arXiv subjects

Brandon Runnels

Publications and source records attributed to Brandon Runnels.

At least 19 recordsLinked to original sources

arXiv2026

Mechanics of incompatible asymmetric grain boundary migration

Grain boundary (GB) migration governs microstructure evolution and can mediate plastic deformation through sliding or shear coupling. Numerous experimental and numerical studies have reported a wide range of behaviors associated with boundary migration, such as defect emission or mode switching. Notably, recent studies have reported directionally asymmetric migration rates under symmetric loading, attributing this behavior to intrinsically asymmetric mobility; however, a mechanistic mesoscale explanation for this behavior remains lacking. In this work, we introduce a constitutive flow rule for grain-boundary eigendeformation within a multiphase-field framework, in which interfacial shear evolves in response to its mechanically conjugate driving force through the phase field Allen-Cahn equations. The formulation systematically employs regularized grain boundary shear kinematics informed by crystallography, and enables elastic compatibility to modulate boundary motion. Migration thresholds, residual back-stress, and apparent directional asymmetry appear naturally as emergent mechanical behavior. Simulations of symmetric and asymmetric tilt grain boundaries under mechanical, synthetic, and curvature-driven loading reveal persistent defect-like residuals following incompatible migration, transitions from planar motion to lamination at large inclinations, and even "ratcheting" behavior. These results provide a mechanically transparent explanation for behaviors such as effective mobility asymmetry and establish elastic compatibility as a constitutive mechanism in mesoscale models of boundary-mediated plasticity.

cond-mat.mtrl-sci↗

arXiv2025

Predicting void nucleation in microstructure with convolutional neural networks

Void nucleation in ductile materials subjected to high strain-rate loading remains a critical yet elusive phenomenon to understand. Traditional methods to understand void nucleation typically rely on experiments and molecular dynamics and do not capture the underlying factors leading to void nucleation. In this study, a convolutional neural network, specifically a U-Net enhanced with attention gates is developed, to predict void nucleation probability in pristine tantalum microstructures. The approach leverages a multi-channel input, incorporating four channels of grain orientations and an additional channel of grain boundary energy calculated via the lattice matching method. Void nucleation probability fields are determined from post-mortem micrographs and serve as ground truth, distinguishing void from no-void regions at the pixel level. Pixel-level class imbalance, commen in such images, is addressed by using Focal loss to guide the network's training to predict void nucleation sites more effectively. The model not only predicts void nucleation sites consistent with ground-truth but also reveals additional potential void nucleation sites, capturing the stochastic nature of void nucleation. This study shows that CNN-based models can predict void nucleation sites while considering combined interplay of factors such as grain boundary energy and grain orientation. In this way, machine learning can serve as a means to understand the underlying factors leading to void nucleation thereby contributing to a fundamental understanding of failure due to spallation in ductile materials.

cond-mat.mtrl-sci↗

arXiv2025

Inverse method for determining general molecular weight distribution from polymer rheology

Determination of polymer molecular weight distribution (MWD) from rheological measurements is desirable due to the ease and low cost of rheometry compared to other methods such as gel permeation chromatography. However, relating MWD to rheology requires the inversion of rheological models, for which there is no analytic solution. Prior approaches assume a functional form for the MWD (such as a lognormal or generalized exponential distribution), minimizing the error with respect to the functional form's degrees of freedom. While this is a powerful and robust technique for determining general polymer properties, such as average MWD or polydispersity, it requires former knowledge of the shape of the MWD. This work presents a generalized approach to solving the inverse problem directly, with no former knowledge of the MWD or assumptions regarding its functional form. To close the inverse problem and establish uniqueness, Lagrange multipliers constraints on the MWD are included. The method is applied with reptation-based models to a variety of polycarbonate, polyethylene and polystyrene polymers. For samples whose rheology are well-described by reptation, the predicted MWD is shown to match experimental measurements very well. For samples that are not well-described by reptation, the predicted MWD naturally differs from experiment. Nevertheless, the results still offer insight into how reptation-described polymers differ from their counterparts. This establishes the proposed inverse method as a viable practical tool for rheology-based characterization.

cond-mat.soft↗

arXiv2025

The structure and migration of twin boundaries in tetragonal $\beta$-Sn: an application of machine learning based interatomic potentials

