Energy‐principle‐based analysis of elastic instability in polymer cylinders subject to surface tension

• Published in: Journal of applied polymer science Vol. 141; no. 32
• Main Authors: Huang, Dianwu, Liu, Hongfei
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 20.08.2024; Wiley Subscription Services, Inc
• Subjects: Boundary conditions; Cylinders; Elastic analysis; Elastic instability; Equilibrium equations; Functional analysis; Harmonic functions; intrinsic scale; Microelectromechanical systems; Modulus of elasticity; Nanoelectromechanical systems; polymer cylinder; Polymers; Shear modulus; Stability criteria; Surface stability; Surface tension; Wavelengths
• ISSN: 0021-8995; 1097-4628
• DOI: 10.1002/app.55751

An elastic instability model of polymer cylinder subject to surface tension is studied by energy functional analysis. The no‐classical boundary conditions and equilibrium equation are derived by introducing stress double harmonic function. The criteria of instability with surface tension contribution are deduced by substituting stress solution into boundary conditions. The results show that the criterion equation of elastic instability is relevant to the radius and intrinsic scale and instable wavelength or wavenumber of cylinder. Therefore, the relation between shear modulus and surface tension has the same trend comparing with the result of Barrierès' et al. This study provides insights into the instability of polymer and has important implications for the development of nanoscale cylindrical element in micro electro mechanical systems (MEMS) or nano electro mechanical systems (NEMS). Beginning with the energy principle, the energy functional of isotropic elastic colloidal systems was studied. Governing equations and boundary conditions were derived, stress was solved using the stress function, and then substituted into the boundary conditions to obtain the criterion equation for instability.