The origin of compression influences geometric instabilities in bilayers

Andres, S., Steinmann, P. and Budday, S. (2018) The origin of compression influences geometric instabilities in bilayers. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 474(2217), 20180267. (doi:10.1098/rspa.2018.0267)

Andres, S., Steinmann, P. and Budday, S. (2018) The origin of compression influences geometric instabilities in bilayers. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 474(2217), 20180267. (doi:10.1098/rspa.2018.0267)

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Abstract

Geometric instabilities in bilayered structures control the surface morphology in a wide range of biological and technical systems. Depending on the application, different mechanisms induce compressive stresses in the bilayer. However, the impact of the chosen origin of compression on the critical conditions, post-buckling evolution and higher-order pattern selection remains insufficiently understood. Here, we conduct a numerical study on a finite-element set-up and systematically vary well-known factors contributing to pattern selection under the four main origins of compression: film growth, substrate shrinkage and whole-domain compression with and without pre-stretch. We find that the origin of compression determines the substrate stretch state at the primary instability point and thus significantly affects the critical buckling conditions. Similarly, it leads to different post-buckling evolutions and secondary instability patterns when the load further increases. Our results emphasize that future phase diagrams of geometric instabilities should incorporate not only the film thickness but also the origin of compression. Thoroughly understanding the influence of the origin of compression on geometric instabilities is crucial to solving real-life problems such as the engineering of smart surfaces or the diagnosis of neuronal disorders, which typically involve temporally or spatially combined origins of compression.

Item Type:Articles
Additional Information:This study was kindly supported by the German Research Foundation (grant no. STE 544/50) and by the Cluster of Excellence Engineering of Advanced Materials (EAM) to P.S. and S.B. P.S. acknowledges a Wolfson Award from the Royal Society.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Steinmann, Professor Paul
Authors: Andres, S., Steinmann, P., and Budday, S.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences
Publisher:The Royal Society
ISSN:1364-5021
ISSN (Online):1471-2946
Published Online:19 September 2018
Copyright Holders:Copyright © 2018 The Authors
First Published:First published in Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences 474(2217): 20180267
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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