Nature has always had randomness in many ways. Natural cellular structures, specifically, have used randomized microarchitectures to form mechanically efficient materials, such as wood, sponge, and trabecular bone. Mechanical metamaterials are a class of artificial microarchitected materials designed to carry tensions and compressions with lightweight. However, there had been some limitations regarding the range of mechanical properties and geometrical parameters of regular honeycomb mechanical metamaterials. Also, it is not possible for extreme auxetic honeycomb mechanical metamaterials, which are with extreme negative Poisson’s ratio, to have a high level of stiffness. The addition of randomness had been proven to extend the properties of mechanical metamaterials.

In this project, through the approach of the combination of bending- and stretching-dominated structures, based on the level of nodal connectivity of the structures, we aimed to explore the range of properties in both the in-plane and the out-of-plane contexts. In terms of in-plane properties, we proposed a simple design that can achieve extreme auxetic or double-side auxetic lattices, the corner-plus design. The design successfully created lattices with an over -0.8 negative Poisson’s ratio value and a 6 to 10 times level of stiffness as regular honeycomb metamaterials. Through recognition and rearrangement of the openings, the peninsula-like region that expands under tension, over one million different lattices are generated with extreme negative Poisson’s ratio values and a high level of stiffness. The design had expanded the stiffness versus Poisson’s ratio region compared to the ordinary materials and regular honeycomb mechanical metamaterials.

Furthermore, in total six meta-plates were designed from the selected metamaterials and additively manufactured for the investigation of out-of-plane behavior. Experimentally and computationally, their deformation and curvatures presented that the induced curvature along the transverse direction was adjustable, which can be manipulated with the level of connectivity and the value of Poisson’s ratio. Openings in these meta-plates also played a big role in the formulation of surface contours and induced curvatures both locally and globally.

In general, openings had evident contributions to the auxeticity and the unique surface contours, which can be a key factor in the future design of the random mechanical metamaterials. The extreme auxeticity and the modular surface topology can be further implemented into the design of wearable prostheses or medical implants for future applications.