## 2 Materials and Methods
### Deformation Behavior Testing  
To investigate the deformation behavior, the clear aligners were subjected to occlusal forces using a purpose-made test stand developed in order to allow for controlled force application and to precisely determine the displacements of the aligners. The present study evaluated the following three different aligner materials and systems: CA(r) Pro+ Clear Aligner (Scheu Dental, Iserlohn, Germany), Taglus Premium (Taglus Company, Mumbai, India), and Spark Trugen (Ormco Corp., Orange, CA, USA). The clear aligners were placed on 3D-printed dental arches, which in turn were fixed on hard resin dental casts that were fixed in a dental articulator. Thus, the mechanical hinged fixture could simulate the bite closure movement. The lower part of the articulator (the lower jaw) was rigidly fixed on the base plate of the stand. In order to use the digital image correlation (DIC) method, markers were placed on the gingival and incisal part of the aligner for the upper and lower incisors as well as for lower incisors and canines on the frontal plane of the aligners (Figure 1). The loading force of up to 500 N was applied, equivalent to the human biting force, the maximum molar occlusal force. Muscle activity during chewing was assessed to be normal during clear aligner use. The average magnitude of the biting force of a human is nearly 500 N [13]. The forces were measured directly using a S9 force transducer (produced by Hottinger Baldwin Messtechnik, HBM GmbH, Darmstadt, Germany) placed directly on the upper hard resin dental cast model. Force data acquisition was performed by Spider 8 PC measurement electronics (produced by Hottinger Baldwin Messtechnik, HBM GmbH, Darmstadt, Germany) linked to a PC running a Catman Easy/AP software version 2.2. \begin{table}
\begin{tabular}{c c c c} \hline
**Group** & **Aligner System** & **Manufacturer** & **Composition and Material Thickness** \\ \hline \multirow{3}{*}{**CA (n = 15)**} & \multirow{3}{*}{CA® Pro+ Clear Aligner} & Scheu Dental, Iserlohn, Germany & Three layers (0.75 mm): 1. Copolyester layer (0.25 mm) 2. Thermoplastic elastomer (TPE) (0.25 mm) 3. Copolyester layer (0.25 mm) \\  & & & 3. Copolyester layer (0.25 mm) \\ \hline \multirow{3}{*}{**TG (n = 15)**} & \multirow{3}{*}{Taglus Premium} & Taglus Company, Mumbai, India & Polyethylene terephthalate glycol (PET-G) (0.75 mm) \\ \hline \multirow{3}{*}{**SP (n = 15)**} & \multirow{3}{*}{Spark Trugen} & Ormco Corp., Orange, CA, USA & TruGEN Technology (0.75 mm) \\ \cline{1-1} \cline{3-4}  & & & \\ \end{tabular}
\end{table} 
Table 1: Distribution of the samples and the material compositions. The deformation behavior of the materials was assessed using a digital image correlation (DIC) system. This is a contactless and non-destructive measurement technique that can compute 2D or 3D coordinates from an image series recorded with a stereo camera. By interpreting local displacements between the 2D or 3D coordinates, strain values and strain rates can be calculated. The DIC method uses reference images captured by the left and the right camera to determine the 3D coordinates of various points that will be analyzed, by subtracting the 3D coordinates from all recorded stages over time from the 3D coordinates of the reference stage which led to 3D displacement values. Before carrying out the measurements, the calibration procedure was performed in order for the possible measurement errors to remain low. The measurement of the displacements and deformations was performed through the DIC system ARAMIS 3D 12M Camera (Carl Zeiss, Jena, Germany) running the PONTOS software version v6.3.1-1 (PONTOS Software GmbH, Jena, Germany). PONTOS Live is based on the triangulation principle and analyses components of different sizes--from a few millimeters to a few meters--point by point, regardless of the material. The DIC hardware system parameters are presented in Table 2.  
Considering the field of view, calibration was performed, resulting in a measuring area of 420 \(\times\) 330 \(\times\) 300 mm.