Design and numerical characterization of two-dimensional, in-plane isotropic lattice materials with poisson ratios near 0 or 1

Lattice materials offer a promising alternative to dense solids due to their low weight and high specific mechanical, thermal, acoustic, and vibrational properties. While additive manufacturing technologies have accelerated the design of lattices with desirable properties, including a negative Poisson ratio, lattices with a zero Poisson ratio remain scarce, despite their unique monoclastic curvature under pure bending. These materials are highly sought after for morphing cylindrical panel applications. On the other end of the spectrum are the lattice materials with a Poisson ratio of near one, such as the perfect hexagonal lattice, which possess exceptional energy absorption capabilities. In this study, we present fourteen newly developed in-plane isotropic two-dimensional lattice materials. Among these, seven exhibit a Poisson ratio close to one, while three display a Poisson ratio close to zero at low relative densities. Among the remaining four lattices, two share similarities with the Kagome lattice, showing a Poisson ratio of approximately 0.33 at low relative densities. The other two lattices have Poisson ratios of approximately 0.51 and 0.85, respectively, at low relative densities. Finite element analyses were conducted to characterize the in-plane elastic properties of the developed lattices. The Poisson ratios of all three zero Poisson ratio lattices are nearly independent of relative density. Two of these lattices undergo stretching-dominated deformation under external loads, while the third lattice experiences bending-dominated deformation. The seven lattice materials with a Poisson ratio near one are bending-dominated like the perfect hexagonal lattice. However, four of these materials possess a greater stiffness than the perfect hexagonal lattice.