Density-graded Voronoi honeycombs – A local transversely isotropic description

Abstract

Density-graded cellular materials, in which their relative density varies with location, are amenable to design for multi-functions, and have been used in mechanical buffers and protective structures. To estimate the force–deformation responses of density-graded cellular materials efficiently without resorting to modelling individual cells, a constitutive model based on local transverse isotropy is adopted. Metallic Voronoi honeycomb-like specimens with cell sizes that vary with position, are fabricated via 3D printing, to represent a density-graded cellular material with local transverse isotropy that varies with position. From quasi-static compression tests and cell-based finite element (FE) simulations, the influence of relative density on the continuum constitutive model is investigated and demonstrated to be significant. The model is then used to predict the global stress–strain response and deformation of cellular materials with positive and negative density-gradients, defined along the loading direction, subjected to uniaxial quasi-static compression, quasi-static indentation, and dynamic compression. The results show that for quasi-static compression, severe plastic deformation progresses from the low relative density region to the high relative density region; however, impact loading and indentation of negative density-gradient Voronoi honeycombs generates two zones of gross deformation – in the vicinity of the applied load and the opposite lower density end. Predictions based on the proposed constitutive model display good correlation with experimental and cell-based FE results.