Localized necking and tensile failure under global compression in metallic hierarchical solids

Engineered hierarchical solids have attracted increasing attention for their superior mass-specific mechanical properties. Using a remeshing-based continuum finite element (FE) framework, we reveal that two-scale metallic hierarchical solids exhibit a distinct, localized deformation mode that involves necking and fracture of microscale tension members even at small, in-plane compressive strains (0.03–0.05). Such tensile failure is always preceded by plastic buckling of a complementary compression member. This combined necking-buckling (NB) mode explains the premature microscale fracture observed in compression experiments on hierarchical solids. We show that truss action in macroscale members induces tension in some microscale members, and hence triggers the NB mode in hierarchical solids with diverse macroscale geometries (hexagon, diamond, re-entrant hexagon) paired with triangular substructures. For slender microscale members, necking is sometimes prevented by a competing failure mode that involves coordinated buckling (CB) of multiple members. We conduct a theoretical elastoplastic stability analysis to delineate the parametric regions over which the NB and CB modes predominate for hexagonal macrostructures. The NB mode prevails at high densities or high scale ratios, and the CB mode at low densities and low scale ratios. Importantly, our custom remeshing-based FE scheme is indispensable to resolve the localized large plastic strains, ductile failure, and complex local deformation patterns (including cusp formation) that are characteristic of the NB and CB modes. The occurrence of these modes has consequences for energy absorption by hierarchical solids, and hence influences their design.