Residual Stresses and Poisson’s Effect Drive Shape Formation and Transition of Helical Structures
- 692 Downloads
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.
KeywordsMisfit strain Residual stress Poisson’s effect Helices Nanoribbon Actuator
Mathematics Subject Classification (2010)74B10 74G15 70C20
Unable to display preview. Download preview PDF.
- 14.Xu, D., Zhang, L., Dong, L., Nelson, B.J.: Nanorobotics for NEMS using helical nanostructures. In: Encyclopedia of Nanotechnology, pp. 1715–1721 (2012) Google Scholar
- 28.Chen, Z., Majidi, C., Srolovitz, D.J., Haataja, M.: Continuum elasticity theory approach for spontaneous bending and helicity of ribbons induced by mechanical anisotropy. arXiv:1209.3321
- 29.Armon, S., Aharoni, H., Moshe, M., Sharon, E.: Shape selection in chiral ribbons: from seed pods to supramolecular assemblies. Soft Matter (2014) Google Scholar
- 32.Landau, L.D., Lifshitz, E.M.: Theory of Elasticity, 3rd edn. Pergamon, Elmsford (1986) Google Scholar
- 38.Guo, Q., Zheng, H., Chen, W., Chen, Z.: Modeling bistable behaviors in morphing structures through finite element simulations. Bio-Med. Mater. Eng. 24, 557–562 (2014) Google Scholar
- 40.Efrati, E., Irvine, W.T.M.: Orientation-dependent handedness and chiral design. Phys. Rev. X 4, 011003 (2014) Google Scholar
- 46.Lachenal, X., Weaver, P.M., Daynes, S.: Influence of transverse curvature on the stability of pre-stressed helical structures. Int. J. Solids Struct. 468, 1230–1251 (2012) Google Scholar