Origami metamaterials have garnered significant attention in recent years due to their unique deformation modes and outstanding mechanical properties. A key challenge for engineering applications is how to program and regulate these properties. However, most prior research has focused on adjustments to geometrical or material parameters such as design angles, panel edge lengths, and folding angles, while overlooking the role of mountain-valley assignments in crease patterns. In fact, these seemingly simple designs of the mountain-valley lines largely determine the geometry and mechanical performance of the origami structures.
        Recently, Professor Yan Chen's team from the School of Mechanical Engineering at Tianjin University systematically studied how varying mountain-valley assignments affects the geometry and mechanical properties of double-corrugated origami metamaterials. By establishing a parametric model, the team successfully predicted and regulated mechanical properties, offering a fresh perspective for programming origami metamaterials and expanding their application potential in areas such as energy absorption and adjustable stiffness structures.
        First, the research team designed a series of double-corrugated origami metamaterials with distinct folding characteristics by adjusting the mountain-valley assignments (Figure 1) and analyzed the changes in geometric scale and Poisson’s ratio. They found that configurations with the same directions of pathway (DC-1 and DC-2, DC-3 and DC-4) exhibited a proportional relationship in geometric scale (Figure 2). Specifically, DC-1 and DC-2 share the same geometric scale in the x-direction (w), while DC-2’s scales in the y and z directions (l and h) are twice that of DC-1. A similar geometric relationship exists between DC-3 and DC-4. This scale correlation enables configurations with the same directions of pathway to exhibit consistent Poisson’s ratios.

Fig. 1. Double-corrugated origami metamaterials

Fig. 2. Geometric scale and Poisson’s ratio

        In further research, the team used finite element simulations and experiments to study the deformation process and mechanical properties of these origami metamaterials under quasi-static compression (Figure 3). Since these metamaterials follow the rigid origami deformation mode, the team developed a parametric model for mechanical properties based on a fixed plastic hinge model. By calculating the rate of instantaneous angular changes and the total angular variation during compression, they determined the trends in normalized stiffness and specific energy absorption (SEA) for different configurations (Figure 4).

Fig. 3. Deformation process and plastic strain contour map of different origami metamaterials

Fig. 4. Rate of instantaneous angular changes and the total angular variation

        To further explore the mechanical potential of origami metamaterials, the research team mixed configurations with the same directions of pathway based on their geometric correlation, creating mixed metamaterials with more complex geometric characteristics (Figure 5). These mixed metamaterials not only exhibit greater geometric diversity but also possess unique mechanical properties. Specifically, the SEA of the mixed structures is primarily influenced by the total angular variation during compression, and it depends on the number and type of origami units involved in the mixed arrangement. By rationally combining different units, the SEA of the metamaterial can be programmed, providing targeted solutions to meet diverse application needs.

Fig. 5. Mixed origami metamaterials

        For the stiffness characteristics of mixed origami metamaterials, taking DC-M as an example, this structure contains fewer creases connecting the upper and lower layers of origami units, resulting in insufficient stress transfer during compression and nonuniform deformation throughout the material. This causes the lower-stiffness DC-2 units to deform first (Figure 6, strain 0-0.43), reducing the overall stiffness. Once the upper and lower layers make contact, the structure deforms simultaneously (Figure 6, strain 0.43-0.68), increasing overall stiffness. The graded stiffness characteristic observed in the stress-strain curve further verifies this phenomenon (Figure 7). Therefore, by adjusting the mountain-valley assignments in crease patterns, the deformation modes and mechanical properties of origami metamaterials can be precisely programmed and controlled. This strategy not only offers more possibilities for the fine-tuning of metamaterials but also enhances design flexibility and diversity, providing new ideas and opportunities for the widespread use of metamaterials in practical applications.

Fig. 6. Deformation process and the PEEQ contour map of mixed metamaterials

Fig. 7. Stress versus strain curves and mechanical properties of mixed metamaterials

        This study was recently published in the Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences journal. The corresponding author is Professor Yan Chen from Tianjin University, and the first author is Ph.D. student Mengyue Li. This research systematically explores the influence of mountain-valley assignments on the mechanical properties of origami metamaterials, revealing the intrinsic mechanism between mountain-valley changes and the mechanical performance of the metamaterials. It provides a novel approach for programming the mechanical properties of metamaterials, with broad application prospects in energy absorption and adjustable stiffness structures.

Li M, Peng R, Ma J, Chen Y*. Programming the mechanical properties of double-corrugated metamaterials by varying mountain-valley assignments. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2024, 382: 20240004.
(https://doi.org/10.1098/rsta.2024.0004)