Aperiodic tiling-based metamaterial generation for structural property exploration

Advancements in additive manufacturing have enabled the creation of artificial cellular structures with unique properties unavailable in natural materials or solid continua. Specifically, filament-based structures are well known for producing lightweight structures with very high strength, auxetic behavior, and energy absorption capabilities. In recent years, numerous research studies have been conducted on generating algorithms and frameworks to obtain unusual properties using cellular geometry and material variations. However, most of these structures exhibited anisotropic behavior. To obtain isotropic, or nearly isotropic, behavior there is a need to remove the inherent periodicity. Here, an Aperiodic Tiling-based Metamaterial Generation (ATMetGen) framework is presented leveraging an aperiodic tiling representation, a complementary energy-based curved beam structural analysis method, and deep learning-powered inverse design. Despite using only a few design parameters, the framework achieves a wide range of effective elastic moduli and Poisson's ratios, encompassing both anisotropic and nearly isotropic structures. Notably, ATMetGen generates isotropic architectures exhibiting negative, near-zero, and positive Poisson's ratios. Furthermore, the proposed complementary energy-based analysis method accelerates property evaluation by nearly an order of magnitude. Experimental testing of a physical prototype validates the zero Poisson's ratio behavior of one newly proposed tiled structure. Beyond this, the proposed ATMetGen framework is anticipated to be applicable to general periodic metamaterials as well, enabling the design and discovery of new structures exhibiting exceptional mechanical, thermal, electric, or magnetic properties.