## 2 Materials and Methods
### Modeling Plastic Behavior/Region During Indentation  
#### 2.2.1 Determination of Plastic Properties for FEA  
Loading-unloading curves from nanoindentation were used to calculate the hardness and modulus. Plastic behavior is another important property that had to be considered in the modeling. Due to the unavailability of uniaxial testing for our samples, stress and strain were determined through  
Figure 1: Schematics of indentation orientation and indent position in a single row (orientation 0\({}^{\circ}\)), column (orientation 90\({}^{\circ}\)), and 3 \(\times\) 3 matrix. \(d\)—spacing between indents. the loading-unloading curve from nanoindentation testing. Considering the research from [PERSON] and [PERSON] [23], the effective indentation stress is expressed as:  
\[\sigma_{eff}=\frac{1}{\alpha}\frac{P}{\pi a_{c}^{2}} \tag{3}\]  
and the effective indentation strain as:  
\[\varepsilon_{eff}=\frac{\beta}{\sqrt{1-(a_{c}/R)^{2}}}\frac{a_{c}}{R}, \tag{4}\]  
where \(\alpha\) is an indentation stress constraint factor, \(\beta\) is an indentation strain constraint factor, \(P\) is the force acting on the indenter, \(a_{c}\) is the radius of the contact, and \(R\) is the radius of indenter. This method consists of two unknown parameters (\(\alpha\) and \(\beta\)) to be determined using uniaxial true stress and strain data. Two unknown parameters make it difficult to find the best match between experimental and modeled loading-unloading curves. Taking this into account, as well as the fact that uniaxial stress data were unavailable, the [PERSON]'s method of calculating indentation strain was considered to eliminate the unknown parameter \(\beta\) and simplify the modeling process. The indentation strain is defined as [25]:  
\[\varepsilon_{\text{ind}}=0.2\frac{\alpha_{c}}{R}. \tag{5}\]  
To model the indentation process, ABAQUS version 2019 software was used. The Young's modulus of polystyrene required for nanoindentation modeling was calculated from experimental data using Equation (2). The plastic property, yield stress, and plastic strain, applied to ABAQUS were obtained from indentation strain \(\varepsilon_{ind}\) and effective indentation stress \(\sigma_{eff}\) which were calculated from Equations (3) and (5) using the indentation stress constraint factor \(\alpha\) determined from the loading-unloading curve. To simplify procedure, the indenter was assumed to have a conical shape with radii of \(R\) = 250 nm, and total included angle of 142.3\({}^{\circ}\) that gives the same nominal contact area per unit depth as a Berkovich indenter. Indentation strain, \(\varepsilon_{ind}\), and effective indentation stress, \(\sigma_{eff}\), with different indentation stress constraint factor \(\alpha\) were applied to finite element analysis in order to define the satisfactory indentation curve. An example of obtaining most fitted parameters for ABAQUS analysis with \(h\) = 5 \(\upmu\)m is presented in Table 1 and Figure 2. The [PERSON]'s modulus of polystyrene, \(E_{PS}\) = 4.495 GPa was obtained from experimental interfacial modulus, \(Er\) = 4.866 GPa using Equation (2). Indentation strain \(\varepsilon_{ind}\) and effective indentation stress \(\sigma_{eff}\) with different indentation stress constraint factor,\(\alpha\), obtained from Equations (3) and (5) are shown in Table 1. The loading-unloading curves from ABAQUS compared with the experimental curve are shown in Figure 2. The indentation strain and effective indentation stress with \(\alpha\) = 2.5 showed the highest accuracy at maximum indentation load/depth and was chosen for finite element analysis for depth \(h\) = 5 \(\upmu\)m. The yield stress and plastic strain calculated from \(\varepsilon_{ind}\) and \(\sigma_{eff}\) that were obtained at \(\alpha\) = 2.5 were applied as the plastic property for further ABAQUS modeling. Detailed information on strain-stress values with different values as well as ABAQUS modeled curves for \(h\) = 1 \(\upmu\)m and 10 \(\upmu\)m can be found in Supporting Information S1.