# On the Design of Bionic Hierarchical H-Type Whip Restraints for Nuclear Power Plants
## 1 Introduction  
In nuclear power systems, pipelines commonly transport fluids under high temperature and pressure. If these pipelines rupture, the forceful ejection of the medium can cause pipe whipping, releasing substantial energy [1, 2, 3]. To prevent secondary damage to nearby safety-critical facilities and more severe safety incidents, it is crucial to implement preventive measures [4, 5]. Pipe whip restraints play an essential role in protection by restricting the movement of broken pipes and absorbing the resulting impact energy. These structural mechanisms are generally classified into tension-based and pressure-based designs: tension-based systems, like U-bolt restraints [6], limit the displacement of broken pipes to prevent further accident escalation, as shown in Figure (a)a, while pressure-based systems, such as H-type restraints (Figure (b)b), absorb impact energy through plastic deformation [7]. In designing whip restraints for nuclear power plants, the primary focus has been on maximizing energy absorption efficiency and ensuring adaptability to different scenarios. H-type restraints, as a typically thin-walled structure, are widely used in energy absorption devices due to their low processing costs, lightweight nature, and efficient energy absorption capability [8]. To date, scholars have conducted extensive research into thin-walled hollow metal tubes with diverse cross-sectional shapes, such as square tubes [9], circular tubes [10], hexagonal tubes [11], triangular tubes [12], and tapered tubes [13]. Several filler materials are used to fill structures, including aluminum [14], foam [15], lattice [16], and composite materials [17; 18], which are also widely used to enhance the crashworthiness of thin-walled tubes. Furthermore, scholars have been pursuing the improvement of crashworthiness by considering surface defects [19], truss structure [20], as well as gradient wall thickness [21]. Over the past decade, multi-cell structures have been proven to present higher crashworthiness than conventional tubes [22; 23; 24; 25], which are a combination of single cells. Numerous scholars have conducted comprehensive research on various types of multi-cell tubes, including traditional multi-cell square tubes [26], multi-cell concentric square tubes [27], and hierarchical multi-cell tubes [28]. In comparison to the traditional structure, the hierarchical structure demonstrates outstanding mechanical performance and superior energy absorption capacity. Various types of hierarchical structures have been studied, including types utilizing substructures instead of vertexes [29], types utilizing substructures instead of edges [30], and types utilizing substructures instead of subunits [31]. Among these investigations, some are inspired by biological structures. Due to natural selection, the structures of natural organisms often exhibit multifunctionality to adapt to complex environments. Therefore, bioinspired structures have become an important source of inspiration for energy absorbers. For example, inspired by the coconut tree profile, [PERSON] et al. [32] devised a conical corrugation tube. They demonstrated the tube's superiority over a circular straight tube and a tapered tube in terms of crashworthiness. [PERSON] et al. [33] proposed a graded honeycomb cellular structure based on the microstructure of bamboo. Furthermore, they evaluated gradient deformation by in-plane compressive testing and finite element analysis. [PERSON] et al. [34] constructed thin-walled tubes based on a simplified double-ring cross-section feature and the gradient distribution features of bamboo knots to enhance the energy absorption capacity of thin-walled tube for multiple load cases. The exploration of bionic structures inspired by animals and plants has become prevalent, such as those based on the structures of honeycomb [35; 36], lotus root [37], leaf venation [38], sponges [39], and pine cones [40].