A numerical study on the minimum number of cells for the homogenized compression properties of plate, bar and cubic geometry BCC lattice-cored sandwich structures

Three different sandwich lattice cored geometries, a plate lattice having 2 numbers of cells in the thickness, a bar lattice having 4 cells in the cross-section and a cubic lattice were numerically compressed at increasing cell numbers in order to determine the effect of number of cells for the homogeneous properties. The numerical studies were performed in LSDYNA on two AlSi10Mg BCC lattices having the cell length and strut diameter of sequentially 10 and 1 mm and 5.5 and 0.7 mm, corresponding to the relative densities of 0.049 and 0.078, respectively. The results showed that the number of cells, the type of geometry and relative density significantly affected the deformation stresses of the investigated lattices. In the sequential collapse of the layers in each geometry, the top and bottom half layers were compressed at the end of the deformation before the densification. In plate geometry, the initial peak stress increased as the number of cells increased in the x-direction (x=y). The percentage change in the peak stress was found to be 5% at 10 cells and 2% at 12 cells. As the relative density increased, the minimum cell number for homogeneous deformation decreased. In the bar lattices, the homogeneous mechanical response was attained after about 4 cells in the thickness direction. The percentage change in stresses was found just below 5% in cubic lattices of 6 cells, showing that the homogeneous mechanical behavior was not attained until about x=y=z=6 cells. The numerical model stress-strain curves were also shown to well predict the trends in the experimental stress-strain curves of the selected selective laser melt AlSi10Mg lattice structures.