Although atomistic simulations have contributed significantly to our understanding of twin boundary structure and migration in metals and alloys with hexagonal close packed (HCP) crystal structures, few direct atomistic studies of twinning have been conducted for other types of low symmetry materials, in large part due to a lack of reliable interatomic potentials. In this work, we examine twin boundary structure and migration in a tetragonal material, $\beta$-Sn, comparing high resolution Transmission Electron Microscopy (TEM) images of deformation twins in $\beta$-Sn to the results of direct atomistic simulations using multiple interatomic potentials. ML-based potentials developed in this work are found to give results consistent with our experimental data, revealing faceted twin boundary structures formed by the nucleation and motion of twinning disconnections. We use bicrystallographic methods in combination with atomistic simulations to analyze the structure, energy and shear coupled migration of observed twin facets in $\beta$-Sn. In analogy to Prismatic-Basal (PB/BP) interfaces in HCP metals, we discover low energy asymmetric Prismatic-A-plane (PA/AP) interfaces important to twin growth in $\beta$-Sn. A Moment Tensor Potential (MTP) and Rapid Artificial Neural Network (RANN) interatomic potential suitable for studying twinning and phase transformations in Sn are made publicly available as part of this work.

cond-mat.mtrl-sci↗

arXiv2025

Energetics of the nucleation and glide of disconnection modes in symmetric tilt grain boundaries

GBs evolve by the nucleation and glide of disconnections, which are dislocations with a step character. In this work, motivated by recent success in predicting GB properties such as the shear coupling factor and mobility from the intrinsic properties of disconnections, we develop a systematic method to calculate the energy barriers for the nucleation and glide of individual disconnection modes under arbitrary driving forces. This method combines tools from bicrystallography to enumerate disconnection modes and the NEB method to calculate their energetics, yielding minimum energy paths and atomistic mechanisms for the nucleation and glide of each disconnection mode. We apply the method to accurately predict shear coupling factors of [001] symmetric tilt grain boundaries in Cu. Particular attention is paid to the boundaries where the classical disconnection nucleation model produces incorrect nucleation barriers. We demonstrate that the method can accurately compute the energy barriers and predict the shear coupling factors for low temperature regime.

cond-mat.mtrl-sci↗

arXiv2025

The Alamo multiphysics solver for phase field simulations with strong-form mechanics and block structured adaptive mesh refinement

Alamo is a high-performance scientific code that uses block-structured adaptive mesh refinement to solve such problems as: the ignition and burn of solid rocket propellant, plasticity, damage and fracture in materials undergoing loading, and the interaction of compressible flow with eroding solid materials. Alamo is powered by AMReX, and provides a set of unique methods, models, and algorithms that enable it to solve solid-mechanics problems (coupled to other physical behavior such as fluid flow or thermal diffusion) using the power of block-structured adaptive mesh refinement.

physics.comp-ph↗

arXiv2025

A diffuse boundary method for phase boundaries in viscous compressible flow

Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that may exhibit topological transitions and high curvature. Such conditions can also lead to numerical instability. Diffuse boundary methods such as the phase field method are an attractive way to describe systems with complex boundaries, but coupling such methods to hydrodynamic flow solvers is nontrivial. This work presents a systematic approach for coupling flow to arbitrary implicitly-defined diffuse domains. It is demonstrated that all boundary conditions of interest can be expressed as suitable fluxes, noting that angular momentum flux is necessary in order to account for cases such as the no-slip condition. Moreover, it is shown that the diffuse boundary formulation converges exactly to the sharp interface solution, resulting in a well-defined error bound. The method is applied in a viscous compressible flow solver with block-structured adaptive mesh refinement, and the convergence properties are shown. Finally, the efficacy of the method is demonstrated by coupling to other classical flow problems (vortex shedding), problems in solidification (coupling to dendritic growth), and flow through eroding media (coupling to the Allen Cahn equation).

physics.flu-dyn↗

arXiv2024

Fundamental Microscopic Properties as Predictors of Large-Scale Quantities of Interest: Validation through Grain Boundary Energy Trends

Correlations between fundamental microscopic properties computable from first principles, which we term canonical properties, and complex large-scale quantities of interest (QoIs) provide an avenue to predictive materials discovery. We propose that such correlations can be efficiently discovered through simulations utilizing approximate interatomic potentials (IPs), which serve as an ensemble of "synthetic materials." As a proof of principle we build a regression model relating canonical properties to the symmetric tilt grain boundary (GB) energy curves in face-centered cubic crystals, characterized by the scaling factor in the universal lattice matching model of Runnels et al. (2016), which we take to be our QoI. Our analysis recovers known correlations of GB energy to other properties and discovers new ones. We also demonstrate, using available density functional theory (DFT) GB energy data, that the regression model constructed from IP data is consistent with DFT results, confirming the assumption that the IPs and DFT belong to same statistical pool and thereby validating the approach. Regression models constructed in this fashion can be used to predict large-scale QoIs based on first-principles data and provide a general method for training IPs for QoIs beyond the scope of first-principles calculations.

