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Mathematical Problems in Thin Elastic Sheets: Scaling Limits, Packing, Crumpling and Singularities

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Vector-Valued Partial Differential Equations and Applications

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2179))

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Abstract

Thin elastic objects have fascinated mathematicians and engineers for centuries and more recently have also become an object of intense study in theoretical physics, biology and material design. While there have been a number of mathematical theories for thin elastic objects for a long time, a new rigorous variational approach has only emerged more recently. In these lectures I will review some of the variational tools which have emerged and discuss a number of open and challenging problems.

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Acknowledgements

The work reported here would not have been possible without the support and inspiration of many colleagues and friends over a long period of time, in particular S. Conti, G. Friesecke, R.D. James, R.V. Kohn and H. Olbermann. I thank J. M. Ball, P. Marcellini and E. Mascolo for their invitation to prepare these lecture notes and for providing such a delightful and stimulating atmosphere at the C.I.M.E. summer school at Cetraro. I also thank H. Olbermann and R.V. Kohn for a careful reading of the notes and their very helpful suggestions for improvements. In particular R.V. Kohn suggested the structuring into different classes of problems described at the end of Sect. 1.1. Of course responsibility for all remaining errors, omissions and inadequacies rests solely with me.

My work has been supported by the DFG through the CRC 1060 ‘The mathematics of emergent effects’ and the excellence cluster EXC 59 ‘Mathematics: foundations, models, applications’.

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  1. Hausdorff Center for Mathematics & Department of Applied Mathematics, University of Bonn, Bonn, Germany

    Stefan Müller

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Correspondence to Stefan Müller .

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  1. Mathematical Institute, University of Oxford , Oxford, United Kingdom

    John Ball

  2. Dipartimento di Matematica, Università di Firenze, Firenze, Italy

    Paolo Marcellini

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Müller, S. (2017). Mathematical Problems in Thin Elastic Sheets: Scaling Limits, Packing, Crumpling and Singularities. In: Ball, J., Marcellini, P. (eds) Vector-Valued Partial Differential Equations and Applications. Lecture Notes in Mathematics(), vol 2179. Springer, Cham. https://doi.org/10.1007/978-3-319-54514-1_3

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