## 3 Finite Element Model of STACER
### Finite Element Model of STACER
The tensile specimen geometry and stress-strain curves of the Co\({}_{40}\)CrNiMo alloy are shown in Figure 4. The tensile tests were carried out on a DDL50 testing machine (Changchun mechanical research institute, Changchun, China) in the longitudinal direction. The tensile tests were repeated three times to obtain the stress-strain curves. The yield strength, tensile strength, and elastic modulus were 1291 MPa, 1452 MPa and 205 GPa respectively. The deformation of the STACER was conducted by a method of continuous bending forming under tension and compression conditions. Based on the press bending mold, the tension is applied on both sides of the strip, while the strip is pulled out from one side. When the strip is inserted at a certain angle at the normal orientation to the mold, the forming of the STACER can be achieved from a strip. It is quite important that all the functions and actions of the STACER closely rely on the material's properties and deformation method. Figure 4: Finite element model of STACER with stress–strain curves and specimen geometry. This model needs to ensure that the top end of the spring reel is connected to the top rod, and the bottom end of the reel is in contact with the storage barrel. The spring reel and the top rod connection position is required to move together and satisfy the mutual rotation relationship. It is necessary to establish a local coordinate system for the riveting joint and the storage barrel respectively, so that the outward movement in the diameter direction can be achieved at the contact position of the bottom end of the reel and the storage barrel. There is a small hole at the top of the spring reel, and the center of the hole is the riveting position of the spring reel and the top rod. A reference point is established at the center of the circle in order to ensure that the center of the circle can be rotated. The reference point and each point round the hole are coupled and constrained. It is necessary to perform a coupling constraint on the riveting position with a local coordinate system in order to ensure that the constrained point can be rotated. The gathering process of STACER is a typical nonlinear process with a large deformation and complicated calculations. Therefore, the explicit computing method is used and the mass amplification factor is set to increase the calculation speed. The model establishment process is appropriately simplified, considering only the contact friction between the inner and outer layers of the spring reel. The simplification on the STACER model includes the contact state of the outermost spring reel and the wall of the storage barrel. In the process of simplification, the contact state of the outermost spring reel and the wall of the storage barrel is simulated by applying the pressure between the spring reel and the wall of the storage barrel. A rigid and elastic model is applied to study the elastic deformation of the STACER. That is due to the requirement that the mechanism is used in its elastic stage. When the stress exceeds the yield stress of Co\({}_{40}\)CrNiMo alloy in the simulation, the plastic deformation may occur on the spring reel of a STACER. It leads to a failure on the packaging or deploying process so as to lose its function. When the model is calculated, it will be affected by a convergence, which is not beneficial for the results. As long as the step size is small enough, the calculation can be achieved. However, the explicit algorithm takes a longer time for the simulation. The actual spring reel is in a state of layered phase with pressure. The model of the STACER is simplified compared to the actual model. In order to reduce the influence of the state of outermost reel layer on the inner reel, pressure is applied to the outermost reel portion of the STACER in order to ensure it completely contacts to the wall of the storage barrel, as shown in Figure 4. A gathered model is established to analyze the factors that affecting the gathering process of the STACER.