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Published August 26, 2022 | Supplemental Material
Journal Article Open

Growth rules for irregular architected materials with programmable properties


Biomaterials display microstructures that are geometrically irregular and functionally efficient. Understanding the role of irregularity in determining material properties offers a new path to engineer materials with superior functionalities, such as imperfection insensitivity, enhanced impact absorption, and stress redirection. We uncover fundamental, probabilistic structure–property relationships using a growth-inspired program that evokes the formation of stochastic architectures in natural systems. This virtual growth program imposes a set of local rules on a limited number of basic elements. It generates materials that exhibit a large variation in functional properties starting from very limited initial resources, which echoes the diversity of biological systems. We identify basic rules to control mechanical properties by independently varying the microstructure's topology and geometry in a general, graph-based representation of irregular materials.

Additional Information

© 2022 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. https://www.sciencemag.org/about/science-licenses-journal-article-reuse This is an article distributed under the terms of the Science Journals Default License. This paper is dedicated to the memory of Prof. John H. Conway (1937–2020) for his "Game of Life," which inspired this research. We acknowledge M. Gumin for helpful discussions and generously sharing his 3D WaveFunctionCollapse demo codes. We also thank M. Deagen for creating online interactive plots that demonstrate the 3D database and E. Sanders for helping to plot the elastic surfaces. Funding: US National Science Foundation grant 1835735 (CSSI); Caltech Carver Mead New Adventures Fund; Caltech SURF program; and Peking University College of Engineering. Author contributions: Conceptualization: K.L. and C.D.; Methodology: K.L.; Investigation: K.L. and R.S.; Visualization: K.L.; Funding acquisition: C.D. and K.L.; Project administration: C.D.; Supervision: C.D.; Writing—original draft: K.L.; Writing—review and editing: K.L., C.D., and R.S. Data and materials availability: All data are available in the main text or the supplementary materials. The authors declare that they have no competing interests.

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August 22, 2023
October 20, 2023