Deformation-induced topological transitions in mechanical metamaterials and their application to tunable non-linear stiffening

Mechanical metamaterials are periodic lattice structures with complex unit cell architectures that can achieve extraordinary mechanical properties beyond the capability of bulk materials. A new class of metamaterials is proposed, whose mechanical properties rely on deformation-induced transitions in nodal-topology by formation of internal self-contact. The universal nature of the principle presented, is demonstrated for tension, compression, shear and torsion. In particular, it is shown that by frustration of soft deformation modes, large highly non-linear stiffening effects can be generated. Tunable non-linear elasticity can be exploited to design materials mimicking the complex mechanical response of biological tissue.