An Efficient Computational Frameworks for Design and Analysis of Metamaterials

Advancement in additive manufacturing helps in building artificial lattice structures with unique properties that are not available in naturally occurring materials or in continuum structures. Specifically, beam-based lattices 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 based on the variation in the cell geometry and material properties. However, the exploration of the full design space is hampered in practice primarily due to restrictions on cell tiling variation. Additionally, the lattices are very intricate, and the existing structural analysis methods for those structures heavily relied on the finite element approach, making the analysis quite computationally inefficient. This dissertation attempts to address these challenges with a novel Complementary Energy (CE) based analysis method and tiling-based structure generation technique. This dissertation presents efficient computational frameworks for multiscale metamaterial design, focusing on three key aspects: structural representation and generation, structural analysis, and inverse design. To achieve extreme and unprecedented properties, a novel representation technique is introduced for the first time, based on einstein (aperiodic-monotile) and periodic tilings. This structure generation framework utilizes reflection, rotation, glide reflection, translation, and combinations thereof to tile the lattice structure. As a result, we obtain an ultra-wide range of properties, including a negative Poisson’s ratio and isotropic auxetic structures that have not been observed before with a very small number of design parameters. To improve computational efficiency in analyzing the generated structures, a new force-based method utilizing a CE-based formulation is proposed to (semi) analytically derive the flexibility and stiffness matrices. This approach eliminates the need for extensive finite element discretization and accelerates the property evaluation process. The CE-based method demonstrated a more than tenfold improvement in computational efficiency compared to conventional finite element approaches. To achieve on-demand properties or structural characteristics, inverse design techniques based on deep learning and topology optimization (TO) are employed, yielding high-accuracy predictions. These computational pipelines are demonstrated on effective elastic properties and fundamental natural frequencies. Lastly, fabrication and experimental tests were conducted on the proposed structures, confirming their negative and zero Poisson's ratio behavior. I anticipate that this framework will be applicable to any periodic metamaterial, facilitating the design and discovery of novel structures with exceptional thermal, electrical, mechanical, or magnetic properties.