Shaping of Elastic Sheets by Prescription of Non-Euclidean Metrics

By Yael Klein, Efi Efrati, Eran Sharon. Science, 2007

617 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Electronic, Optical and Magnetic Materials, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/f4cad7dbae146519cf46b0563afb9a47578eba28

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. Marino Arroyo
2. Antonio DeSimone
3. Efi Efrati
4. Eran Sharon
5. R. Trask

In Electronic, Optical and Magnetic Materials

1. J. Lewis
2. L.P Liu

In Mechanical Engineering

1. Marino Arroyo
2. Antonio DeSimone
3. R. Trask
4. Efi Efrati
5. J. Lewis
6. A. Seddon
7. Kate Oliver
8. Eran Sharon

Citations in the corpus

• Elastic theory of unconstrained non-Euclidean plates (2008, background): “stic deformations and nonhomogeneous growth processes, however, cannot be mapped into such discrete geometries. Recent experiments in torn plastic sheets [22] and environmentally responsive gel discs [23] have attracted attention to a specic class of non-Euclidean elastic bodies: thin bodies whose s”
• Morphing in nature and beyond: a review of natural and synthetic shape-changing materials and mechanisms (2016, background): “A simple case is the variation of monomer concentration: gradients in monomer concentration throughout the injection forming of NIPAM sheets may be used to program the Gaussian curvature in a circular sample, allowing the spontaneous formation of domes and hyperbolic frills when heated [197].”
• Morphogenesis of thin hyperelastic plates: A constitutive theory of biological growth in the Föppl-von Kármán limit (2009, background): “…G : Ẽ ¼ 12ðF TF GT G Þ. (43) For growth of two-dimensional samples GT G can be identified to the so-called target metric, a concept developed by Marder and coworkers (Marder and Papanicolaou, 2006; Marder et al., 2007), and by Sharon and coworkers (Klein et al., 2007; Efrati and Sharon, 2008).”
• Gaussian curvature from flat elastica sheets (2011, neutral): “…analogous to ours has been analysed by Ben Amar et al. in the elasticity of botanical systems and Sharon et al. in NIPA gel sheets, when anisotropic growth creates internal stresses and forces planar systems into the third dimension (Klein et al. 2007; Dervaux & Ben Amar 2008; Müller et al. 2008).”