## 1 Introduction
A recent study has explored three types of cell structures: the standard honeycomb, the conventional hexagonal structure, and a configuration combining both structures [24]. These have been subjected to compression tests to assess both their mechanical behavior and their capacity to absorb energy. The first two structures showed higher energy absorption at low temperatures, while the alternating configuration, with higher density, demonstrated better performance for compressions close to the material's glass transition temperature. Some studies analyze various configurations of the body-centered cubic (BCC) structure by adding different circular elements, with three different pattern thicknesses, respectively: 0.6 mm, 0.8 mm, and 1 mm. The circular-element structures showed fewer defects than traditional BCC structures. They also have better compression and energy absorption behavior. In other studies, recovery occurs following dynamic stress, as in [26], where various types of auxetic structures stressed by impact with different speeds were studied. From the obtained results, the best solutions were those that included a version with double elastic-superelastic material and concave corners that improve energy absorption. Some studies [25] have analyzed the response to the impact of three types of structures, simple cubic, BCC, and face-centered cubic (FCC), as well as hybrid structures made by combining the former. The best structure is that which combines the three SC geometries, BCC, and FCC, as they are not only the densest but also demonstrate a 70% increase in toughness and a higher specific energy absorption capacity than conventional lattices. Furthermore, the distribution of plates in each element structure in the hybrid configuration plays a crucial role in mitigating damaging failure modes, transforming the brittle fracture into progressive damage to flat lattice structures. Density significantly affects both the mechanical strength and energy absorption capacity of structures [27]. In particular, structures with higher energy absorption are those with a higher density. The energy absorption of structures has been frequently studied [28]. However, it is less common for research to analyze this capacity after various stress cycles, which can significantly affect the performance of structures over time. In general, energy absorption properties are studied for 30% of studies on cell structures [29]. Studies on bending [30,31] are also less frequent compared to compression and impact studies. In addition, the studies carried out so far do not consider the analysis of the deformation and shape recovery cycles nor the energy absorbed during these processes [32,33]. In this study, three types of cell structures--chiral, wavy, and honeycomb--are analyzed to assess their bending behavior and energy absorption capacity. In addition, an analysis of load cycles and shape recovery was carried out, applied with limited time intervals, with form recovery carried out immediately after the spring back. The relative density of the structures has been set at 50%, measured by 3D modelling software. The thermal stimulus required for shape recovery was applied through immersion in a hot water bath at a temperature of 55 \({}^{\circ}\)C, a value that remains below the material's glass transition temperature. The aim of the present study is to investigate different types of lattice structures subjected to bending, to determine their mechanical strength and their ability to absorb energy after multiple loading cycles.