Carnegie Mellon University

Rendering of a dislocation stress field

Calculating Behavior: CEE Student Builds Mathematical Models to Inform Material Design

Designing new materials is a complicated business, explains Chiqun Zhang. He would know—he’s spent most of the last five years studying material defects, modeling, and behavior at Carnegie Mellon, earning both a master’s degree and a PhD in the Civil & Environmental Engineering Department, as well as a second master’s degree in computer science.

For his PhD, Zhang worked closely with CEE Professor Amit Acharya, utilizing both his computing and his engineering knowledge to develop mathematical models that predict the influence of topological line defects in solid and liquid crystal on material behavior. While an ideal crystal has a perfect lattice throughout its structure, most crystal lattices actually have imperfections that cause stress fields in the materials. These stress fields then interact with other defects in the crystal structure and ultimately change important material properties like strength and ductility (the ability to be stretched without fracturing).

“Understanding stress fields and defect dynamics is especially significant in the material manufacturing industry,” explains Zhang. “For example, we want to create alloys for building cars and planes that will have high strength and high ductility, so that the alloy can be shaped without cracking. We also want to optimize liquid crystal to have a long lifetime and good optical properties for displays and biological systems.”

Determining how to best create and refine such materials, however, requires using models to predict the material’s structure and properties. Unfortunately, with many types of intricate crystalline defect microstructures in existence, researchers have not yet developed a complete theory or model for predicting material behavior under all specified conditions or stresses.

Working with Professor Acharya, Zhang developed theories and models that will help researchers to understand material behaviors specifically related to the reach and impact of disclination defects.

“During the past five years, my advisor and I have extended the generalized disclination theory and applied it to solve defect problems at various grain boundaries and phase boundaries,” says Zhang. “Our model as well as our simulations underscore the complementary importance of topology, geometry, and energetics in understanding defect mechanics.”

The generalized disclination theory solves the statics and dynamics of line defects involving distortion discontinuity and is critical for studying grain and phase boundaries. Because this theory is used to predict stress and deformation fields of material with these defects, it’s particularly valuable for understanding a material’s strength for manufacturing and use.

Having completed his PhD in September 2017, Zhang now works at Verdigris as a data scientist, applying machine-learning techniques and numerical analysis for designing smart buildings.

“My current work uses my knowledge from both my master’s degrees and my skills in mathematical modeling and numerical simulation that I developed during my PhD,” says Zhang, who adds, “CMU prepared me very well for my career. They equipped me with the ability to manage my time and workload and the ability to adapt to any challenges I might face in my future.”

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