McGill University researchers have discovered a new way to fold flat sheets into smooth, curved shells that can switch from floppy and flexible to stiff and load-bearing on demand. By designing a special origami pattern and threading cable-like elements through it, they can control the material's final three-dimensional shape and how rigid it becomes. The result, a "doubly curved lens box," could advance the technology of such objects as temporary emergency tents, morphing robots and smart fabrics, the researchers said.
"Existing foldable structures face a trade-off: if they are smooth and nicely curved, they tend to be soft and floppy; if they are strong and stiff, they usually look faceted, jagged or uncomfortable, and their shape is hard to tune once built," said Damiano Pasini, study co-author and Professor of Mechanical Engineering. "This is a major limitation for technologies such as wearable supports, medical implants, soft robots and deployable space structures, which often need both smooth shapes and reliable strength to sturdily withstand externally applied forces."
To overcome this limitation, the team designed an origami pattern with curved creases that folds into smooth, doubly curved surfaces, such as spheres or tori (doughnut shapes), and can then be "locked" into a rigid, load-bearing state. By adding internal tendons whose tension can be adjusted, the same structure can be reprogrammed to be ultra soft or very stiff, without altering its shape or materials.
Adjustable cables to tune rigidity
The new fold pattern combines curved and straight creases, allowing flat sheets to transform into continuous, smooth surfaces rather than the faceted forms typical of conventional origami.
Starting from a desired curved shape (such as a sphere, torus or vase-like surface), the researchers used differential geometry - mathematical theories for origami tiling and developable surfaces - followed by numerical optimization to compute the exact crease pattern needed so that, once folded and locked, the origami shell would match the target geometry.
They next laser-cut and folded paperboard sheets into these patterns, assembled them into shells, and embedded thin cables ("tendons") through specific points.
"By tightening or loosening the tendons, we measured how the stiffness changed and showed that the shells could go from saggy and flexible to rigid and resistant to twisting and bending," Pasini said.
The researchers validated the findings with mechanics theory, rigid-origami and geometric simulations to confirm that the folding kinematics, or the object's motions, are feasible. These simulations also confirmed that the surfaces would remain smooth and that the pattern can be scaled and tiled.
A 'new design paradigm'
Pasini described the findings as a new design paradigm for origami metamaterials.
"Our approach opens new avenues for the design of deployable and adaptive load-bearing curved structures. Our findings challenge the idea that you need complex materials or external systems to get tunable stiffness, showing that smart geometry alone can do much of the work," he said.
About this study
"Smooth doubly curved origami shells with reprogrammable rigidity," by Morad Mirzajanzadeh and Damiano Pasini, was published in Nature Communications.
The study was funded by the Canada Research Chairs program, the Natural Sciences and Engineering Research Council of Canada, the McGill Engineering Doctoral Award and the Fonds de recherche du Québec - Nature et technologies.
