# Modeling and simulation of thin sheet folding

@article{Bartels2021ModelingAS, title={Modeling and simulation of thin sheet folding}, author={S{\"o}ren Bartels and Andrea Bonito and Peter Hornung}, journal={ArXiv}, year={2021}, volume={abs/2108.00937} }

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… Expand

#### References

SHOWING 1-10 OF 31 REFERENCES

Bilayer Plates: Model Reduction, $\Gamma$-Convergent Finite Element Approximation and Discrete Gradient Flow

- Mathematics
- 2015

The bending of bilayer plates is a mechanism which allows for large deformations via small externally induced lattice mismatches of the underlying materials. Its mathematical modeling, discussed… Expand

A Theorem on Geometric Rigidity and the Derivation of Nonlinear Plate Theory from Three-Dimensional Elasticity

- Physics, Mathematics
- 2002

The energy functional of nonlinear plate theory is a curvature functional for surfaces rst proposed on physical grounds by G. Kirchhoff in 1850. We show that it arises as a 0-limit of… Expand

Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence

- Mathematics, Physics
- 2002

Abstract We show that the nonlinear bending theory of shells arises as a Γ -limit of three-dimensional nonlinear elasticity. To cite this article: G. Friesecke et al., C. R. Acad. Sci. Paris, Ser. I… Expand

Plate theory for stressed heterogeneous multilayers of finite bending energy

- Mathematics
- 2007

Abstract We derive a plate theory for (possibly slightly stressed) heterogeneous multilayers in the regime of finite bending energies from three-dimensional elasticity theory by means of… Expand

Approximation of Large Bending Isometries with Discrete Kirchhoff Triangles

- Mathematics, Computer Science
- SIAM J. Numer. Anal.
- 2013

A simple numerical method based on a discrete Kirchhoff triangle to deal with second order derivatives and convergence of discrete solutions to minimizers of the continuous formulation of large bending isometries is devised and analyzed. Expand

LDG approximation of large deformations of prestrained plates

- Mathematics, Computer Science
- Journal of Computational Physics
- 2022

A reduced model for large deformations of prestrained plates consists of minimizing a second order bending energy subject to a nonconvex metric constraint and a local discontinuous Galerkin (LDG) finite element approach that hinges on the notion of reconstructed Hessian is proposed. Expand

On the derivation of homogenized bending plate model

- Mathematics, Physics
- 2012

We derive, via simultaneous homogenization and dimension reduction, the $$\Gamma $$Γ-limit for thin elastic plates of thickness $$h$$h whose energy density oscillates on a scale $$\varepsilon… Expand

Folded developables

- Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1982

A plane, inextensible sheet may be folded or creased along a curved line to produce two connected but distinct developable surfaces. Various theorems applying to this folding process are identified… Expand

A Hierarchy of Plate Models Derived from Nonlinear Elasticity by Gamma-Convergence

- Mathematics
- 2006

We derive a hierarchy of plate models from three-dimensional nonlinear elasticity by Γ-convergence. What distinguishes the different limit models is the scaling of the elastic energy per unit volume… Expand

The Föppl-von Kármán plate theory as a low energy Γ -limit of nonlinear elasticity

- Mathematics
- 2002

We show that the Foppl–von Karman theory arises as a low energy Γ-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a generalization to higher derivatives of our… Expand