We develop a mathematical model for the sliding of a gel sheet adhered to a moving substrate. The sliding takes place by the motion of detached region between the gel sheet and the substrates, i.e. the propagation of a Schallamach wave. Efficient numerical methods are developed to solve the problem. Numerical examples illustrate that the model can describe the Schallamach wave and are consistent with the existing experiments qualitatively.
|Original language||English (US)|
|Journal||Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|State||Published - Sep 1 2020|
Bibliographical noteFunding Information:
Data accessibility. Data available from: http://doi.org/10.5281/zenodo.3895746 . Authors’ contributions. X.X. collaborated in the model, analysis and performed the numerical simulations. M.C.C. collaborated in the model, and jointly with D.H., developed the asymptotic analysis. D.H. collaborated in the model, and jointly with M.C.C. developed the asymptotic analysis. M.D. provided the background of the problem and the experimental information. All authors drafted or revised the paper, approve the final version and agree to be held accountable for all aspects of the work. Competing interests. We declare we have no competing interest. Funding. X.X. acknowledges the financial support by the National Key R&D Program of China under grant nos. 2018YFB0704304 and 2018YFB0704300 and the NSFC grant no. 11971469. M.C.C. acknowledges the National Science Foundation grant no. DMS-1616866, and also the outstanding hospitality of Beihang University. M.D. acknowledges the High-End Foreign Experts Project by Ministry of Science and Technology 2019 under grant no. G20190001580. D.H. acknowledges the School of Mathematics of the University of Minnesota for the warm hospitality, as well as the Chilean Ministry of Science & Technology for funding his research through FONDECYT projects 1150038 and 1190018.
© 2020 The Author(s).
- Schallamach wave
- calculus of variations
- minimum dissipation