  When used in bulk applications, mechanical metamaterials set forth a
multiscale problem with many orders of magnitude in scale separation between
the micro and macro scales. However, mechanical metamaterials fall outside
conventional homogenization theory on account of the flexural, or bending,
response of their members, including torsion. We show that homogenization
theory, based on calculus of variations and notions of Gamma-convergence, can
be extended to account for bending. The resulting homogenized metamaterials
exhibit intrinsic generalized elasticity in the continuum limit. We illustrate
these properties in specific examples including two-dimensional honeycomb and
three-dimensional octet-truss metamaterials.
