# Characterization of a Rectangular-Cut Kirigami Pattern for Soft Material Tuning
## 1 Introduction  
Kirigami and origami have been utilized in engineering for various purposes in the design and production of sensors and actuators. The reported cutting patterns of kirigami can be divided into those with an even distribution on the base material and those with a non-uniform distribution. Similarly, the cuts can be classified into simple and complex cuts. Simple cuts consist of linear cuts distributed along the base material, sometimes forming a combination of straight lines, such as trapezoidal cuts and triangular cuts. Complex cuts are defined as cuts forming curves of greater complexity than a simple straight line, such as circular cuts, spiral cuts, and other shapes of greater complexity. The effects of simple cuts on different base materials and geometries have been analyzed in [1, 2, 3, 4, 5, 6, 7, 8] with the aim of creating actuators and sensors that exploit material property tuning and deformations. Refs. [9, 10, 11, 12, 13] investigate various cutting patterns using more complex geometries arranged in a regular pattern on the base material, with cuts ranging from micrometric dimensions to a few centimeters. The applications of kirigami are diverse. For instance, in the field of soft robotics, a triangular-cut kirigami pattern was used as a snakeskin on a pneumatic actuator in [14], increasing the actuator's drag capacity through a mechanism inspired by snake scales. In [15] the author proposed a kirigami-like soft elastomeric skin used to cover a snake-arm robot conformed by compliant vertebrae and controlled with cables. Other patterns were also proposed in [16] that, when cut into a flat material and placed around a pneumaticactuator, increase its drag capacity. Flexible robots inspired by kirigami utilizing this type of dragging actuation have been developed for medical applications. Ref. [17] demonstrated the development of a robot in which kirigami patterns facilitate the navigation of robots through cavities of the human body under complex conditions and restrictions using hexagonal kirigami patterns. Meanwhile, ref. [18] showcases the development of a flexible robot for medication dosing within the human body, proposing the combined use of two kirigami patterns, one for navigation and another for medication dosing. Other actuators that use kirigami as a key design element can be found in [19; 20; 21; 22]. In the realm of sensing applications, kirigami has been widely applied for the development of sensors. The cuts allow for the deformation of the material and its ability to adapt to complex surfaces, enabling the indirect measurement of stresses or deformations produced through the modification of the material's geometry under external forces. Some of the sensors reported in the literature include a heart rate sensor [23], an ECG signal probe [24], angular deformation sensors for robotic actuators [25], and a biocompatible strain sensor [26]. The pattern of simple linear cuts has been widely studied and applied to various base materials [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22], even in different cut configurations, with most authors approximating the cut thickness to be equal to zero for simplicity of analysis. The applications of this pattern have been varied, including the development of actuators and sensors [30]. The pattern of rectangular cuts has attracted the attention of researchers in various fields, and its study has been conducted from different perspectives and with different configurations. Ref. [33] presents an experimental study of the rectangular cut configuration manufactured on TPU. In their study, the experiment was conducted on a single column of material upon which a rectangular cut was made followed by bonding material with the next rectangular cut. The experimentation considers five cells of rectangular cuts and obtains the parameters of rupture tension, elongation, and stiffness to characterize the behavior of the cutting pattern. Meanwhile, ref.