Anisotropic elastic-plastic behavior of architected pyramidal lattice materials

Abstract

The initial and subsequent yield surfaces for architected pyramidal lattice materials are investigated analytically. Considering lattice struts as elastic-perfectly plastic thin beams subjected to both axial force and bending moment, a set of nonlinear elastic-plastic constitutive relations for a strut is proposed. Moreover, we phenomenologically present anisotropic pressure-dependent yield functions for pyramidal lattices. Comparison of planar yield surfaces of pyramidal lattices predicted by analytical approach to the ones obtained from phenomenological models shows a good agreement for the type of external loads and range of strains investigated in this study. Investigating the normality between the plastic strain vectors and yield surfaces, the obtained results demonstrate the associative nature of the flow rule. We have also emphasized on utilizing hollow-tapered struts as the constituent of pyramidal lattices. To this end, we analytically found that hollow-tapered struts can remarkably improve the effective stiffness and yield strength of bending-dominant pyramidal lattices.