Multiscale and Failure Analysis of Periodic Lattice Structures

A full-cycle, multiscale analysis technique was developed for periodic lattice structures with geometric repetition, aiming for more efficient modeling to predict their failure loads. The full-cycle analysis includes both upscaling and downscaling procedures. The objective of the upscaling procedure is to obtain the effective material properties of the lattice structures such that the lattice structures can be analyzed as continuum models. The continuum models are analyzed to determine the structures’ displacements or buckling failure loads. Then, the downscaling process is applied to the continuum models to determine the stresses in actual lattice members, which were applied to the stress and stress gradient based failure criterion to predict failure. Example problems were presented to demonstrate the accuracy and reliability of the proposed multiscale analysis technique. The results from the multiscale analysis were compared to those of the discrete finite element analysis without any homogenization. Furthermore, physical experiments were also conducted to determine the failure loads. Then, multiscale analysis was undertaken in conjunction with the failure criterion, based on both stress and stress gradient conditions, to compare the predicted failure loads to the experimental data.