Theoretical and numerical analysis of the mechanical responses of BCC and FCC lattice structures

Analytical and numerical analyses for predicting the mechanical responses of BCC and FCC lattice structures under compressive loading were performed and verified by comparing them to experimental data. The analytical and numerical results are in excellent correlation, while the error between the experimental and numerical results is about 5.8 ~ 15.3 %, which was caused by the inconsistent lattice strut diameter and the material elastic modulus. The measured lattice strut diameter is smaller than the designed diameter by thermal shrinkage, so the thermal shrinkage should be taken into the lattice structure design in additive manufacturing processes. Based on the same analytical and numerical techniques, a parametric investigation of the elastic moduli of BCC and FCC lattice unit cells with respect to the strut aspect ratio, specific density and strut angle was performed. Finally, the elastic moduli of multi-cell BCC and FCC lattice structures with the same density were investigated by varying the number of rows and columns of lattice unit cells in both unconstrained and constrained boundary conditions. As the strut aspect ratio, density and angle increase, the elastic moduli of both BCC and FCC lattice increase. FCC elastic modulus is higher than that of BCC lattice with respect to the strut aspect ratio, density and angle, while BCC elastic modulus could be found to be higher than of FCC lattice for a constrained boundary condition.