## 1 Introduction  
In recent years, clear aligners have revolutionized the field of orthodontics, providing an aesthetically pleasing and comfortable alternative to traditional braces. However, understanding the mechanical deformation behavior of aligners is crucial for optimizing their design and performance [1]. Clear aligners, typically made from thermoplastic polymers, work by applying controlled forces to teeth, gradually moving them into the desired position [2]. Unlike braces, aligners are removable and nearly invisible, which has contributed to their growing popularity. Despite their advantages, the success of aligners hinges on their mechanical behavior, particularly their ability to withstand deformation while delivering consistent forces over the treatment period [1; 2]. Clear aligner treatment requires periodic refinements which are undesirable, costly, and unrecyclable. One of the reasons for refinements is the material from which the aligner is made. Polyethylene terephthalate glycol (PET-G) is currently the most widely used clear aligner material [3]. Polymers with shape memory properties for direct 3D printing, such as TC-85, a photocurable resin, have been proposed as new clear aligner materials [4]. New aligner materials seek to apply a constant force over a considerable period of time, with increased elasticity, strength, and transparency, and a more precise fit [1]. However, the force exerted by clear aligners decreases in 1-3 days due to the stress relaxation of the viscoelastic aligner materials. Clear aligners deform and wear in spots where attachments are fixed [3,5]. Temperature, oral functional and parafunctional forces induced by chewing, talking, drinking, swallowing, bruxism, and unilateral mastication may also modify the mechanical behavior of aligner materials [6]. Aligners made of the same material but printed on different 3D printers show significantly different mechanical properties [7]. The most suitable mechanical properties of aligner materials are characterized by stiffness, high yield strength, and a flat relaxation curve with low-stress relaxation levels [8]. Aligners with high stiffness are difficult to insert and remove, whereas aligners with decreased elasticity may not provide the force necessary to move teeth [9]. The initial removal of clear aligners is believed to make the material return to its initial shape and become wider transversally and shorter longitudinally [10]. The following finite element analysis and experimental methods were used for studying the mechanical behavior and the forces exerted by clear aligner materials [11], expressed as measurements of elasticity, strength, stiffness, and shape memory: the three-point bending test [3], compression tests such as tensile yield stress, stress relaxation, creep recovery, elastic modulus, and Young's modulus tests [4,8,9], Martens hardness test, instrumented indentation testing [12], the U-shape bending test and the shape recovery ratio [4], von Mises stress distribution in Finite Element Analysis (FEA)/Finite Element Modeling (FEM) [10,11,13], the RSA3 Dynamic Mechanical Analyzer (Texas Instruments, Dallas), and the INSTRON Universal Testing System (Instron Corp, Wilmington/Norwood) [8,9]. Clear aligner wear expressed as microcracks, abrasion, and changes in clear aligner thickness were assessed by scanning electron microscopy, energy dispersive X-ray microanalysis, 3D models of clear aligners at different reference occlusal points, and the software Geomagic Qualify 2013 (3D Systems, Rock Hill, SC, USA). The behavior of the materials used in dentistry can also be assessed by the DIC (Digital Image Correlation) technique, which consists of a contact-free optical method for measuring deformations, motions, and changes in the shape of object surfaces [6].