# Characterization of a Rectangular-Cut Kirigami Pattern for Soft Material Tuning
## 4 Discussion  
The effect of rectangular kirigami cuts was primarily evidenced in the tensile tests conducted on each specimen with rectangular cuts. The variations resulting from changes in the size of the cuts were observed in these tests, and the behavior was validated through finite element method (FEM) simulations. This confirms that the results align with the parameters used in the simulation, ensuring consistency between the experimental and simulated behaviors. The slope of the stress-strain curves corresponds to the stiffness of the test specimen being tested. As seen in Figures 9 and 10, for test specimens with equal cuts, the behavior trend is the same, whereas when comparing test specimens with different cuts, there is a variation in behavior. This allows for the adjustment of variables such as total deformation and test specimen stiffness in a macroscopic behavior. Figures 9 and 10 provide a summary of the behavior in both maximum extension and stiffness for each test group. It can be observed that as the variation in the width of the rectangular cut increases, the total elongation also increases, but stiffness decreases. For tests where the cut width was greater, the maximum elongation averaged 218 percent, whereas for tests with the minimum cut, the maximum elongation decreased to an average of 176.63 percent, representing an approximate 42% variation due to the increased cut width. Regarding stiffness, tests with a rectangular cut width of 1.5 mm had an approximate average stiffness of 1635 N/m, whereas for tests with a 1.0 mm width cut, the average stiffness increased to 3264.84 N/m. Finally, for tests with the minimum cut, stiffness increased to 4020.29 N/m. In other words, as the cut width increases, stiffness decreases while maximum deformation increases. Finite element simulation validates the way in which strain occurs along the nodes of the specimen, as well as the behavior of stress response as strain increases. Furthermore, the FEM simulation demonstrates that deformation propagates regularly through the test specimen with rectangular cuts, except for those cuts located at the end of the cell just as it occurs in the experimental stage. In other words, the analysis of a specific test specimen can be used to approximate the behavior of an entire test specimen with \"m\" cuts distributed along its length, and FEM simulation can predict the behavior of a design using a rectangular pattern using TPU. While FEM simulation validates that the variation in the specimen corresponds to the evolution of deformation observed in the experimental tests, the variation observed in the experimental tests is primarily attributed to the manufacturing process of the specimens. Despite being manufactured under the same conditions, the entropy associated with the 3D printing process is reflected in the behavior of the tensile tests. These structures are proposed for deployment in both deformable robot development and artificial muscle as potential applications. In Figure 13a, a proposed rehabilitation device is depicted, in which a force is being applied to the test specimen with rectangular cuts. This device can be tailored to the rehabilitation needs of the patient. In Figure 13b, the device is shown when no force is being applied (at rest state). Figure 13: Potential applications of rectangular kirigami-adjusted actuators. (**a**) Device under an axial load produced by the effort of opening the arm; rectangular cells deform under an axial load similar to the case in the study conducted. (**b**) Device in a resting state; cells return to a resting state close to the rectangular shape, albeit with the effect of residual stresses. Conversely, the rectangular-cut pattern is viable for incorporation into structural elements constructed with TPU, such as the Fin Ray effect-inspired flexible gripper structures depicted in Figure 14. Investigation will assess the potential enhancement of gripper adaptability and grasping by strategically integrating rectangular cuts.