge, which requires a new modeling paradigm that incorporates such features with both robustness and simplicity.In this work, we propose a data-driven methodology for multi-scale, statistically consistent modeling of anomalous failure processes. At the micro-scale, the goal is to study the dynamics of dislocations, which play a vital role in plasticity and crack nucleation mechanisms, and shows anomalous features across different time and length-scales. We start by investigating the dislocation mobility properties at the nano-scale and propose a surrogate model for dislocation motion based on a Kinetic Monte Carlo method, where the dislocation motion is emulated as a random-walk on a network following a Poisson process. The surrogate learns the rates of the corresponding Poisson process directly from high-fidelity, Molecular Dynamics (MD) simulations. The surrogate is capable of efficiently obtaining uncertainty measures for the mobility parameter, which can be then propagated to more complex simulations in upper scales. At the meso-scale, the collective behavior of dislocation dynamics leads to avalanche, strain bursts, intermittent energy spikes, and nonlocal interactions. We develop a probabilistic model for dislocation motion constructed directly from trajectory data from Discrete Dislocation Dynamics (DDD). We obtain the corresponding Probability Density Function for the dislocation position, and propose a nonlocal transport model for the PDF. We use a bi-level Machine Learning framework to learn the parameters of the nonlocal operator and the coefficients of the PDF evolution equation, facilitating a continuum representation of the anomalous phenomena.At the macro-scale, parametric material uncertainties substantially affect the predictability of failure at the component level. We develop an Uncertainty Quantification (UQ) and Sensitivity Analysis (SA) framework for propagation of parametric uncertainties in a stochastic phase-field model of damage and fatigue, and we use the Probabilistic Collocation Method (PCM) as a building block. A Global SA indicates the most influential parameters in solution uncertainty and shows that damage initiation is sensitive to parameters associated with classical free-energy potential definitions, providing another motivation to incorporate the heavy-tail processes as observed in the meso-scale. We extend the framework and develop a Machine Learning (ML) framework for failure prediction phase-field models for brittle materials. We combine a classification algorithm with a pattern recognition scheme using virtual nodes from the phase-field damage model to generate patterns of material softening at each time-step. The framework identifies the presence and location of cracks and is robust even under noisy data, whether from model, parametric, or experimental uncertainties.