Mechanical metamaterial inspired by biological tissues

We introduce an amorphous mechanical metamaterial inspired by how cells pack in biological tissues. The spatial heterogeneity in the local stiffness of these materials has been recently shown to impact the mechanics of confluent biological tissues and cancer tumors (Li et al Phys. Rev. Lett. 123, 058101 (2019)). Here we use this bio-inspired model as a design template and show that this heterogeneity can give rise to amorphous cellular solids with large, tunable phononic bandgaps. Unlike in phononic crystals, the band gaps here are directionally isotropic due to their complete lack of positional order. The size of the bandgap can be tuned by a combination of local stiffness heterogeneity and the local elasticity modulus. Finally, we also investigated the possibility of introducing a topological nature in the mechanical response using a hexagonal lattice version of the same model. By tuning the local elasticity moduli, we demonstrate the emergence of a pseudo-spin state and as well chiral mechanical response. This constitutes a mechanical analogue of the quantum spin Hall effect.