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.

Shear deformation dominates in the soft adhesive layers of the laminated structure of flexible electronics

“…Since the soft adhesive layers play an important role in the realization of splitting of the neutral mechanical plane, to achieve the optimal design of a flexible electronics, quantitative investigation of the mechanical behavior of the laminated structure, including the soft adhesive layers, is necessary. Actually, there have been some recently published literatures developing the mechanics models for such laminated structures ( Li et al, 2014;Li et al, 2016;Lu et al, 2014;Shi et al, 2014;Su et al, 2015b ). However, previous studies fall into two categories: those simply taking into account the normal strain-induced deformation and neglecting the shear deformation of the soft adhesive layers ( Li et al, 2014;Shi et al, 2014 ), and those incorporating the shear deformation of the soft adhesive layers ( Li et al, 2016;Su et al, 2015b ).…”

“…However, this design is not achievable in practice. Recently, splitting of the neutral mechanical plane has been proposed ( Lu and Yang, 2015 ) and further applied ( Li et al, 2016;Su et al, 2015b ). It is also known as the local-neutral-axis design ( Li et al, 2014 ) and is probably the best approach to the optimal and practical design.…”

Mechanical Analyses and Structural Design Requirements for Flexible Energy Storage Devices

“…Aside from the use of a mechanical neutral plane to minimize destruction resulting from bending force, the splitting of a mechanical neutral plane [127][128][129] should also be considered to avoid a large modulus mismatch and premature failure in typical multilayer electronics, as a result of their difference from the simple hypothesis involving an entire stack. Rationally designing the lamination of devices against mechanical failure also provides a refined design guideline for flexible devices.…”

Multilayer Substrate to Use Brittle Materials in Flexible Electronics

“…However, these approaches resulted in inferior performance, productivity and process compatibility, compared to the brittle conventional materials. Researchers also studied the use of conventional materials in flexible electronic devices by manipulating the location of neutral plane with additional layers on top [15][16][17][18] . However, this methodology has focused on embedding active components between polymeric materials with a proper thickness and Young's modulus.…”