Introduction

        In recent years, foldcore sandwich structures inspired by origami and kirigami have shown significant potential as efficient energy-absorbing devices, gradually emerging as effective alternatives to traditional honeycomb structures. In the fields of aerospace, transportation, and civil engineering, spacecraft landing, vehicle collision protection, and bridge collision avoidance are widely involved in energy absorption under low-velocity impact, so the dynamic response of sandwich structure is crucial. Particularly under dynamic loads, the inertial effects of the structure can increase the initial peak stress, resulting in higher energy absorption. However, an ideal energy absorption device needs to possess both low peak stress and high energy absorption capacity, which is often challenging to achieve simultaneously under low-velocity impacts.
        To address this challenge, the research team led by Professor Jiayao Ma from the School of Mechanical Engineering at Tianjin University systematically investigated the energy absorption characteristics of pyramid foldcore structures based on kirigami design under low-velocity impacts, and revealed an inertia enhancement deformation mechanism that differs from that observed under quasi-static loading. By employing a graded geometric design method, the team developed a multi-layer graded pyramid foldcore that exhibits low initial peak stress and high energy absorption capacity under impact loads. Compared to traditional quadrilateral honeycomb and Miura-ori foldcore, the load uniformity of the graded pyramid foldcore with optimal parameters is reduced by 70.9% and 80.5%, respectively, while the specific energy absorption is increased by 0.97% and 138.37%.
        The pyramid foldcore structure is composed of two tip-to-tip eggbox structures and four parallelogram facets for connections (Figure 1a). According to the rotation of the parallelogram facets, both left-handed and right-handed units with four-fold rotational symmetry can be created (Figure 1b). A multi-layer pyramid foldcore can be constructed through the three-dimensional tessellation of these different units. The independent geometric parameters include the bottom edge length of the eggbox, the sector angle of each eggbox, and the thickness of the triangular facets of each eggbox (Figure 1c).

Figure 1 Geometric design of pyramid foldcore

        Through the combination of finite element simulation and experimental verification, the deformation mechanisms and energy absorption characteristics of double-layer pyramid foldcore with uniform parameters under various constant impacts were systematically studied (Figure 2). It was found that as the impact velocity increases, the initial peak stress of the double-layer foldcore rises significantly, and energy absorption also increases to a certain extent. During the buckling stage, the inertial resistance of the foldcore delays the buckling deformation, leading to the formation of fixed plastic hinges at the corners of the eggbox, while the triangular facets near the crushing head bend inward, resulting in initial localized deformation. The numerical simulation reveals both low and high-order buckling modes of the pyramid foldcore. The increase in initial peak stress due to impacts triggers the high-order buckling mode, leading to the formation of additional static plastic hinges during the post-buckling stage, and consequently higher compressive stress (Figure 3). Furthermore, an analysis of the influence of geometric parameters on the energy absorption performance of the foldcore indicates that a taller and thicker pyramid foldcore exhibits higher initial peak stress and energy absorption capacity under various impact loads. Additionally, the influence of geometric parameters on the energy absorption performance of the foldcore was investigated. The results indicate that, under various impact loads, a taller and thicker pyramid foldcore exhibits higher initial peak stress and energy absorption capacity.

Figure 2 Energy absorption and deformation mode of pyramid foldcore under low-velocity impacts

Figure 3 The buckling and post-buckling deformation mechanism of pyramid foldcore

        To ensure efficient energy absorption while minimizing the initial peak stress during impacts, the research team designed the graded pyramid foldcores with varying sector angles and thickness parameters. The numerical simulation results indicate that the graded height, influenced by the sector angle, not only provides controllable deformation and graded stress response but also optimizes the effective compression stroke of each layer (Figure 4). The graded thickness design demonstrates a more independent sequence deformation and more significant graded behavior (Figure 5). Regardless of whether it is the graded height or graded thickness, the initial deformation of the foldcore primarily occurs at the top layer in contact with the crushing head. Consequently, a graded pyramid foldcore with a larger positive gradient (where structural stiffness increases from the top to the bottom layer) exhibits lower initial peak stress while maintaining the overall energy absorption efficiency of the structure.

Figure 4 Deformation mode and energy absorption of pyramid foldcore with graded height under low-velocity impacts

Figure 5 Deformation mode and energy absorption of pyramid foldcore with graded thickness under low-velocity impacts

        Additionally, through a parametric analysis of foldcores with simultaneous gradients in height and thickness, the research team found that pyramid foldcore with maximum positive gradients in both height and thickness achieved the lowest initial peak stress and the highest energy absorption (Figure 6). Since the height and wall thickness of the uppermost layer is minimized, the initial peak stress of this layer under impact loading is further reduced compared to structures with a single parameter gradient. At the same time, the effective stroke of each layer gradually increases from the thinner upper layer to the thicker lower layer, resulting in layers with greater structural stiffness experiencing enhanced proportion in energy absorption (Figure 7). Compared to the uniform model, the initial peak stress of the graded pyramid foldcore with optimal parameters under impacts is reduced by more than 50%, while energy absorption efficiency is improved by approximately 5%.

Figure 6 Parametric analysis of pyramid foldcore under simultaneous gradient of height and thickness

Figure 7 Deformation mode and energy absorption of pyramid foldcore with maximum positive gradient of height and thickness under low-velocity impact

        Based on this, the research team compared the energy absorption indices of the graded pyramid foldcore with optimal performance parameters against those of typical quadrilateral honeycomb, Miura-ori foldcore, graded Miura-ori foldcore, and origami honeycomb under low-velocity impact conditions (Figure 8). The results indicate that when compared to the quadrilateral honeycomb, origami honeycomb, Miura-ori foldcore, and graded Miura-ori foldcore, the load uniformity of the graded pyramid foldcore is reduced by 70.9%, 75.4%, 80.5%, and 78.6%, respectively. Meanwhile, its energy absorption capacity is comparable to that of the quadrilateral honeycomb and is 91.98%, 138.37%, and 152.60% higher than that of the origami honeycomb, Miura-ori foldcore, and graded Miura-ori foldcore, respectively.

Figure 8 Comparison of energy absorption of graded pyramid foldcore with other typical core materials

        The aforementioned research paper was recently published in the International Journal of Mechanical Sciences. The corresponding author is Professor Jiayao Ma from Tianjin University, with co-first authors being master’s student Houhua Chen and Ph.D. student Sibo Chai, both from Tianjin University. This study systematically analyzes the deformation mechanisms of pyramid foldcore under low-velocity impacts and further designs a pyramid foldcore with graded geometry. The findings demonstrate the excellent energy absorption efficiency of the pyramid foldcore with graded design under the impact, showcasing its potential as a high-performance sandwich structure for energy buffering in impact engineering applications.

Chen H#, Chai S#, Ma J*. Energy absorption of the kirigami-inspired pyramid foldcore sandwich structures under low-velocity impact. International Journal of Mechanical Sciences, 2024. 284: 109774.
(https://doi.org/10.1016/j.ijmecsci.2024.109774)