We develop a numerical methodology for the calculation of mode-I R-curves of brittle and elastoplastic lattice materials, and unveil the impact of lattice topology, relative density and constituent material behavior on the toughening response of 2D isotropic lattices. The approach is based on finite element calculations of the J-integral on a single-edge-notch-bend (SENB) specimen, with individual bars modeled as beams having a linear elastic or a power-law elasto-plastic constitutive behavior and a maximum strain-based damage model. Results for three 2D isotropic lattice topologies (triangular, hexagonal and kagome) and two constituent materials (representative of a brittle ceramic (silicon carbide) and a strain hardening elasto-plastic metal (titanium alloy)) are presented. We extract initial fracture toughness and R-curves for all lattices and show that (i) elastic brittle triangular lattices exhibit toughening (rising R-curve), and (ii) elasto-plastic triangular lattices display significant toughening, while elasto-plastic hexagonal lattices fail in a brittle manner. We show that the difference in such failure behavior can be explained by the size of the plastic zone that grows upon crack propagation, and conclude that the nature of crack propagation in lattices (brittle vs ductile) depends both on the constituent material and the lattice architecture. While results are presented for 2D truss-lattices, the proposed approach can be easily applied to 3D truss and shell-lattices, as long as the crack tip lies within the empty space of a unit cell.

Composite armors systems containing ceramic components are capable of offering greater ballistic protection than those of monolithic metals alone. The level of protection afforded by a composite armor depends sensitively on the materials utilized and their spatial configuration. Using numerical simulation, we investigate the effects of relevant design parameters on the ballistic performance of thin, unbonded ceramic-metal bilayers and trilayers subject to normal impact by steel spheres. The deformation behavior of the constituent phases is described by established constitutive laws. The predictive capability of the numerical model is validated through comparisons of simulation results with experimental measurements of displacement profiles of the back facesheet of a reference trilayer. The simulation results indicate that the ceramic-metal bilayer with the ceramic at the impact side offers the highest ballistic resistance; removing metal from the rear of the structure and placing it on the impact side (forming a trilayer) results in reduced ballistic resistance. Additionally, the onset of target penetration is found to correlate with high levels of energy dissipated within the target. The implication is that composite armors should be designed to maximize the energy dissipated in the projectile, not in the armor. Accordingly, effective designs at resisting failure are found to have high ceramic-to-metal mass ratios, with a finite (though small) amount of metal on the back face.