Estimation of the effective Young’s modulus for open cell porous titanium based on $3D$ Gibson - Ashby cell array

The objective of study is to determine the effective Young’s modulus of open cell porous titanium based on the Gibson – Ashby model. Two novel models are proposed in the form of $3D$ Gibson – Ashby cell arrays with two variants for connecting vertical and horizontal beams – hinged support and rigid clamping. Calculations made on the basis of the developed models are compared with results of known models and literature data. It is proved the assumption that at high porosity, the deformation of samples occurs to a greater extent due to the deflection of horizontal beams, and with a decrease in porosity, the compressive deformation of vertical beams is playing an important role.