Constitutive relations and failure criterion of planar lattice composites

In this paper, analytical elastic constitutive relations and failure criterion of planar lattice composites are established based on the assessment of static equilibrium and deformation relations of the representative unit cell. Finite element simulations are carried out to validate the analytical solutions. Furthermore, optimizations are performed to minimize the weight of a cantilever sandwich beam for a given flexibility for four different categories of cellular core materials, including metal foam, metal hexagonal honeycomb, metal lattice and lattice composite. It is found that the out-of-plane constraint plays an important role in the in-plane strength of lattice materials made of unidirectional fiber reinforced composites. The present analytical approach is capable of identifying this effect. The sandwich beam of laminate lattice composite possesses the best bending performance among all the sandwich beams considered, which suggests its superiority for application as a bending bearing structure.