Research

Solid composite propellants (SCPs) have been a staple of propulsion for decades. In our group we develop methods for simulating the deflagration (burn) of SCPs at multiple scales, allowing for optimization and design of next generation motors.

For more information, check out the relevant articles in the publication list.

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 JCP paper. For some of the applications, see below

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 this paper or this paper on phase field emergent disconnections.

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. For information, check out our CMAME paper on phase field fracture.

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.

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.