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Crumpled Sheets

In the fall of 2024, I studied the invariant steady-state distribution of creases along a folded, one-dimensional interval of paper for upcoming generalization to higher-dimensional, physical folded sheets as computational surrogates for crumpled materials. 

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Recently, there has been enormous growth in the ability of scientists in many fields to collect data. While this is promising, it has given scientists a new challenge to tackle: how might we extract scientific insight from massive datasets? Machine learning (ML) is one possible tool for data analysis. It has proven useful for automating everyday tasks, such as image classification, but it is less clear how to analyze the results of an ML model to advance scientific understanding.
I plan to improve this through the lens of crumple theory. My research will build upon the previous results of my research group, the Rycroft Group at the University of Wisconsin-Madison, and is an ideal test case for studying new methods in data-driven science and modeling.

Crumpling is a familiar phenomenon, but it is underpinned by complex physical processes that are poorly understood. When a sheet is crumpled, a disordered network of creases is formed. A previous study by Hoffmann et al. [1] used experimental data of crumpled Mylar sheets as inputs into an ML model to predict these crease structures. A simple computational surrogate, flat-folded sheets, augmented with the experimental data, was essential for making good predictions. 
Networks of creases from unexplored sheet geometries and fold procedures beg for such elegant modeling. I aim to create new computational surrogates and couple them with ML regimes to predict more holistic crumpling behavior.
The study of crumpling is a relevant problem requiring advanced computational methodology. Successful surrogates for crumpling require an understanding of the limiting behavior after many folds, which involves large and highly complex synthetic datasets. Experimental data can be even more convoluted. The techniques required to analyze these data thus have the potential to strengthen connections between scientific understanding of data-rich, disordered systems and high-performance computing on a broad scale. Further, these studies will allow experimentalists and theoretic scientists to better exploit crumpling in technological applications. The conclusions of this research are intended to apply to other mechanical systems that feature damage accumulation under repeated loading.

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[1] J. Hoffmann, Y. Bar-Sinai, L. M. Lee, J. Andrejevic, S. Mishra, S. M. Rubinstein, C. H. Rycroft, Machine learning in a data-limited regime: Augmenting experiments with synthetic data uncovers order in crumpled sheets (2019), Science Advances. 

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Updates coming soon, along with nice graphics.

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