## 1 Introduction  
Membrane materials have found wide-ranging applications in various engineering fields such as civil engineering, aerospace, biotechnology, and medical devices due to their light weight, flexibility, and ability to separate different mediums [1, 2, 3]. The typical tensile membrane structure is shown in Figure 1, which is the famous architecture at Tokyo university [4]. However, in practical applications, membranes are often subjected to various types of damage, including the formation of slits or cuts, which can significantly affect their mechanical behavior and load-carrying capacity [5, 6, 7].  
Understanding the strength characteristics of a tensile membrane with initial damage is of great significance to ensure its reliability and durability in civil engineering. To understand the research status of scholars in this field and provide reference for follow-up experiments, the recent research is analyzed. Recent studies have employed experimental tests, numerical simulations, and analytical models to explore various aspects of membrane strength. [PERSON] et al. [8] investigated the tearing behavior of fabric by high-speed imaginganalysis. Their studies showed that the high-speed imaging technique is a suitable way to observe the performance of the test of fabric. [PERSON] et al. [9] have conducted an analysis for textile-reinforced soft composites for a tensile structure by bi-axial tensile tests. They observed and analyzed the failure mechanisms of a ripped sample. [PERSON], [PERSON] et al. [10; 11] have studied the tearing test and the determination of fracture toughness of PVC-coated fabric. They used the tearing test and found that the uniaxial central tearing test could be replaced by the corresponding single-edge notched tearing test to minimize the usage of test materials and they gave the appreciate value of the fracture toughness. [PERSON] [12; 13; 14; 15] ran a lot of tests. The mechanical principle and properties of fiber were found on the basis of the experiments. And [PERSON] [16; 17; 18] and [PERSON] [19; 20] studied the same topic; they used the theoretical method to deduce a formula to calculate the mechanical properties of the membrane.  
Recent research on the strength of membranes with slits in civil engineering structures has contributed to advancing our understanding of their behaviour and performance. Experimental investigations, numerical simulations, and analytical models have provided valuable insights into the effects of the slit configuration, loading case, and durability considerations. Further research is warranted to optimize the design guidelines and develop innovative solutions for enhancing the structural integrity and longevity of slit membrane structures.  
This research aims to investigate the strength characteristics of membranes with slit defects, focusing on elucidating how the presence of slits influences their mechanical behavior under different loading cases. Through the uniaxial tear test of the damaged membrane structure, a three-dimensional optical scanner was used to photograph and scan, and the three-dimensional deformation map of the membrane was obtained when the membrane was stretched and finally damaged, so as to better show the deformation of the membrane. Through the summary of the test data, the calculation formula of the ultimate stress of the slit of the membrane is obtained.