# Computational Modeling of U-Shaped Seismic Dampers for Structural Damage Mitigation
## 1 Introduction  
Large earthquakes can result in significant human and financial losses, exemplified by the substantial damage caused by the two highest magnitude earthquakes in recent years: Chile, with USD 30 billion [1], and Japan, with USD 300 billion [2]. To mitigate such damage, anti-seismic devices such as passive, active, semiactive, and hybrid systems modify the response of a structure to seismic action by isolating, restraining, or dissipating energy [3, 4, 5, 6, 7, 8]. Among these, passive dissipation systems offer lower costs compared to other types and are one of the most suitable for maintaining the integrity of structures under seismic loads [9]. For instance, metallic dampers that function under plastic deformation [10] present a variety of proposed geometries, such as plates [3, 11], vertical bars [12], arch shapes [13], and U shapes [14, 15, 16, 17, 18, 19, 20, 21, 22]. U-shaped seismic dampers (USSDs) were first proposed in 1972 by [PERSON] et al. [14]. Subsequent enhancements to the original design have been introduced, such as the modification proposed by [PERSON] et al. [15], who proposed a USSD with both ends symmetrically closed, demonstrating that the thickness of the damper is a key geometric characteristic that improves its performance in terms of cycle number, deformation amplitude, and resistance loss percentage [15]. Moreover, [PERSON] et al. [16] introduced an adaptation that incorporates three ribs, which are different sizes and positioned perpendicular to the plate faces, with the aim of increasing the stiffness and strength of the damper. This modification significantly increased the stiffness, strength, and energy dissipation according to the rib size. U-shaped seismic dampers are applied to the damping-isolation of buildings [23] under steel frames [24] or girders [25; 26], and in bracings [27; 28]. U-shaped dampers placed under components for base isolation could be integrated with rubber bearings and do not transmit vertical force [29]. These U-shaped dampers proposed as a simple base isolation control for medium-rise buildings have been reported to be installed in structures such as Isahaya City Hall and the Japanese Red Cross Ishinomaki Hospital [30]. In the case of lightweight structures, adaptive control of load-bearing structures manipulates internal stresses through actuators [31], thus requiring more complex components, and maintenance for functional safety and reliability, as well as energy consumption. With proper design, U-shaped seismic dampers show potential for passive seismic dissipation of lightweight structures. Nippon Steel, a Japanese company specializing in global structural technology, commercially distributes a U-shaped damper that features increased thickness and a reduced width-to-length ratio. A study conducted by [PERSON] et al. [17] on this model concluded that it is highly unlikely to fracture during a single seismic event. Additionally, it has been established that the rate of change of the load is negligible for the damper. Currently, several studies have explored different types of U-shaped steel dampers and proposed advanced methods to analyze their behavior under cyclic loading. Although simplified approaches, such as the use of weighted least-squares support vector machine algorithms, as suggested by [PERSON] et al. [18], can be effective in optimizing performance indices and proposing new damper models, they may not fully capture the complex localized behavior of these devices. Accurately assessing local stress, strain, and energy dissipation often requires the development of detailed analytical and numerical models [20; 21; 22]. U-shaped dampers, through numerical modeling, allow determining the effects of geometric parameters on the energy dissipation capacity and deformation capacity under cyclic loading. Detailed finite element analysis is crucial to capturing the complex behavior of U-shaped steel dampers. However, a significant research gap exists in ensuring adequate meshing strategies for reliable numerical modeling of USSDs.