## 1 Introduction  
Braided corrugated hose is used in many places as an important mechanical component, such as chemical plants, the automobile industry and the aerospace industry [1, 2]. Due to the special structure of the braided corrugated hose, it can minimize vibration and compensate displacement when suffering from the dynamic load caused by gas and liquid. The braided corrugated hose is mainly composed of three parts: metal bellows, the metallic braided tube, and joint. Figure 1 shows the schematic diagram of the braided corrugated hose. Metal bellows are made using a forming process applied on thin metal sheets and it can compensate for the displacement when suffering axial loads. The metallic braided tube is braided with wires on the braiding machine, and it can protect the internal bellows, minimize the vibration, and withstand the axial loads. The bellows and the braided tube are connected by joints at both ends. According to the literature, scholars have thoroughly studied the modeling of the bellows. They have mainly used the mechanical analysis modeling and finite element methods to study the mechanical properties of the bellows. [PERSON] [3] studied the effect of plastic strain and residual stress after hydroforming on cyclic life fatigue. He found that as the elongation increases, the number of cycles decreases, and the numerical estimation is lower than the experimental results and the localization of the crack weak area can be detected. [PERSON] [4] proposed a mathematic description of the reinforced S-shaped bellows and discussed the mechanical characteristics under internal pressure, forced axial, and bending displacement. He found that the pressure capability of the bellows decreases slightly with the increase of the number of layers, but the decrease is limited and the S-shaped bellows tends to have weak nonlinear characteristics under axial tensile. [PERSON] [5] studied the failure life under the repeating of the bending process. He found that the failure point of the corrugated metal hose was located at the wave trough during the ultimate repeated bending process, and the cracks were distributed along the circumferential direction. The crack propagation and the failure mechanism of the hose under bending deformation was characterized. Although the previous scholars have done a lot of research on the mechanical properties and fatigue characteristics of the bellows, the use of the metallic braided tube leads to a major difference in the mechanical properties of the braided corrugated hose and the bellows. Nowadays, the simulation studies on the metallic braided tube can be divided into two categories, one of which treats metallic braided tubes as a homogeneous composite material. The constitutive model of the braided tube was established by tensile test. [PERSON] [3] treated the braid as a discrete diamond cell unit by finding the relationship between braiding angle and axial strain in theoretical derivation, and solved the constitutive model of the braid using the UMAT subroutine in ABAQUS. It was found that the constitutive model is in good agreement with the test results when the elongation is less than 30 mm. Based on the constitutive model of [PERSON], [PERSON] [6] proposed the acceleration coefficient to modify the change of the braiding angle and explained the mechanical mechanism of inconsistent experimental and simulation results through lateral contact between metal fibers. Other methods for simulation studies of the braided tube were to create the quasi-entity braided tube model in finite element software. The quasi-entity model of the braid can be divided into two types, one method is to set up the finite model with each wire in the braid, and the other is to set up the equivalent model with each strand in the braid. [PERSON] [7] established three models of the metal braid, the micro-scale model, the mesoscale model, and the macro-scale model, respectively.