Acta Mechanica Sinica

, Volume 33, Issue 1, pp 71–76 | Cite as

Bending-induced extension in two-dimensional crystals

  • Douxing Pan
  • Yao Li
  • Tzu-Chiang WangEmail author
  • Wanlin GuoEmail author
Research Paper


We find by ab initio simulations that significant overall tensile strain can be induced by pure bending in a wide range of two-dimensional crystals perpendicular to the bending moment, just like an accordion being bent to open. This bending-induced tensile strain increases in a power law with bent curvature and can be over 20% in monolayered black phosphorus and transition metal dichalcogenides at a moderate curvature of \(2\,\hbox {nm}^{-1}\) but more than an order weaker in graphene and hexagon boron nitride. This accordion effect is found to be a quantum mechanical effect raised by the asymmetric response of chemical bonds and electron density to the bending curvature.


Monolayer black phosphorus Bending to extension Accordion effect Density functional theory 



This project was supported by the 973 program (Grants 2012CB937500, 2013CB932604), the National Natural Science Foundation of China (Grants 51535005, 51472117, 11021262, 11172303, 11132011), and the Fundamental Research Funds for the Central Universities (Grant NP2013309). We thank X.F. Liu for helpful discussions and W.H. Tang for help in drawing some of the geometrical figures.

Supplementary material

10409_2016_602_MOESM1_ESM.doc (4 mb)
Supplementary material 1 (doc 4051 KB)


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.State Key Laboratory of Nonlinear Mechanics, Institute of MechanicsChinese Academy of SciencesBeijingChina
  2. 2.University of Chinese Academy of SciencesBeijingChina
  3. 3.State Key Laboratory of Mechanics and Control for Mechanical Structures and Key Laboratory for Intelligent Nano Materials and Devices (MOE)Nanjing University of Aeronautics and AstronauticsNanjingChina

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