Introduction
Recently mechanics society have huge interest in the wrinkles of nano and microstructures, especially wrinkles of thin stiff films on soft substrate. Graphene wrinkles on PDMS substrate was studied by using finite element method (FEM) and period doubling bifurcations of wrinkles was observed [1]. The Abaqus python scripts are posted, which were used to make the wrinkles so that others who are interested in it may have benefit.
Script files
If you run the following python scripts with abaqus cae, then you can simulate finite element method, Then run the m-file with MATLAB and get the bifurcation graph (subfigure (b) below).1.makeImperfection.py
This script makes imperfection to trigger wrinkle. Note that at each run with new parameters, you should optimize stabilization manually since constant stabilization is used.
2.expandCompress.py
This script expand (pre-stretch) the substrate, attach the film, and then compress the substrate.
3.writeOutputs.py
This script write outputs (heights of wrinkle valleys) from output database file (.odb).
4.bifurcationGraph.m
This Matlab script draws bifurcation graph. Note that you should change the folder path in the file to the folders where you put the files.
Note that my scripts may have errors: I did not major mechanics but physics, and I am a novice to FEM simulation. If you use the scripts in your research, please cite my work [1].
Results
Briefly, finite element method was used. PDMS was modeled as an Ogden model. The details of the modeling methods are in the literature [1]. The shapes of the wrinkles are shown below.
References
- Jong Hyun Jung, Jaehyun Bae, Myoung-Woon Moon, Kyung-Suk Kim, and Jisoon Ihm, “Numerical Study on Sequential Period-doubling Bifurcations of Graphene Wrinkles on a Soft Substrate,” Solid State Commun. 222 (2015): 14–17, http://dx.doi.org/10.1016/j.ssc.2015.08.020.
Highlights
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- Graphene wrinkles on a soft substrate were studied using finite element methods.
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- Sequential period-doubling bifurcations of wrinkles were obtained.
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- A delicate energy balance between graphene and substrate was found.
Abstract
A compressed stiff film on a soft substrate may exhibit wrinkles and, under increased compressive strain, post-buckling instabilities as well. We numerically analyze wrinkling behaviors of graphene attached on a polydimethylsiloxane (PDMS) substrate under lateral compression. The finite element method is used to simulate the equilibrium shape of the wrinkles as a function of compressive strain. Two-dimensional stretching and bending properties of graphene are obtained by density functional theory analysis, which are then converted to equivalent elastic properties of a continuum film with finite effective thickness. The PDMS is described using an Ogden or a neo-Hookean material model. Wrinkles first appear at extremely small strain. As the lateral compression increases, due to the nonlinear elasticity of the PDMS, sequential period-doubling bifurcations of the wrinkle mode are activated until the bifurcation stops and the film folds. We show that the bifurcations are consequences of a delicate balance between the deformations of the film and the substrate to minimize the total energy.
Keywords
- A. Graphene;
- C. Wrinkle;
- D. Bifurcation;
- D. Period-doubling
