Elastic modulus and Poisson's ratio determination of micro-lattice cellular structures by analytical, numerical and homogenisation methods

The mechanical properties of micro-lattice structures made of interconnected metallic struts are calculated analytically, in order to derive their elastic modulus and Poisson's ratio in the three Cartesian directions. The geometry of the investigated unit cell is a body centered cuboid, which is a more generic case of the well-known body centered cubic geometry. The Bernoulli-Euler and Timoshenko beam theories are used for the analytical solution of the unit cell response under complex loading. The derived elastic constants are compared to the relative numerical ones. The influence of geometrical parameters on the stiffness coefficients of the cellular structure is parametrically determined. The derived elasticity matrices are introduced in a homogenised numerical model of the core and its results are compared to a numerical model with explicit representation of the core geometry indicating an excellent accuracy, while the solution time is considerably reduced.