Cubically Symmetric Mechanical Metamaterials Projected from 4th-Dimensional Geometries Reveal High Specific Properties in Shear

Abstract

In this paper, we present an emerging class of cubically symmetric mechanical metamaterials based on 3-space geometrical shadows of 4th-dimensional geometries (4-polytopes) that are optimized for high shear resistance and minimized weight. We show that by employing a genetic algorithm-based optimization framework, the mechanical metamaterials can achieve an increase of more than 40-fold in their specific shear properties. Experimental results reveal that the metamaterial structure with the highest specific shear resistance, the 5-cell (pentatope), exhibits specific shear stiffness that is almost 2-fold higher than that of a gyroid, while the 8-cell (tesseract) structure exhibits the highest specific shear yield strength that is 2.4 times higher than that of a hexagonal honeycomb tested in the out-of-plane direction.

Mode III Tear Resistance of Bombyx mori Silk Cocoons

“…Figure f). The correlations observed in Figure could be perceived as unusual, since cellular materials subjected to shear will typically show the reverse trends, in that their specific properties will rise, not fall, as a function of increasing relative density . Nevertheless, there is clear evidence from the literature that torn textiles do behave in this manner. − This is because increased porosity in textiles provides additional spaces for fiber stretching, which distributes stress more evenly among neighboring fibers.…”

Machine Intelligence in Metamaterials Design

“…The literature suggests that although evolutionary algorithms take significant time to converge and are not the most efficient approach, they are robust methods and perform consistently well in all optimization problems [83]. GA algorithms can very efficiently elucidate minute geometrical alterations in mechanical metamaterials to maximize mechanical performance [10], [182] and recently Cerniauskas and Alam [183] revealed > 4000% improvements in specific shear properties were achievable from their base structures through GA regulated parametric optimization, Figure 12.…”

“…In this branch of metamaterials, the two main directions of research are performance prediction and inverse design. Since mechanical metamaterials exhibit by default, a hierarchy in design for properties, machine intelligence will need to look beyond specifically performance prediction and inverse design, as other aspects such as manufacturing constraints [183], microstructural design for macroscopic properties, and the optimization of operation controls [249]. An emergent branch of mechanical metamaterials is, 'unfolding structures'.…”

Mode III tear resistance ofBombyx morisilk cocoons

“…Figure 4(f)). The correlations observed in Figure 4 could be perceived as unusal, since cellular materials subjected to shear will typically show the reverse trends, in that their specific properties will rise, not fall, as a function of increasing relative density, 59 . Nevertheless, there is clear evidence from the literature that in fact torn textiles do behave in this manner 52,[60][61][62][63] .…”