cond-mat.mtrl-sci↗

arXiv2024

Atomistic-informed phase field modeling of magnesium twin growth by disconnections

The nucleation and propagation of disconnections play an essential role during twin growth. Atomistic methods can reveal such small structural features on twin facets and model their motion, yet are limited by the simulation length and time scales. Alternatively, mesoscale modeling approaches (such as the phase field method) address these constraints of atomistic simulations and can maintain atomic-level accuracy when integrated with atomic-level information. In this work, a phase field model is used to simulate the disconnection-mediated twinning, informed by molecular dynamics (MD) simulations. This work considers the specific case of the growth of $\{10\bar{1}2\}$ twin in magnesium. MD simulations are first conducted to obtain the orientation-dependent interface mobility and motion threshold, and to simulate twin embryo growth and collect facet velocities, which can be used for calibrating the continuum model. The phase field disconnections model, based on the principle of minimum dissipation potential, provides the theoretical framework. This model incorporates a nonconvex grain boundary energy, elasticity and shear coupling, and simulates disconnections as a natural emergence under the elastic driving force. The phase field model is further optimized by including the anisotropic interface mobility and motion threshold suggested by MD simulations. Results agree with MD simulations of twin embryo growth in the aspects of final twin thickness, twin shape, and twin size, as well as the kinetic behavior of twin boundaries and twin tips. The simulated twin microstructure is also consistent with experimental observations, demonstrating the fidelity of the model.

cond-mat.mtrl-sci↗

arXiv2024

Finite-temperature grain boundary properties from quasistatic atomistics

Grain boundary (GB) properties greatly influence the mechanical, electrical, and thermal response of polycrystalline materials. Most computational studies of GB properties at finite temperatures use molecular dynamics (MD), which is computationally expensive, limited in the range of accessible timescales, and requires cumbersome techniques like thermodynamic integration to estimate free energies. This restricts the reasonable computation (without incurring excessive computational expense) of GB properties to regimes that are often unrealistic, such as zero temperature or extremely high strain rates. Consequently, there is a need for simulation methodology that avoids the timescale limitations of MD, while providing reliable estimates of GB properties. The Gaussian Phase-Packet (GPP) method is a temporal coarse-graining technique that can predict relaxed atomic structures at finite temperature in the quasistatic limit. This work applies GPP, combined with the quasiharmonic approximation for computing the free energy, to the problem of determining the free energy and shear coupling factor of grain boundaries in metals over a range of realistic temperatures. Validation is achieved by comparison to thermodynamic integration, which confirms that the presented approach captures relaxed-energy GB structures and shear coupling factors at finite temperature with a high degree of accuracy.

cond-mat.mtrl-sci↗

arXiv2023

Facet and energy predictions in grain boundaries: lattice matching and molecular dynamics

Many material properties can be traced back to properties of their grain boundaries. Grain boundary energy (GBE), as a result, is a key quantity of interest in the analysis and modeling of microstructure. A standard method for calculating grain boundary energy is molecular dynamics (MD); however, on-the-fly MD calculations are not tenable due to the extensive computational time required. Lattice matching (LM) is a reduced-order method for estimating GBE quickly; however, it has only been tested against a relatively limited set of data, and does not have a suitable means for assessing error. In this work, we use the recently published dataset of Homer et al. [1] to assess the performance of LM over the full range of GB space, and to equip LM with a metric for error estimation. LM is used to generate energy estimates, along with predictions of facet morphology, for each of the 7,304 boundaries in the Homer dataset. In keeping with prior work, it is observed that LM predictions of low energy boundaries matches well with MD results. Moreover, there is a good general agreement between LM and MD, and it is apparent that the error scales approximately linearly with the predicted energy value; this makes it possible to establish an empirical estimate on error for future LM calculations. An essential part of the LM method is the faceting relaxation, which corrects the expected energy by convexification across the compact space (S2) of boundary plane orientations. The original Homer dataset did not allow for faceting, but upon extended annealing, it was shown that facet patterns similar to those predicted by LM were emerging.

cond-mat.mtrl-sci↗

arXiv2023

Grain boundary network plasticity: reduced-order modeling of deformation-driven microstructure evolution

