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Residual Stresses and Poisson’s Effect Drive Shape Formation and Transition of Helical Structures

Abstract

Strained multilayer structures are extensively investigated because of their applications in microelectromechanical/nano-elecromechanical systems. Here we employ a finite element method (FEM) to study the bending and twisting of multilayer structures subjected to misfit strains or residual stresses. This method is first validated by comparing the simulation results with analytic predictions for the bending radius of a bilayer strip with given misfit strains. Then, the FEM simulations are used to study the deformation of a bilayer strip subjected to a certain residual stress to examine the influence of Poisson’s effect. As predicted by elasticity theory, a nearly purely twisted ribbon results for a given mis-orientation angle, although the residual stress only has one non-zero principal component. Our results further show that for the same Poisson’s ratio, a transition from a twisted ribbon to a nearly cylindrical helical shape can occur, either when the strip becomes wide and thin enough or when the driving force is large enough. The combined effects of the residual stress and the Poisson’s ratio are also examined. Our work demonstrates the effective use of finite element simulations in controllable design of strained multilayer structures, which have broad potential applications in NEMS, sensors, drug delivery, morphing structures, active materials, optoelectronics, and bio-inspired robotics.

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Acknowledgements

Z.C. acknowledges the support from the Society in Science-Branco Weiss fellowship, administered by ETH Zürich. The authors thank the anonymous reviewers for helpful comments. The authors also thank Eric Dai and Jayne I. Hanlin for comments.

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Correspondence to Zi Chen.

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Chen, Z., Han, X. & Zheng, H. Residual Stresses and Poisson’s Effect Drive Shape Formation and Transition of Helical Structures. J Elast 119, 321–333 (2015). https://doi.org/10.1007/s10659-015-9525-6

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  • DOI: https://doi.org/10.1007/s10659-015-9525-6

Keywords

  • Misfit strain
  • Residual stress
  • Poisson’s effect
  • Helices
  • Nanoribbon
  • Actuator

Mathematics Subject Classification (2010)

  • 74B10
  • 74G15
  • 70C20