In recent years, origami-inspired mechanical metamaterials have gained significant attention in fields such as aerospace and robotics due to their unique structural deformation and mechanical response advantages. Through precise geometric designs, these materials can achieve complex deformations under external forces, demonstrating exceptional energy absorption and stress distribution regulation. However, most current origami metamaterial designs are optimized for a single objective, such as improving energy absorption in one direction or achieving smooth mechanical responses. Therefore, one of the key challenges is how to design origami metamaterials that exhibit distinct folding characteristics in different directions, thereby achieving different mechanical responses in each direction.
        To address this challenge, a research team led by Professors Yan Chen and Jiayao Ma from the School of Mechanical Engineering at Tianjin University has conducted an innovative study. They designed an origami metamaterial that exhibits entirely different folding modes and mechanical properties in the three orthogonal directions (x, y, z). This metamaterial not only displays distinct mechanical responses in each direction but also allows for multi-directional performance optimization and tunability through precise control of design parameters. The research team also developed theoretical models to deeply analyze the impact of design and folding parameters on the mechanical properties in each direction, providing a powerful tool for understanding and predicting material behavior under different loading conditions.
        Firstly, based on common deformation modes in origami metamaterials—rigid folding, non-rigid folding, and the transition between rigid and non-rigid folding—the team designed an origami metamaterial that exhibits different folding behaviors in the x, y, and z directions (Fig. 1). In the x-direction, the metamaterial can fully fold flat (I); in the y-direction, further folding is restricted due to geometric limitations; in the z-direction, partial folding occurs, followed by a self-locking phenomenon caused by physical interference (III) (Video 1).

Fig. 1. Design of the origami metamaterial

Video 1 Folding process of the metamaterial

        Using finite element simulations and experimental analysis, the research team explored the quasi-static compressive mechanical behavior of this origami metamaterial in all three directions (Fig. 2). In the x-direction, the metamaterial exhibits a typical rigid folding mode, with deformation concentrated mainly in the creases, resulting in low specific energy absorption (SEA) and compressive stiffness. In the y-direction, a non-rigid folding mode occurs, with significant buckling deformation in the panels, leading to higher SEA and stiffness, three times greater than in the x-direction. In the z-direction, before the self-locking point, the metamaterial undergoes a rigid folding mode; beyond the self-locking point, non-rigid deformation occurs. Thus, in the z-direction, the metamaterial exhibits a transition between rigid and non-rigid folding modes, with SEA and stiffness values between those of the x and y directions. This unique structural design enables significant differences in mechanical properties across the three directions.

Fig. 2. Deformation and mechanical response of the origami metamaterial in three directions

        To further explore the influence of design parameters on the mechanical performance of the metamaterial, the research team combined kinematic and plastic mechanics theories to develop theoretical models for the mechanical properties in the x and z directions. These models provide detailed insights into the effects of design parameters (such as design angle, folding angle, a/b, and a/c ratios) on SEA (Fig. 3). The results indicate that SEA in the x-direction is nearly unaffected by changes in length parameters, remaining within the range of 4.02 J/g to 4.88 J/g. In contrast, SEA in the z-direction increases significantly as the a/b ratio increases and the a/c ratio decreases. Furthermore, changes in design and folding angles have opposite effects on SEA in the x and z directions.

Fig. 3. Contour plot of SEA variations in the x and z directions with design parameters

        Building on these results, the research team conducted a comprehensive analysis of the mechanical properties in all three directions in relation to various design parameters (Fig. 4). The results demonstrate that design and folding angles are key factors influencing the mechanical properties in all three directions. Notably, changes in these angles lead to opposite trends in mechanical performance in the x and z directions. In contrast, length parameters (a/b and a/c) primarily affect the mechanical properties in the z direction, with SEA and compressive stiffness increasing as the a/b ratio increases. However, these parameters have minimal impact on the x and y directions. Therefore, by adjusting the design parameters, performance can be optimized or balanced across different directions, or enhanced in a specific direction without significantly affecting the mechanical properties in other directions. This multi-dimensional performance tuning strategy provides flexible design options for future applications of origami metamaterials, allowing for optimization of mechanical responses in various directions to achieve multifunctional performance.

Fig. 4. Parametric analysis of mechanical properties

        This research has been recently published in the International Journal of Mechanical Sciences. The corresponding authors are Professors Yan Chen and Jiayao Ma from Tianjin University, with Ph.D. student Mengyue Li and master's student Houhua Chen as the co-first authors. This study innovatively proposes an origami metamaterial with distinct mechanical properties in three orthogonal directions, showcasing its unique potential and advantages in applications that require multi-objective performance.

Li M#, Chen H#, Ma J*, Chen Y*. An Origami Metamaterial with Distinct Mechanical Properties in Three Orthotropic Directions. International Journal of Mechanical Sciences, 2024, 283:109713.
(https://doi.org/10.1016/j.ijmecsci.2024.109713)