Thickness dependence of viscoelastic stress relaxation of laminated microbeams due to mismatch strain  

作　　者：Xiaosheng CAI Nenghui ZHANG Hanlin LIU 

机构地区：[1]Shanghai Institute of Applied Mathematics and Mechanics,Shanghai Key Laboratory of Mechanics in Energy Engineering,School of Mechanics and Engineering Science,Shanghai University,Shanghai 200072,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2022年第4期467-478,共12页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.12172204,11772182,11272193,and 10872121);the Program of Shanghai Municipal Education Commission(No.2019-01-07-00-09-E00018)。

摘　　要：Time-dependent behaviors due to various mismatch strains are very important to the reliability of micro-/nano-devices.This paper aims at presenting an analytical model to study the viscoelastic stress relaxation of the laminated microbeam caused by mismatch strain.Firstly,Zhang’s two-variable method is used to establish a mechanical model for predicting the quasi-static stress relaxation of the laminated microbeam.Secondly,the related analytical solutions are obtained by combining the differential method and the eigenvalue method in the temporal domain.Finally,the influence of the substrateto-film thickness/modulus ratio on the relaxation responses of the laminated microbeam subject to a step load of the mismatch strain is studied.The results show that the present predictions are consistent with the previous theoretical studies.Furthermore,the thickness dependence of stress relaxation time of the laminated microbeam is jointly determined by the intrinsic structural evolution factors and tension-bending coupling state;the stress relaxation time can be controlled by adjusting the substrate-to-film thickness/modulus ratio.

关 键 词：laminated structure stress relaxation mismatch strain tension-bending coupling effect analytical method 

分 类 号：O345[理学—固体力学]