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The architecture of mechanical metamaterialsis designed to harness geometry,non-linearity and topology to obtain advanced functionalities such as shapemorphing, programmability and one-way propagation. While a purely geometricframework successfully captures the physics of small systems under idealizedconditions, large systems or heterogeneous driving conditions remainessentially unexplored. Here we uncover strong anomalies in the mechanics of abroad class of metamaterials, such as auxetics, shape-changers or topologicalinsulators: a non-monotonic variation of their stiffness with system size, andthe ability of textured boundaries to completely alter their properties. Thesestriking features stem from the competition between rotation-baseddeformations---relevant for small systems---and ordinary elasticity, and arecontrolled by a characteristic length scale which is entirely tunable by thearchitectural details. Our study provides new vistas for designing, controllingand programming the mechanics of metamaterials in the thermodynamic limit.

A characteristic lengthscale causes anomalous size effects and boundary programmability in mechanical metamaterials