Open Access
| Issue |
ESAIM: M2AN
Volume 60, Number 3, May-June 2026
|
|
|---|---|---|
| Page(s) | 1247 - 1268 | |
| DOI | https://doi.org/10.1051/m2an/2026033 | |
| Published online | 01 June 2026 | |
- S. Bartels, Approximation of large bending isometries with discrete Kirchhoff triangles. SIAM J. Numer. Anal. 51 (2013) 516–525. [Google Scholar]
- S. Bartels, Numerical Methods for Nonlinear Partial Differential Equations. Springer Series in Computational Mathematics. Vol. 47. Springer, Cham (2015). [Google Scholar]
- S. Bartels, Numerical solution of a Füppl–von Kármán model. SIAM J. Numer. Anal. 55 (2017) 1505–1524. [Google Scholar]
- S. Bartels, A. Bonito and R.H. Nochetto, Bilayer plates: model reduction, Γ-convergent finite element approximation, and discrete gradient flow. Comm. Pure Appl. Math. 70 (2017) 547–589. [Google Scholar]
- S. Bartels, A. Bonito and P. Hornung, Modeling and simulation of thin sheet folding. Interfaces Free Bound. 24 (2022) 459–485. [Google Scholar]
- A. Bonito, R.H. Nochetto and D. Ntogkas, Discontinuous Galerkin approach to large bending deformation of a bilayer plate with isometry constraint. J. Comput. Phys. 423 (2020) 109785. [Google Scholar]
- D. Braess, Finite Elements, 3rd edition. Cambridge University Press, Cambridge (2007). Theory, fast solvers, and applications in elasticity theory. Translated from the German by Larry L. Schumaker. [Google Scholar]
- J. Braun and B. Schmidt, An atomistic derivation of von-Kármán plate theory. Netw. Heterog. Media 17 (2022) 613–644. [Google Scholar]
- P.G. Ciarlet, A justification of the von Kármán equations. Arch. Ration. Mech. Anal. 73 (1980) 349–389. [Google Scholar]
- M. de Benito Delgado and B. Schmidt, Energy minimising configurations of pre-strained multilayers. J. Elasticity 140 (2020) 303–335. [Google Scholar]
- M. de Benito Delgado and B. Schmidt, A hierarchy of multilayered plate models. ESAIM Control Optim. Calc. Var. 27 (2021) S16. [Google Scholar]
- A.I. Egunov, J.G. Korvink and V.A. Luchnikov, Polydimethylsiloxane bilayer films with an embedded spontaneous curvature. Soft Matter 12 (2016) 45–52. [PubMed] [Google Scholar]
- M. Finot and S. Suresh, Small and large deformation of thick and thin-film multi-layers: effects of layer geometry, plasticity and compositional gradients. J. Mech. Phys. Solids 44 (1996) 683–721. Available from: http://www.sciencedirect.com/science/article/pii/0022509696845480. [Google Scholar]
- L.B. Freund, Substrate curvature due to thin film mismatch strain in the nonlinear deformation range. J. Mech. Phys. Solids 48 (2000) 1159–1174. [Google Scholar]
- G. Friesecke, R.D. James and S. Müller, A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Commun. Pure Appl. Math. 55 (2002) 1461–1506. [Google Scholar]
- G. Friesecke, R.D. James and S. Müller, A hierarchy of plate models derived from nonlinear elasticity by Γ-convergence. Arch. Ration. Mech. Anal. 180 (2006) 183–236. [Google Scholar]
- K. Jonsson, Y. Ma, A.-L. Routier-Kierzkowska and R. Bhalerao, Multiple mechanisms behind plant bending. Nat. Plants 9 (2022) 1–9. [Google Scholar]
- C.S. Kim and S.J. Lombardo, Curvature and bifurcation of MgO–Al2O3 bilayer ceramic structures. J. Ceram. Process. Res. 9 (2008) 93–96. [Google Scholar]
- C. Lee, X. Wei, J.W. Kysar and J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321 (2008) 385–388. Available from: https://www.science.org/doi/abs/10.1126/science.1157996. [CrossRef] [Google Scholar]
- M. Lewicka and D. Lučić, Dimension reduction for thin films with transversally varying prestrain: oscillatory and nonoscillatory cases. Comm. Pure Appl. Math. 73 (2020) 1880–1932. [Google Scholar]
- M. Lewicka, L. Mahadevan and M.R. Pakzad, The Füppl–von Kármán equations for plates with incompatible strains. Proc. R. Soc. London Ser. A. Math. Phys. Eng. Sci. 467 (2011) 402–426. [Google Scholar]
- C.B. Masters and N.J. Salamon, Geometrically nonlinear stress-deflection relations for thin film/substrate systems. Int. J. Eng. Sci. 31 (1993) 915–925. Available from: http://www.sciencedirect.com/science/article/pii/0020722593901032. [Google Scholar]
- D. Padilla-Garza, Dimension reduction through gamma convergence for general prestrained thin elastic sheets. Calc. Var. Part. Differ. Equ. 61 (2022) 187. [Google Scholar]
- R. Sachse, A. Westermeier, M. Mylo, J. Nadasdi, M. Bischoff, T. Speck and S. Poppinga, Snapping mechanics of the venus flytrap (Dionaea muscipula). Proc. Nat. Acad. Sci. 117 (2020) 16035–16042. [Google Scholar]
- N.J. Salamon and C.B. Masters, Bifurcation in isotropic thinfilm/substrate plates. Int. J. Solids Struct. 32 (1995) 473–481. Available from: http://www.sciencedirect.com/science/article/pii/002076839400129K. [Google Scholar]
- M. Santilli and B. Schmidt, A Blake-Zisserman-Kirchhoff theory for plates with soft inclusions. J. Math. Pures Appl. 175 (2023) 143–180. [Google Scholar]
- B. Schmidt, Minimal energy configurations of strained multi-layers. Calc. Var. Part. Differ. Equ. 30 (2007) 477–497. [Google Scholar]
- B. Schmidt, Plate theory for stressed heterogeneous multilayers of finite bending energy. J. Math. Pures Appl. 88 (2007) 107–122. [Google Scholar]
- J.W. Suk, R.D. Piner, J. An and R.S. Ruoff, Mechanical properties of monolayer graphene oxide. ACS Nano 4 (2010) 6557–6564. [Google Scholar]
- Z. Zhang, K. Pei, H. Wu, M. Sun, H. Chai, H. Wu and S. Jiang, Bistable characteristics of hybrid composite laminates embedded with bimetallic strips. Compos. Sci. Technol. 212 (2021) 108880. Available from: https://www.sciencedirect.com/science/article/pii/S0266353821002360. [Google Scholar]
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