  We resort to variational methods to evaluate the asymptotic behavior of fine
metamaterials as a function of cell size. To zeroth order, the metamaterial
behaves as a micropolar continuum with both displacement and rotation degrees
of freedom, but exhibits linear-elastic fracture mechanics scaling and
therefore no size effect. To higher order, the overall energetics of the
metastructure can be characterized explicitly in terms of the solution of the
zeroth-order continuum problem by the method of {\Gamma}-expansion. We present
explicit expressions of the second-order correction for octet frames. As an
application, we evaluate the compliance of double-cantilever octet specimens to
second order and use the result to elucidate the dependence of the apparent
toughness of the specimen on cell size. The analysis predicts the discreteness
of the metamaterial lattice to effectively shield the crack-tip, a mechanism
that we term lattice shielding. The theory specifically predicts
anti-shielding, i. e., coarser is weaker, in agreement with recent experimental
observations.
