Honors Undergraduate Thesis

Ensuring Positive Definiteness in Linear Viscoelastic Material Functions

While working towards my Bachelor’s in Aerospace Engineering, I jumped at the opportunity to pursue an honors undergraduate thesis. I was grateful when Dr. Kwok agreed to be my thesis chair and suggested I push my undergraduate research, within the Structures and Material Design Lab, into my thesis.

My first venture into seriously researching material science began with the article “Interconversion of linearly viscoelastic material functions expressed as Prony series: a closure”, whose two interconversion algorithms were being used in the lab. Continuing along these avenues of research for my thesis, I worked to create a method to ensure we could apply our prony series to the two anisotropic algorithms. This method had to ensure prony series found through experimentation and computational fitting would have the positive-definiteness the algorithms required.

Indeed, I tried many complex and extraordinary methods, to no avail. From deciphering the errors within these methods I explored, extended, and developed my original understanding and affirmed my passion for my research. Finally, I found the simple method of finding the nearest semi-positive-definite matrix solved our problem. This method also allowed for prony series fitting to continue in the manner previously utilized, and attempted to correct any errors the data had accumulated. For this work, I designed a Python library, with a full set of functions to gather data, ensure needed properties, interconvert with either material function as the source, and a check to ensure the data converted properly. Later I added a MATLAB library with the same capabilities. I maintain these libraries for the Structures and Material Design Lab, and on GitHub, for any it would benefit.

The paper can be found under my publications section, and links to the libraries are provided below.

Python Library
MATLAB Library