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Abstract Theoretical models for polycrystalline grain growth are deterministic. However, although computer simulations based on these models reproduce average features and trends, they do not reliably predict experimental growth trajectories for individual grains. Disagreement between experiment and simulation has generally been attributed to shortcomings in the computational instantiation; however, even after several decades of improving the physical bases of computational models, a perfect match has not been achieved. In this study, we examine the sources of uncertainty in simulation and experiment during polycrystalline grain growth. In ensembles of nominally identical molecular dynamics simulations, growth trajectories of individual grains can vary significantly due to discrete events (topological transformations) that have cascading effects on the microstructural ensemble. The type and timing of these microstructural events are extraordinarily sensitive to atomic-scale processes. When we compare ensemble simulation results to experimental outcomes, we find that the ensemble simulation delineates a range of possible outcomes, and the experimental results fall within that range. The implication is that polycrystalline grain growth has a fundamental, aleatoric uncertainty that limits our ability to predict its outcomes. Simulation and experiment can never agree perfectly; however, simulations can predict the range of possible experimental outcomes. 

Abstract Twin boundaries play a central role in the functional behavior of martensitic materials; yet, the mechanisms governing the initiation of their motion remain poorly understood for twins lying along irrational crystallographic directions. Here, we present an atomistic investigation of the onset of motion of both rational and irrational twin interfaces in a two-dimensional model lattice with rectangular unit cells. Using quasistatic shear loading and full linear stability analysis, we show that the initiation of twin boundary motion is signaled by a nonlocal linear instability, marked by the vanishing of the lowest eigenvalue of the Hessian; the corresponding eigenmode predicts the atomic displacements that initiate motion. We find that irrational twin boundaries have significantly lower critical shear stress to initiate motion compared to rational twin boundaries. Furthermore, we find that they display unusual mechanisms to initiate motion such as the formation of microtwins in directions orthogonal to the overall twin boundary. Finally, we compare various local measures against the nonlocal stability analysis and find that the former do not capture that irrational twin boundaries initiate their motion at lower stresses compared to rational boundaries. 

Abstract This study uses high‐energy X‐ray diffraction microscopy of SrTiO₃to identify correlations between grain boundary (GB) area changes and the motion direction of neighboring GBs to investigate interfacial energy minimization mechanisms during grain growth. The local GB area changes were measured near triple lines (TLs) to isolate the effects of neighboring GBs. These area changes were then correlated to the migration direction and curvature of the neighboring GBs present at the TL, providing an alternative metric associated with lateral expansion for describing GB migration. Additionally, this study extracted GB dihedral angles, which reflect the relative GB energy, to test whether low energy GBs replace high energy GBs (i.e., GB replacement mechanism) and, thus, can be used to predict a GB's migration direction. The majority of GBs did not exhibit local area changes reflective of the GB replacement mechanism, and the dihedral angles were not reliable indicators of GB motion. However, the expansion and shrinkage of GBs moving away from their center of curvature was more often consistent with the grain boundary replacement mechanism. These results suggest that growth for certain GB configurations is governed by relative energy differences while others are governed by curvature. 

Abstract This study investigates computationally the impact of particle size disparity and cohesion on force chain formation in granular media. The granular media considered in this study are bi-disperse systems under uniaxial compression, consisting of spherical, frictionless particles that interact through a modified Hookean model. Force chains in granular media are characterized as networks of particles that meet specific criteria for particle stress and inter-particle forces. The computational setup decouples the effects of particle packing on force chain formations, ensuring an independent assessment of particle size distribution and cohesion on force chain formation. The decoupling is achieved by characterizing particle packing through the radial density function, which enables the identification of systems with both regular and irregular packing. The fraction of particles in the force chains network is used to quantify the presence of the force chains. The findings show that particle size disparity promotes force chain formation in granular media with nearly-regular packing (i.e., an almost-ordered system). However, as particle size disparities grow, it promotes irregular packing (i.e., a disordered systems), leading to fewer force chains carrying larger loads than in ordered systems. Further, it is observed that the increased cohesion in granular systems leads to fewer force chains irrespective of particle size or packing. 

The goal of this note is to present regularity results regarding problems of the type [Formula: see text] in [Formula: see text], [Formula: see text] on [Formula: see text] which depend only on [Formula: see text] and not on the monotone function [Formula: see text]. This uses nice techniques developed by H. Brezis and collaborators.