•A 2D cellular structure with alternating rectangular indents on the ribs was designed.•The Poisson's ratio of the model was studied via experimental and FEM approaches.•The Poisson's ratio of the cellular structure is tunable from positive to negative.•The stiffness of the model can be higher than regular honeycomb.A novel 2D cellular structure achieved by alternating rectangular surface indents on the vertical ribs of the unit cells was designed. And the Poisson's ratios of several structures were determined using the finite element method(FEM) as a function of geometric parameters. The simulation results showed that the Poisson's ratio of the 2D cellular structure was sensitive to the cell dimensional ratio, and the value can be tuned from positive to negative(the minimum can reach −1.05). Samples with identical geometric variables were fabricated via 3D printing, and their Poisson's ratios were measured and compared with the ones from simulation. Excellent agreement was found between the experimental results and the simulation. The stiffness of the model can be higher than honeycomb made of regular hexagons with appropriate geometric parameters.

•A 2D quadrilateral cellular structure made from bi-material strips was designed.•Thermal deformations were studied via experimental, analytical and FEM approaches.•Poisson’s ratio of the model is tunable from '+' to '−' with a change in temperature.•A maximum absolute value of the Poisson's ratio is approximately 12.In this paper, a two-dimensional quadrilateral cellular structure made from bi-material strips was designed and its thermal deformation behaviors were studied via experimental, analytical and numerical approaches. It has been shown that the cell shape of the structure can be tuned from convex to concave (or vice versa) and hence the Poisson’s ratio from positive to negative (or vice versa) with a change in temperature. At any specific temperature with a non-zero ΔT, the absolute value of the structure’s Poisson’s ratio decreased rapidly at first with an increasing compression strain εy and then more slowly as it approached a constant of approximately 1 when εy>0.1. A maximum absolute value of the Poisson’s ratio of approximately 12 was found at εy=0.001 at a 10 °C temperature change.

•A method for determining the Poisson׳s ratio of isotropic spheres was provided via resonant ultrasound spectroscopy (RUS) for the full range (−1 to +0.5).•The steel, SiO2, re-entrant copper foam, pure Indium and 13.5 wt% In–Sn alloy spheres were prepared and the Poisson׳s ratios of them were determined experimentally via RUS.•Experimental measurements were compared with the numerical results, and good agreement was found between the measurements and predictions.•The effects of slight deviation in shape from an ideal sphere are analyzed for various Poisson׳s ratios.The method for determining the Poisson׳s ratio of isotropic spheres was studied via resonant ultrasound spectroscopy (RUS). To that end, The mode structure maps for freely vibrating isotropic spheres were obtained via finite element method over the full range of Poisson׳s ratio (−1 to+0.5). RUS measurements for spherical samples (indium, steel, SiO2, 13.5 wt% In–Sn, and copper foam) were compared with the numerical results and the Poisson׳s ratios were determined as +0.4, +0.3, +0.2, −0.08, and −0.3, respectively. The effects of slight shape imperfection upon the first 12 modes were analyzed for various Poisson׳s ratios, and were found to be negligible in interpretation of the experimental results.