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Park et al. Soft Sci 2024;4:28 https://dx.doi.org/10.20517/ss.2024.22 Page 9 of 28

predicts the mechanical stress distribution in multi-layered structures, identifies the location of neutral
planes, and assesses the potential for delamination or cracking [14,16,25,39,118] .

For example, FEA simulations have been utilized to analyze how variations in modulus and thickness of
adhesives affect stress distribution across the entire device and impact adjacent elastic layers. Kim et al.
demonstrated that using extremely soft adhesives prevents damage to electrodes by splitting the neutral
[90]
plane . They experimentally tested whether the indium tin oxide (ITO) electrodes formed on polyethylene
terephthalate (PET) films were damaged during bending tests, depending on the modulus of the adjacent
adhesive, by measuring the resistance of the electrodes. As shown in Figure 4A, the device with low
modulus adhesives operated well without any damage to the ITO electrode.

Another study by Ma et al. reported how the modulus of adhesives in rollable devices affects the location of
[119]
the neutral plane and strain decoupling in adjacent layers . They indicated that by adjusting the properties
of the adhesive layers, it is possible to place the neutral plane in brittle and hard-to-replace layers such as
thin-film transistors (TFT), electroluminescent (EL) layers, and electrodes, thereby enhancing the
mechanical stability of the device [Figure 4B].

Li et al. conducted research showing that the primary deformation of adhesives during flexible operations is
shear deformation . They found that thicker adhesives better facilitate the formation of neutral planes
[120]
through shear deformation, effectively decoupling strain in rigid layers [Figure 4C]. Strain decoupling
[40]
refers to the phenomenon where a layer with extremely low modulus between two high modulus layers
causes stress inversion through shear deformation in the middle layer, resulting in independent strain
behavior in the top and bottom layers. These studies suggest that a stack structure with alternating high-
elastic films and extremely low-modulus adhesives can effectively alleviate stress in the device by facilitating
the formation of multiple neutral planes, thereby ensuring mechanical stability .
[121]

The aforementioned studies assumed that adhesives behave as linear elastic materials. However, this
approach does not account for the complex shear deformations caused by hyperelasticity and viscoelasticity,
leading to notable discrepancies when simulating smaller folding radii or more complicated deformations
[26]
such as rollable or stretchable forms . Hyperelasticity represents nonlinear elastic behavior, while
viscoelasticity reflects changes in material properties over time .
[122]
To accurately predict the real behavior of devices, it is necessary to use theoretical models that account for
both hyperelasticity and viscoelasticity, matching the measured properties of adhesives and incorporating
these into simulations [25,26,92,122-125] . Hyperelasticity is typically derived from stress-strain curves and
represented using models such as the Ogden, Yeoh, or Mooney-Rivlin models, which are based on the
strain energy density function. Viscoelasticity, which is time-dependent, is represented by properties
extracted from stress relaxation curves or master curves of adhesives, often using the generalized Maxwell
model or the standard linear model, represented by Prony series.

Zhang et al. analyzed the actual behavior of flexible adhesives using various fitting models to determine the
most appropriate one . They measured stress-strain curves at different strain rates to find the optimal
[125]
model for hyperelastic properties and correlated the data with the Yeoh, Ogden, and Mooney-Rivlin
models. They concluded that the 5-parameter Mooney-Rivlin model best fits all data sets regardless of strain
rate. For viscoelastic properties, they measured stress relaxation and master curves at different temperatures
and found that the generalized Maxwell model, using the 3rd Prony series, provided a good fit. This
research underscores the importance of selecting the constitutive model that best represents the genuine
properties of the adhesive, which is crucial for improving the accuracy of simulation results.