Loading capacity prediction of the auxetic tubular lattice structures by multiscale shakedown analysis

Auxetic tubular structures have raised increasing research interest due to their unique and tailored properties. However, the complexity of multiaxial loads eliminates the availability of the classic fatigue evaluation method and the difficulties of connecting lattice unit design with structural capacities have postponed the study on lattices’ fatigue limit loads. To fill this research gap, we present a direct shakedown method using tetrahedron elements with the reduced Gaussian integration point to predict the biaxial bearing capacities for time-varied loadings. The rationality and precision of the approach are validated using the residual stress comparison with the incremental method. The nodal-coupling-based periodic boundary conditions that are proposed and verified facilitate the parameterization study of the tubular lattice structure design. The results reveal that the edge width of the lattice unit positively impacts the elastic shakedown loads while the curvature influences reversely. The circumferential loading capacities of the auxetic tubular lattice have a significant susceptibility to curvature. This work provides an efficient tool for quantitatively evaluating the shakedown loading capacities of auxetic tubular lattice structures and the impacts of design parameters.