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

• Published in: Applied mathematics and mechanics Vol. 43; no. 4; pp. 467 - 478
• Main Authors: Cai, Xiaosheng, Zhang, Nenghui, Liu, Hanlin
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.04.2022; Springer Nature B.V; 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
• Edition: English ed.
• Subjects: Applications of Mathematics; Classical Mechanics; Eigenvalues; Exact solutions; Film thickness; Fluid- and Aerodynamics; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Microbeams; Nanotechnology devices; Partial Differential Equations; Relaxation time; Reliability analysis; Strain; Stress relaxation; Substrates; Time dependence; Viscoelasticity; O345; analytical method; 74D05; laminated structure; mismatch strain; tension-bending coupling effect; stress relaxation; 74K35
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-022-2841-5

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 substrate-to-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.