This link talk about:

Mechanical properties and design of sandwich materials

https://www.sciencedirect.com/science/article/abs/pii/0010436186907494

Compress in one direction and see how much it expands in the other directions. Calculate Poisson's ration from the strains.

René Christensen Thank you for your response. For continuous solid, it is easy to calculate lateral expansion but for honeycomb core how can we approach?

Short answer. For honeycomb core there is no Poisson's ratio, because It is a material property. If you homogenize an honeycomb core you will get a mixure of material and geometry. Also your homogenized Poisson's ratio will be anisotropic.

But in the end you can apply a displacement at one side of the model and measure the displacement in the other direction. You have the lengths of the two directions and therefore you are able to calculate average strains of your problem. With them you get your value. If you rotate your honeycomb core you will get other values.

@ Sadikbasha Shaik Hmm, well I guess it comes down to how want to define it. You could just look at the strains anyway for appropriate sides, and let that be you Poisson's ratio. But otherwise it has to be a homogeneous material to have a 'true' value.

Thank you Christian Willberg and René Christensen for your answers.

You could disaggregate the material and do a more detailed analysis and then apply superposition, without forgetting to consider the comparison with simple unit elements

The calculations are for each sandwitch layer with oriented fibers

put under tension or compression, until breaking, take the longitudinal and lateral deformation, calculate the ratio of lateral deformation / longitudinal deformation

I think it zero