title: Splitting of the neutral mechanical plane depends on the length of the multi-layer structure of flexible electronics.
abstract: Multi-layer structures with soft (compliant) interlayers have been widely used in flexible electronics and photonics as an effective design for reducing interactions among the hard (stiff) layers and thus avoiding the premature failure of an entire device. The analytic model for bending of such a structure has not been well established due to its complex mechanical behaviour. Here, we present a rational analytic model, without any parameter fitting, to study the bending of a multi-layer structure on a cylinder, which is often regarded as an important approach to mechanical reliability testing of flexible electronics and photonics. For the first time, our model quantitatively reveals that, as the key for accurate strain control, the splitting of the neutral mechanical plane depends not only on the relative thickness of the middle layer, but also on the length-to-thickness ratio of the multi-layer structure. The model accurately captures the key quantities, including the axial strains in the top and bottom layers, the shear strain in the middle layer and the locations of the neutral mechanical planes of the top and bottom layers. The effects of the length of the multi-layer and the thickness of the middle layer are elaborated. This work is very useful for the design of multi-layer structure-based flexible electronics and photonics.
authors.affiliation: State Key Laboratory of Nonlinear Mechanics , Institute of Mechanics, Chinese Academy of Sciences , Beijing 100190, People's Republic of China.
authors.forename: Shuang
authors.initials: S
authors.lastname: Li
authors.affiliation: State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China; Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208, USA; Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA.
authors.forename: Yewang
authors.identifier: 0000-0002-5961-0490
authors.initials: Y
authors.lastname: Su
authors.affiliation: State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics , Dalian University of Technology , Dalian 116024, People's Republic of China.
authors.forename: Rui
authors.initials: R
authors.lastname: Li
keywords: flexible electronics; multi-layer structure; neutral mechanical plane; structure design