Helical buckling behaviors of the nanowire/substrate system

Youlong CHEN, Yilun LIU, Xi CHEN

Research output: Book Chapters | Papers in Conference ProceedingsBook ChapterResearchpeer-review


When a nanowire is deposited on a compliant soft substrate or embedded in matrix, it may buckle into a helical coil form when the system is compressed. Using theoretical and finite element method (FEM) analyses, the detailed threedimensional coil buckling mechanism for a silicon nanowire (SiNW) on a poly-dimethylsiloxne (PDMS) substrate is discussed. A continuum mechanics approach based on the minimization of the strain energy in the SiNW and elastomeric substrate is developed, and the helical buckling spacing and amplitude are deduced, taking into account the influences of the elastic properties and dimensions of SiNWs. These features are verified by systematic FEM simulations and parallel experiments. When the debonding of SiNW from the surface of the substrate is considered, the buckling profile of the nanowire can be divided into three regimes, i.e., the in-plane buckling, the disordered buckling in the out-of-plane direction, and the helical buckling, depending on the debonding density. For a nanowire embedded in matrix, the buckled profile is almost perfectly circular in the axial direction; with increasing compression, the buckling spacing decreases almost linearly, while the amplitude scales with the 1/2 power of the compressive strain; the transition strain from 2D mode to 3D helical mode decreases with the Young's modulus of the wire and approaches to 1.25% when the modulus is high enough, which is much smaller than nanowires on the surface of substrates. The study may shed useful insights on the design and optimization of high-performance stretchable electronics and 3D complex nanostructures. © Springer Nature Switzerland AG 2019. All rights reserved.
Original languageEnglish
Title of host publicationHandbook of Nonlocal Continuum Mechanics for Materials and Structures
EditorsGeorge Z. VOYIADJIS
PublisherSpringer, Cham
Number of pages47
ISBN (Electronic)9783319587295
ISBN (Print)9783319587271, 9783319587288
Publication statusPublished - 2019
Externally publishedYes


  • Buckling amplitude
  • Buckling mode
  • Buckling wavelength
  • Continuum mechanics
  • Embedded wire
  • FEM
  • Helical mode
  • In-plane mode
  • Nanowire
  • Post-buckling behaviors
  • Soft substrate
  • Transition


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