The effect of unit cell size and topology on tensile failure behavior of 2D lattice structures

In this paper, a theoretical model is proposed to predict the initial failure location and the failure progression of the lattice structures made from the elastic-brittle bulk materials. The effects of size and topology on the tensile failure behavior of multiple representative lattice structures (2D auxetic, 2D diamond, 2D triangular1 and 2D triangular2), under various geometry design conditions (including cell topology, cell size and number of unit cells), are systematically investigated through the proposed analytical model. From the results, it was shown that the 2D bending-dominated structures with lower nodal connectivity (number of struts that meet in joints) (2D auxetic and 2D diamond) exhibited a relatively progressive crack propagation pattern, while the 2D stretching-dominated structures with higher nodal connectivity (2D triangular1 and 2D triangular2) appear to exhibit rather catastrophic brittle fracture failure. During the failure fracture propagation, the energy absorption of the 2D stretching-dominated structures were significantly higher than that of the 2D bending-dominated structures. Moreover, for all lattice designs, the tensile failure behaviors tend to converge to more consistent patterns when the unit cell numbers increase beyond certain limitations.