  Owing to additive manufacturing techniques, a structure at millimeter length
scale (macroscale) can be produced by using a lattice substructure at
micrometer length scale (microscale). Such a system is called a metamaterial at
the macroscale as the mechanical characteristics deviate from the
characteristics at the microscale. As a remedy, metamaterial is modeled by
using additional parameters; we intend to determine them. A homogenization
approach based on the asymptotic analysis establishes a connection between
these different characteristics at micro- and macroscales. A linear elastic
first order theory at the microscale is related to a linear elastic second
order theory at the macroscale. Relation for parameters at the macroscale is
derived by using the equivalence of energy at macro- and microscales within a
so-called Representative Volume Element (RVE). Determination of parameters are
succeeded by solving a boundary value problem with the Finite Element Method
(FEM). The proposed approach guarantees that the additional parameters vanish
if the material is purely homogeneous, in other words, it is fully compatible
with conventional homogenization schemes based on spatial averaging techniques.
Moreover, the proposed approach is reliable as it ensures that such resolved
additional parameters are not sensitive to choices of RVE consisting in the
repetition of smaller RVEs but depend upon the intrinsic size of the structure.