Microstructural evolution in structural materials is known to occur in response to mechanical loading and can often accommodate substantial plastic deformation through the coupled motion of grain boundaries (GBs). This can produce desirable behavior, such as increased ductility, or undesirable behavior such as mechanically-induced coarsening. In this work a novel, multiscale model is developed for capturing the combined effect of plasticity mediated by multiple GBs simultaneously. This model is referred to as "grain boundary network plasticity." The mathematical framework of graph theory is used to describe the microstructure connectedness, and the evolution of microstructure is represented as volume flow along the graph. By using the principle of minimum dissipation potential, which has previously been applied to grain boundary migration, a set of evolution equations are developed that transfer volume and eigendeformation along the graph edges in a physically consistent way. It is shown that higher-order geometric effects, such as the pinning effect of triple points, may be accounted for through the incorporation of a geometric hardening that causes geometry-induced GB stagnation. The result is a computationally efficient reduced order model that can be used to simulate the initial motion of grain boundaries in a polycrystal with parameters informed by atomistic simulations. The effectiveness of the model is demonstrated through comparison to multiple bicrystal atomistic simulations, as well as a select number of GB engineered and non-GB engineered data obtained from the literature. The effect of the network of shear-coupling grain boundaries is demonstrated through mechanical response tests and by examining the yield surfaces.

cond-mat.mes-hall↗

arXiv2022

Automated determination of grain boundary energy and potential-dependence using the OpenKIM framework

We present a systematic methodology, built within the Open Knowledgebase of Interatomic Models (OpenKIM) framework (https://openkim.org), for quantifying properties of grain boundaries (GBs) for arbitrary interatomic potentials (IPs), GB character, and lattice structure and species. The framework currently generates results for symmetric tilt GBs in cubic materials, but can be readily extended to other types of boundaries. In this paper, GB energy data are presented that were generated automatically for Al, Ni, Cu, Fe, and Mo with 225 IPs; the system is installed on openkim.org and will continue to generate results for all new IPs uploaded to OpenKIM. The results from the atomistic calculations are compared to the lattice matching model, which is a semi-analytic geometric model for approximating GB energy. It is determined that the energy predicted by all IPs (that are stable for the given boundary type) correlate closely with the energy from the model, up to a multiplicative factor. It thus is concluded that the qualitative form of the GB energy versus tilt angle is dominated more by geometry than the choice of IP, but that the IP can strongly affect the energy level. The spread in GB energy predictions across the ensemble of IPs in OpenKIM provides a measure of uncertainty for GB energy predictions by classical IPs.

cond-mat.mtrl-sci↗

arXiv2022

Robust, strong form mechanics on an adaptive structured grid: efficiently solving variable-geometry near-singular problems with diffuse interfaces

Many solid mechanics problems on complex geometries are conventionally solved using discrete boundary methods. However, such an approach can be cumbersome for problems involving evolving domain boundaries due to the need to track boundaries and constant remeshing. In this work, we employ a robust smooth boundary method (SBM) that represents complex geometry implicitly, in a larger and simpler computational domain, as the support of a smooth indicator function. We present the resulting equations for mechanical equilibrium, in which inhomogeneous boundary conditions are replaced by source terms. The resulting mechanical equilibrium problem is semidefinite, making it difficult to solve. In this work, we present a computational strategy for efficiently solving near-singular SBM elasticity problems. We use the block-structured adaptive mesh refinement (BSAMR) method for resolving evolving boundaries appropriately, coupled with a geometric multigrid solver for an efficient solution of mechanical equilibrium. We discuss some of the practical numerical strategies for implementing this method, notably including the importance of grid versus node-centered fields. We demonstrate the solver's accuracy and performance for three representative examples: a) plastic strain evolution around a void, b) crack nucleation and propagation in brittle materials, and c) structural topology optimization. In each case, we show that very good convergence of the solver is achieved, even with large near-singular areas, and that any convergence issues arise from other complexities, such as stress concentrations. We present this framework as a versatile tool for studying a wide variety of solid mechanics problems involving variable geometry.

