Our research interests include a wide variety of current challenges in the field of mechanics of materials and multiscale modeling.

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.

Grain Boundary Energy

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 covariance 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.

Runnels et al, "An analytical model of interfacial energy based on a lattice-matching interatomic energy" JMPS 2016

Microstructural Evolution

While materials tend to behave isotropically and uniformly on the macroscopic scale, they exhibit significant anisotropy on the microscopic scale due to microstructural heterogeneity. The evolution of microstructure can significantly impact bulk material behavior, and is coupled with the mechanical and thermodynamic state of the material.

Grain boundary motion induced by tensile loading (phase field method)
Anisotropic stresses in a polycrystaline sample (finite element method)

We use various techniques to computationally model the evolution of microstructure in materials. Continuum-type simulations are given multifunctionality by exchanging information between the macroscopic stress state and atomistic-based material point calculations.

Interface Morphology

Interfaces demonstrate a wide range of behavior, and can demonstrate exceedingly complex morphologies. While some interfaces are hopelessly disordered, many demonstrate highly ordered faceted structure that is conducive to analysis. Because morphology is linked to many other phenomena such as grain boundary sliding, twinning, and stability, it is of interest to understand and model this behavior.

Visualization of optimal faceting configuration for an asymmetric tilt grain boundary

The relaxation method used with the covariance interface energy model is able to predictively determine the morphology of interfaces with arbitrary character, and to compute the relaxed energy. The results are used to understand grain boundary mechanics, to integrate into multiscale simulations, and to predict optimal manufacturing techniques for composites.

Runnels et al, "A relaxation method for the energy and morphology of grain boundaries and interfaces" JMPS 2015

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.

Molecular dynamics simulation of a [111] symmetric tilt grain boundary (STGB) using LAMMPS

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.

GPU-Accelerated Multiscale Modeling

Finite kinematics computation of Von Mises stress around a crack in a Neo-Hookean body under tension.
Two challenges in the computational mechanics field are (i) adapting high performance simulations to utilize the heterogeneous, GPU-based architectures of modern supercomputers and (ii) bridging scales by creating multiscale material models. These goals are complementary: the computationally expensive (but highly local) multiscale material point computations are ideal for GPUs, while the global solution can be distributed across distributed memory nodes. Current goals are to
  • Improve methods for computational crystal plasticity
  • Implement plasticity with phase transformation and twinning models
  • Integrate interface energy with continuum-based multiscale polycrystalline simulations.

Other Interests / Applications / Ongoing Projects

  • Additive manufacturing
  • Large-deformation continuum mechanics and mechanics of soft matter and membranes
  • Rolling contact fatigue for predicting failure on railroad wheels

Relevant Links

Crystallography and defects