The widespread proliferation of cellular lattices in engineering design has entailed a revolution in the design of lightweight and multifunctional structures. Furthermore, the development of auxetic metamaterials has led to applications in fields ranging from biomedical to civil engineering. However, cellular lattices suffer from the development of localized concentrations of strains during deformation, which lead to sub-optimal mechanical performance. Furthermore, the mechanical properties of cellular lattices are dependent on their macro-scale geometries, limiting their design space. Thus, we seek to both enhance the mechanical properties of lattices by ameliorating strain concentrations and expand the design space of cellular lattices.

In attempting to do so, we can turn to nature. The bio-inspired design motif of the hierarchical arrangement of composite materials has lead to exceptional mechanical characteristics in natural materials. Moreover, morphogenetic processes such as bone remodelling play a vital role in the structural development of natural materials and their hierarchical material arrangement. Motivated by these concepts, we developed an algorithm that optimised the hierarchical material arrangement of hard and soft voxels in an auxetic and non-auxetic unit cell. Our algorithm does so based on a bone remodelling-like approach of strain energy optimisation, whereby elements are transitioned to a hard or soft material based on local strain energy.

Our finite element (FE) simulation results demonstrate the considerable expansion of the range of mechanical properties we can achieve simply by modifying material placement on a micron scale. We also observe clear mitigation of peak strain energies and more homogeneous distributions of strain energy density, which affirm the amelioration of strain concentrations. Furthermore, we were able to increase the stiffnesses of our unit cells without substantially affecting its Poisson’s ratio, disentangling previously interdependent mechanical properties. We further validated our FE simulations by additively manufacturing our optimised unit cells with state-of-the-art voxel-based printing. Both the mechanical properties predicted by our FE simulations and the strain distributions correlated well with digital image correlation recordings, validating our models. Our mechanical testing also revealed the considerable in- creases in ultimate tensile strength of our optimised designs, demonstrating the benefits of hierarchical material arrangement.

To conclude, we demonstrate the efficacy of strain energy-based material optimisation to improve the mechanical properties of unit cells and mitigate strain concentrations. The design paradigms of hierarchical arrangement of composite materials remarkably improved the material space of a unit cell without changing its macro-scale geometry. Findings from this study could enable the optimisation of existing cellular lattices and the development of novel unit cell designs with distinct intrinsic mechanical properties.