# Characterization of a Rectangular-Cut Kirigami Pattern for Soft Material Tuning
## 5 Conclusions  
The kirigami rectangular-cut pattern affects the stiffness and elongation properties of a TPU specimen as the height of the cut is modified. For the studied configuration, stiffness varies by more than 145% from the minimum cut configuration to the condition where the cut height is 1.5 mm, passing through an intermediate state when the cut is 1 mm. The maximum elongation is also affected, varying by 40% for the TPU material with the described configuration when the cut is at a minimum compared to when the cut is 1.5 mm. This feature, enabled using kirigami rectangular patterns, can be employed to fine-tune the properties of a TPU section to adjust the deformation response to an applied load. The consistent behavior of the test groups confirms that the material performance is uniform, even though the specimens were manufactured through 3D printing rather than strictly through material cutting.  
The kirigami rectangular-cut pattern on TPU sheets yields different outcomes compared to those reported by [34; 35], who proposed studies similar to the one presented in this research. However, they utilized different configurations in terms of the distribution of rectangular cuts, boundary conditions, and the characteristics of the specimens used. For example, in the study conducted in [34], the effect caused by out-of-plane deformations in the stress-strain curves is not observed due to the lack of interaction with other groups of continuous cells. When the pattern of linear cuts (non-rectangular) has been applied to other materials, a greater elongation has been achieved at the expense of significantly reducing the structure's stiffness. In the presented case using rectangular cuts, a reduction in structure stiffness is also observed, but it is not as drastic. On the other hand, the total elongation is not as substantial as that reported in other studies applying the linear cut  
Figure 14: The kirigami rectangular-cut pattern will be projected onto TPU structures to adjust their behavior, as seen in Fin Ray-inspired structures for flexible grippers.  
pattern. This may be due to the TPU specimen not necessarily being a sheet but having a thickness of 1 mm. However, for robotic applications, it is undesirable for the structure's stiffness to decrease to levels where it cannot support itself.  
Finally, it is worth mentioning that this study explores the behavior of the kirigami rectangular-cut pattern on a TPU specimen using a different configuration regarding the final distribution and boundary conditions of the test specimens. The interest in studying this cutting pattern applied to TPU material stems from its envisioned integration into actuators and sensors operating within more complex systems related to deformable robotics. It is expected that the development of this study will support the modeling and understanding of applications where this pattern is utilized, as discussed in Section 4. To fully characterize the behavior, fatigue tests and analysis of the plastic zone behavior of the constructed actuators and sensors will be conducted. Additionally, the study of new cut configurations will be carried out, considering that small variations in both the distribution and shape of the cuts could result in significantly different behavior.  
Conceptualization and validation, B.M.-B., E.C.-C. and X.Y.S.-C.; mathematical modelling B.M.-B. and X.Y.S.-C.; methodology, E.C.-C. and M.A.L.; writing--original draft preparation, B.M.-B., E.C.-C., X.Y.S.-C. and M.A.L.; writing--review and editing, X.Y.S.-C. and B.M.-B.; supervision, X.Y.S.-C., M.A.L. and E.C.-C.; project administration, X.Y.S.-C., M.A.L. and E.C.-C. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflicts of interest.