Homogenization and continuum limit of mechanical metamaterials.

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. • The homogenization theory can be extended to account for bending. • Homogenized metamaterials show intrinsic generalized elasticity in continuum limit. • Specific examples, 2-D honeycomb and 3-D octet-truss metamaterials, are analysed. [ABSTRACT FROM AUTHOR]