Geodesic
Modeling and simulation of thin sheet folding
Sören Bartels1 orcid ; Andrea Bonito2 orcid ; Peter Hornung3
1Albert-Ludwigs-Universität Freiburg, Freiburg im Breisgau, Germany
2Texas A&M University, College Station, USA
3Technische Universität Dresden, Germany
Interfaces and free boundaries, Tome 24 (2022) no. 4, pp. 459-485

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DOI

The article addresses the mathematical modeling of the folding of a thin elastic sheet along a prescribed curved arc. A rigorous model reduction from a general hyperelastic material description is carried out under appropriate scaling conditions on the energy and the geometric properties of the folding arc in dependence on the small sheet thickness. The resulting two-dimensional model is a piecewise nonlinear Kirchhoff plate bending model with a continuity condition at the folding arc. A discontinuous Galerkin method and an iterative scheme are devised for the accurate numerical approximation of large deformations.
DOI : 10.4171/ifb/478
Classification : 74-XX, 65-XX
Mots-clés : Nonlinear bending, folding, interface, model reduction, numerical method

Sören Bartels  1   ; Andrea Bonito  2   ; Peter Hornung  3

1 Albert-Ludwigs-Universität Freiburg, Freiburg im Breisgau, Germany
2 Texas A&M University, College Station, USA
3 Technische Universität Dresden, Germany 
Sören Bartels; Andrea Bonito; Peter Hornung. Modeling and simulation of thin sheet folding. Interfaces and free boundaries, Tome 24 (2022) no. 4, pp. 459-485. doi: 10.4171/ifb/478
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     title = {Modeling and simulation of thin sheet folding},
     journal = {Interfaces and free boundaries},
     pages = {459--485},
     year = {2022},
     volume = {24},
     number = {4},
     doi = {10.4171/ifb/478},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/478/}
}
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