Tunable Non-Linear Stiffening by Deformation-Induced Topological Transitions in Mechanical Metamaterials

Mechanical metamaterials are architected to exhibit mechanical properties, which are not found in conventional bulk materials. The topology of such cellular solids, i.e. the number of beams or walls meeting at nodes or edges, governs much of the mechanical properties [1]. Commonly, mechanical metamaterials posses one invariant topological state. Here, we introduce a metamaterial which undergoes a transition in topology when deformed. This transition manifests itself by the formation of internal self-contacts, resulting in a change from a soft, bending-dominated, to a rigid, stretch-dominated deformation mode. Huge non-linear stiffening effects of almost two orders of magnitude can be generated. The universal nature of our approach is demonstrated by designing metamaterials switching topology under tension, compression, shear, and torsion. The large magnitude of the stiffening as well as the stress and strain at which the topology transition takes place can be tuned by selection of the design parameters. The design space is extensively explored using finite element simulations. Physical specimens of the metamaterial are fabricated by only recently developed commercial silicone stereolithography 3D printing. The experimental characterization shows good agreement with the numerical simulations.<br/>The non-linear mechanical response of our metamaterials closely resembles the mechanical behavior of soft biological tissue. Examples for this are the non-linear compressive and torsional behavior of human intervertebral disks [2], or the tensile stiffness of human skin [3]. Hence, the presented principle of topological transitions in mechanical metamaterials has potential application in the bio-medical field, for examples in intervertebral disk implants.<br/><br/><br/><br/>[1] Gibson, L.J. and Ashby, M.F., Cellular Solids: Structure and Properties. Cambridge Solid State Science Series. 1999: Cambridge Univ. Press.<br/>[2] Newell, N., Little, J.P., Christou, A., Adams, M.A., Adam, C., Masouros, S.: Biomechanics of the human intervertebral disc: a review of testing techniques and results. Journal of the mechanical behavior of biomedical materials 69, 420–434 (2017)<br/>[3] Annaidh, A.N., Bruyere, K., Destrade, M., Gilchrist, M.D., Ottenio, M.: Characterization of the anisotropic mechanical properties of excised human skin. Journal of the mechanical behavior of biomedical materials 5(1), 139–148 (2012)