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Mechanical metamaterials are periodic lattice structures with complex unit cell architectures that can achieve extraordinary mechanical properties beyond the capability of bulk materials. Here, we propose a new class of mechanical metamaterials whose mechanical properties rely on deformation induced topological transitions by formation of internal self-contact between nodes. The universal nature of the principle presented is demonstrated by designing metamaterials undergoing topological transitions under tension, compression, shear and torsion. In particular, we show that by frustration of soft in extensional deformation modes, large highly non-linear stiffening effects can be generated in these metamaterials. The topology-induced stiffening can be exploited to design materials that mimic the complex mechanical response of biological tissue, such as human intervertebral discs.

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