# Research

## Massively parallel continuum mechanics based computational materials science

In our group we aim to develop, implement, and test physically-based computational models for materials undergoing mechanical and thermal loading. Our primary focus is on phase-field type methods applied to applications such as microstructure evolution, solid rocket propellant burn, and fracture mechanics. Our code ("Alamo") is developed in-house and is designed with an eye towards scalability and massively parallel performance.

For more information about Alamo, check out the **Alamo main page**; for some of the technical details about the solvers, check out the **arXiv paper**. For some of the applications, see below.

## Grain boundary mobility

Microstructure evolution is a fundamental process in the manufacture and durability of crystalline materials. It facilitated by the motion of grain boundaries (GBs); however, GB migration is complex and highly dependent on crystallographic character, loading conditions, temperature, etc. We apply the phase field method in new ways to study boundary migration. Recent work shows that GB migration has a tendency to move via small steps ("disconnections"), confirming that disconnections can be thermodynamically optimal GB migration mediators.

For more see **our paper on phase field disconnections**.

**Nucleation, growth, and dissociation of "phase field disconnections"**

## Computational Fracture Mechanics

Fracture is a ubiquitous mechanism in the catastrophic failure of many kinds of materials ranging from energetic to structural. The mechanics of fracture constitute highly non-equilibrium, near-singular material behavior that is complex to model.

In our group we apply the phase field method to solving highly complex fracture mechanics problems, involving multiple materials, multiple interface types, and multiple loading conditions. This enables us to examine the fracture behavior of such systems as AP/HTPB energetic composites, Alumina-Nickel interfaces, and inter/intra grain boundary fracture.

Our unique use of block structured adaptive mesh refinement, using a strong-form elastic solver, enables these problems to be solved rapidly.

**Phase field fracture simulation (Alamo) of a crack partially deflecting, partially penetrating, and partially delaminating around a more rigid material.**

## Computational Bicrystallography

The coincident site lattice and, specifically, the `Σ value' of a grain boundary are a ubiquitous metric for experimental classification of grain boundaries. However, the mathematical nature of Σ - a pathological function taking values of either an integer or infinity - has been relatively unexplored. This work presents a framework for interpreting Σ as the inverse of a projection defined using the standard L2 inner product over continuous fields that represent lattices. `Pre-mollifiers' are used to introduce thermal regularization in the context of the inner product, and a closed-form analytic result is derived. For all nonzero values of the regularization parameters, the formulation is mathematically smooth and differentiable, providing a tool for computationally determining experimental deviation from measured low-Σ boundaries at finite temperatures. It is verified that accurate Σ values are recovered for sufficiently low Σ boundaries, and that the numerical result either converges towards an integer value or diverges to infinity.

**Cover of Acta Crystallographica section A**

## Analytical modeling of grain boundaries

Interfaces between grains (grain boundaries) are material defects that are responsible for a wide range of material behavior. At large scales, GB energy can often be safely ignored due to its relatively low energy in comparison to volumetric energy. However, volumetric energy scales as x^3 whereas interface energy scales as x^2--so at small enough scales, interface phenomena dominates. Model prediction for symmetric tilt grain boundary energy in FCC Cu (blue) and Au (green)

The lattice-matching interface energy model is a robust, general, efficient model of crystalline interfaces for use in analysis of micromechanical systems, optimal manufacturing of composites, and integration into multiscale computations. It is combined with the relaxation model to predict grain boundary morphology for complex interfaces with arbitrary geometric character.

**Analytic prediction of grain boundary energy (top) and the corresponding faceted morphology (bottom)**

## Atomistic Simulations

To validate multiscale models, it is frequently necessary to perform simulations that account for atomistic degrees of freedom. Molecular statics/dynamics provides a framework for estimating atomic-level behavior in response to external loading conditions. We use molecular dynamics to generate data for comparison with theoretical multiscale models, and perform analysis to determine the effect of interatomic potential on material properties.

OpenKIM: This project is in collaboration with the Open Knowledgebase of Interatomic Models (OpenKIM). OpenKIM is a cyberinfrastructure for improving the reliability of molecular and multiscale simulations of materials. It includes a repository of interatomic potentials that are exhaustively tested, tools to help select among existing potentials and develop new ones, and standard integration methods for using potentials in major simulation codes. Visit the OpenKIM Website.