Buckling Analysis Of Nanostructures On Compliant Substrates

Thin stiff structures,such as nanobeams and nanofilms,can be buckled with a regular waveform due to mechanical or electrical stimulus when integrated on compliant substrates.Such wavy structures have promising applications in various fields such as stretchable electronics and Micro/Nano-electromechanical Systems(M/NEMS)due to their unique electromechanical coupling property and deformation compatibility.It is of great significance for the application of such wavy structures by investigating the buckling behavior and studying how to fabricate and control such wavy structures.A series of theoretical analyses are conducted on the buckling behavior of nanobeams on elastomeric substrates.Different from macrostructures,small scale effects,including surface effects,non-local effects,may have non-negligible influences on the mechanical responses(such as bending,vibration and buckling)of nano-sized structures.In this paper,the surface effect theory and modified couple stress theory are firstly considered comprehensively in the analyses of the buckling of nanobeams on elastomeric substrates.Theoretical models are established and analytical expressions of the buckling wavelength,amplitude and critical buckling load are obtained respectively based on the energy method.Numerical results are presented to show how the wavy profile and critical load of the buckling are related to the geometric properties,material properties and small scale effect coefficients of the nanostructures.Then,while considering the surface effect,the exact form of the buckling curvature when buckling instability occurs is especially considered.The relationship between buckling wavelength and pre-strain is analyzed by Newton iteration method.In addition,we chose shape memory polymer(SMP)as the substrate.Using the shape memory effect,the influence of time and temperature on the buckling wavelength and amplitude of the nanobeam was analyzed,and the nanobeam buckling control method with the help of SMP substrate was analyzed.The study indicates that the surface effect parameters and the modified couple stress theoretical parameters are size dependent.For nanobeams with small cross section sizes and low bulk modulus,the buckling mode of the structure can be affected.When considering the exact curvature solution,it is found that the buckling wavelength has a great relationship with the pre-strain.This study is expected to be helpful for controlling and predicting the buckling behavior of such wavy structures.