Localized necking under global compression in two-scale metallic hierarchical solids

Abstract

Hierarchically structured cellular 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 global compressive strains (3-5%). The tensile failure is always preceded by plastic buckling of a complementary compression member. This combined necking-buckling (NB) mode critically underlies the collapse of hexagon-triangle (HTH) hierarchical lattices over a wide range of relative densities and length-scale ratios and is also seen in diamond-triangle (DTH) lattices. In lattices with very slender microscale members, necking is prevented by a competing failure mode that involves coordinated buckling (CB) of multiple members. Our custom remeshing FE framework is critical to resolve the localized large plastic strains, ductile failure, and complex local modes of deformation (including cusp formation) that are characteristic of the NB mode. A theoretical buckling analysis supports the inevitability of the NB and CB modes in HTH lattices. The occurrence of the NB mode has consequences for energy absorption by two-scale hierarchical solids, and hence influences their design.