Enhancing Compressive Performance of Gyroid Structures Through Evolutionary Design

Gyroids are fascinating natural structures belonging to a specific family of structures known as triply periodic minimal surfaces (TPMSs). These surfaces are of significant interest to physical scientists, biologists, and mathematicians due to their unique properties characterized by their local minimum surface area with equal periodicity in all three spatial directions, making them continuous and isotropic. Gyroids specifically can be found in various biological systems like butterfly wing scales, bird feathers, etc., where, depending on the occurrence, the intricate pattern of gyroid structures provides characteristic colors, strength, flexibility and necessary insulation.

Although the mathematical model of the gyroid was developed back in the 1970s, the complexity of the structure hindered its practical applications. However, recent developments in 3D printing technologies and design tools have made it possible to manufacture such geometries with intricate details. This has led to innovative applications in various industries, including aerospace, automotive, and biomedical sectors.

In this work, the objective was to enhance the compressive performance of gyroid structures while maintaining the basic aspect ratio. This was achieved by decomposing the gyroid surface into its constituent surface elements and rebuilding it through edge modification based on evolved curves inspired by biomimicry. Taking inspiration from the growth of a plant's auxins towards light, we established a relationship between form and force. An evolutionary program was used to evaluate optimal curves under such criteria. These curves serve as new edges for the new pseudo-gyroid geometry.

Prototypes with different aspect ratios, cell numbers, wall thickness, and materials were produced by using 3D printing. Under compression, the pseudo-gyroid samples performed significantly better than the standard gyroid shapes for every instance. The results were further validated using finite element models, providing good evidence for further research into the modification of such structures to exploit their full potential.