Thermal Buckling Analysis Of Micro-beams Based On Modified Gradient Elasticity Theory

Micro-beams are the basic component of micro-electro-mechanical systems(MEMS).Accurate understanding of the thermodynamic properties of micro-beams is the basis of ensuring the normal operation of MEMS in the high temperature environment.Thermal buckling,as a common failure mode of micro-beams in the thermal environment,has attracted extensive attention of many scholars.However,many experimental results have shown that the mechanical properties of micro-beams exhibit obvious size effect,but this size effect cannot be described by the mechanical models based on classical elasticity theory.To describe the thermal buckling behavior of micro-beams more reasonably,linear and geometrically nonlinear thermal buckling models of micro-beams are presented based on the modified gradient elasticity theory(MGE).Based on the above two models,the critical buckling temperature rises,the axial and transverse displacements of the thermal post-buckling and the thermal post-buckling configuration of the micro-beams under different boundary conditions are analytically solved.Size effect of the post-buckling behavior of micro-beams and the effect of geometric nonlinearity on post-buckling behavior are discussed.The results show that size effect of the critical buckling temperature rise,buckling bifurcation and post-buckling amplitude of the micro-beam is evident.Geometric nonlinearity significantly affect the post-buckling amplitude of micro-beam.The differences are existed in the results of critical buckling temperature rise when different high-order boundary conditions are selected.The above effect and differences cannot be ignored in practical engineering applications.Thermal buckling model of MGE is a new model for thermal buckling analysis of micro/nano electronic devices and has good applicability.Compared with other models,the presented model has the advantages of easy quantization of internal length scales and simple derivation of strain gradient.Size effect of the post-buckling amplitude of micro/nano electronic devices can be described by this model,which cannot be captured by other models.