math.NA↗

arXiv2022

Self-similar diffuse boundary method for phase boundary driven flow

Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such interactions include melting, sublimation, and deflagration, all of which exhibit bidirectional coupling, mass/heat transfer, and topological change of the solid-fluid interface. The diffuse interface method is a powerful technique that has been used to describe a wide range of solid-phase interface-driven phenomena. The implicit treatment of the interface eliminates the need for cumbersome interface tracking, and advances in adaptive mesh refinement have provided a way to sufficiently resolve diffuse interfaces without excessive computational cost. However, the general scale-invariant coupling of these techniques to flow solvers has been relatively unexplored. In this work, a robust method is presented for treating diffuse solid-fluid interfaces with arbitrary boundary conditions. Source terms defined over the diffuse region mimic boundary conditions at the solid-fluid interface, and it is demonstrated that the diffuse length scale has no adverse effects. To show the efficacy of the method, a one-dimensional implementation is introduced and tested for three types of boundaries: mass flux through the boundary, a moving boundary, and passive interaction of the boundary with an incident acoustic wave. These demonstrate expected behavior in all cases. Convergence analysis is also performed and compared against the sharp-interface solution, and linear convergence is observed. This method lays the groundwork for the extension to viscous flow, and the solution of problems involving time-varying mass-flux boundaries.

physics.flu-dyn↗

arXiv2022

Comparison of evolving interfaces, triple points, and quadruple points for discrete and diffuse interface methods

The evolution of interfaces is intrinsic to many physical processes ranging from cavitation in fluids to recrystallization in solids. Computational modeling of interface motion entails a number of challenges, many of which are related to the range of topological transitions that can occur over the course of the simulation. Microstructure evolution in a polycrystalline material that involves grain boundary motion is a particularly complex example due to the extreme variety, heterogeneity, and anisotropy of grain boundary properties. Accurately modeling this process is essential to determining processing-structure-property relationships in polycrystalline materials though. Simulations of microstructure evolution in such materials often use diffuse interface methods like the phase field method that are advantageous for their versatility and ease of handling complex geometries but can be prohibitively expensive due to the need for high interface resolution. Discrete interface methods require fewer grid points and can consequently exhibit better performance but have received comparatively little attention, perhaps due to the difficulties of maintaining the mesh and consistently implementing topological transitions on the grain boundary network. This work explicitly compares a recently-developed discrete interface method to a multiphase field method on several classical problems relating to microstructure evolution in polcrystalline materials: a shrinking spherical grain, the steady-state triple junction dihedral angle, and the steady-state quadruple point dihedral angle. In each case, the discrete method is found to meet or outperform the multiphase field method with respect to accuracy for comparable levels of refinement, demonstrating its potential efficacy as a numerical approach for microstructure evolution in polycrystalline materials.

cond-mat.mtrl-sci↗

arXiv2021

A taxonomy of grain boundary migration mechanisms via displacement texture characterization

Atomistic simulations provide the most detailed picture of grain boundary (GB) migration currently available. Nevertheless, extracting unit mechanisms from atomistic simulation data is difficult because of the zoo of competing, geometrically complex 3D atomic rearrangement processes. In this work, we introduce the displacement texture characterization framework for analyzing atomic rearrangement events during GB migration, combining ideas from slip vector analysis, bicrystallography and optimal transportation. Two types of decompositions of displacement data are described: the shear-shuffle and min-shuffle decomposition. The former is used to extract shuffling patterns from shear coupled migration trajectories and the latter is used to analyze temperature dependent shuffling mechanisms. As an application of the displacement texture framework, we characterize the GB geometry dependence of shuffling mechanisms for a crystallographically diverse set of mobile GBs in FCC Ni bicrystals. Two scientific contributions from this analysis include 1) an explanation of the boundary plane dependence of shuffling patterns via metastable GB geometry and 2) a taxonomy of multimodal constrained GB migration mechanisms which may include multiple competing shuffling patterns, period doubling effects, distinct sliding and shear coupling events, and GB self diffusion.

cond-mat.mtrl-sci↗

arXiv2021

Multiphase field modeling of grain boundary migration mediated by emergent disconnections

Knowledge about grain boundary migration is a prerequisite for understanding and ultimately modulating the properties of polycrystalline materials. Evidence from experiments and molecular dynamics (MD) simulations suggests that the formation and motion of disconnections is a mechanism for grain boundary migration. Here, grain boundary migration is modeled using a multiphase field model based on the principle of minimum dissipation potential with nonconvex boundary energy, along with a stochastic model for thermal nucleation of disconnection pairs. In this model, disconnections arise spontaneously in the presence of an elastic driving force, and that their motion mediates boundary migration. The effect is due to the fact that the formation of the disconnections pairs results in a stress concentration, causing the elastic driving force to exceed the threshold value and driving the propagation of the disconnection along the interface. The model is applied to study the propagation/annihilation of single disconnection pairs, the relaxation of a perturbed interface, and shear coupling at various temperatures. The results are consistent with the current understanding of disconnections, and capture the effect of thermal softening.

cond-mat.mtrl-sci↗