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

doi:10.1007/s10483-022-2841-5

Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (4): 467-478.doi: https://doi.org/10.1007/s10483-022-2841-5

• 论文 • 下一篇

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

Xiaosheng CAI, Nenghui ZHANG, Hanlin LIU

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

收稿日期:2021-10-04 修回日期:2022-02-23 发布日期:2022-03-29
通讯作者: Nenghui ZHANG, E-mail:nhzhang@shu.edu.cn
基金资助:
National Natural Science Foundation of China (Nos.12172204, 11772182, 11272193, and 10872121) and the Program of Shanghai Municipal Education Commission (No. 2019-01-07-00-09-E00018)

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

Xiaosheng CAI, Nenghui ZHANG, Hanlin LIU

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

Received:2021-10-04 Revised:2022-02-23 Published:2022-03-29
Contact: Nenghui ZHANG, E-mail:nhzhang@shu.edu.cn
Supported by:
National Natural Science Foundation of China (Nos.12172204, 11772182, 11272193, and 10872121) and the Program of Shanghai Municipal Education Commission (No. 2019-01-07-00-09-E00018)

摘要/Abstract

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

Abstract: 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.

Key words: laminated structure, stress relaxation, mismatch strain, tension-bending coupling effect, analytical method

中图分类号:

74F05
74K35

Xiaosheng CAI, Nenghui ZHANG, Hanlin LIU. Thickness dependence of viscoelastic stress relaxation of laminated microbeams due to mismatch strain[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(4): 467-478.

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

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

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