Category theory based solution for the building block replacement problem in materials design
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Buehler_Category theory.pdf
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8.16 MB
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Author(s)
Giesa, Tristan
Spivak, David I.
Buehler, Markus J.
Date Issued
June 2012
Journal
Advanced Engineering Materials
Publisher
Wiley Blackwell
Citation
Giesa, Tristan, David I. Spivak, and Markus J. Buehler. “Category Theory Based Solution for the Building Block Replacement Problem in Materials Design.” Advanced Engineering Materials 14.9 (2012): 810–817.
Version
Author's final manuscript
Abstract
An important objective in materials design is to develop a systematic methodology for replacing unavailable or expensive material building blocks by simpler and abundant ones, while maintaining or improving the functionality of the material. The mathematical field of category theory provides a formal specification language which lies at the heart of such a methodology. In this paper, we apply material ologs, category-theoretic descriptions of hierarchical materials, to rigorously define a process by which material building blocks can be replaced by others while maintaining large-scale properties, to the extent possible. We demonstrate the implementation of this approach by using algebraic techniques to predict concrete conditions needed for building block replacement. As an example, we specify structure–function relationships in two systems: a laminated composite and a structure–function analogue, a fruit salad. In both systems we illustrate how ologs provide us with a mathematical tool that allows us to replace one building block with others to achieve approximately the same functionality, and how to use them to model and design seemingly distinct physical systems with a consistent mathematical framework.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1002/adem.201200109
