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Stability and post-bifurcation of film-substrate systems

Akerson, Andrew and Elliott, Ryan S. (2022) Stability and post-bifurcation of film-substrate systems. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 478 (2264). Art. No. 0181. ISSN 1364-5021. doi:10.1098/rspa.2022.0181.

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Morphological instabilities in soft solids with free surfaces lead to an array of deformation modes including wrinkling, creasing, folding and ridge localization. While homogeneous systems tend to form creases, stiff films over soft substrates usually exhibit surface waves. Here, we look to analytically investigate this transition through the effects of film stiffness and finite thickness on the post-bifurcation stability of these surface waves. By considering both the film and substrate as compressible Neo-Hookean solids, we apply bifurcation theory and Lyaponov–Schmidt–Koiter asymptotics to produce a phase diagram of the surface wave stability over the parameter space. While earlier works have studied the effect of film-to-substrate stiffness ratios for thin films on deep substrates in the incompressible setting, we consider the additional effects of both finite film thickness and Poisson ratio. To investigate the further evolution of these surface waves, we turn to computational methods through finite-element simulations with bifurcation branch-following techniques. We see that as the unstable surface waves evolve, they eventually lead to the beginnings of crease formation. Thus, when the surface waves are unstable, we would expect snap-back or snap-through behaviour leading to creases.

Item Type:Article
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URLURL TypeDescription
Akerson, Andrew0000-0002-4382-1226
Elliott, Ryan S.0000-0003-4988-8306
Additional Information:© 2022 The Author(s). Published by the Royal Society. Manuscript received 14/03/2022. Manuscript accepted 18/07/2022. Published online 10/08/2022. Published in print 31/08/2022. R.S.E. would like to acknowledge support from the École Polytechnique and its Laboratore de Mécanique des Solides (LMS). The authors acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources that contributed to the research results reported within this work. The work of R.S.E. was partially supported by the U.S. NSF grant no. CMMI-1462826. Authors' contributions. A.A.: data curation, formal analysis, investigation, methodology, software, validation, visualization, writing—original draft, writing—review and editing; R.S.E.: conceptualization, formal analysis, methodology, project administration, supervision, validation, writing—review and editing. All authors gave final approval for publication and agreed to be held accountable for the work performed therein. We declare we have no competing interests. Data accessibility. All code and data associated with this work is available in the ESM file The data are provided in the electronic supplementary material [28].
Funding AgencyGrant Number
École PolytechniqueUNSPECIFIED
Issue or Number:2264
Record Number:CaltechAUTHORS:20220810-402989000
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Official Citation:Akerson Andrew and Elliott Ryan S. 2022. Stability and post-bifurcation of film-substrate systems. Proc. R. Soc. A. 4782022018120220181;
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:116230
Deposited By: George Porter
Deposited On:11 Aug 2022 17:54
Last Modified:11 Aug 2022 17:55

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