  A discrete-to-continuum transformation to model 2-D discrete lattices as
energetically equivalent 1-D continuum beams is developed. The study is
initiated in a classical setting but results in a non-classical two-scale
micropolar beam model via a novel link within a unit cell between the
second-order macrorotation-gradient and the micropolar antisymmetric shear
deformation. The shear deformable micropolar beam is reduced to a couple-stress
and two classical lattice beam models by successive approximations. The
stiffness parameters for all models are given by the micropolar constitutive
matrix. The four models are compared by studying stretching- and
bending-dominated lattice core sandwich beams under various loads and boundary
conditions. A classical 4th-order Timoshenko beam is an apt first choice for
stretching-dominated beams, whereas the 6th-order micropolar model works for
bending-dominated beams as well. The 6th-order couple-stress beam is often too
stiff near point loads and boundaries. It is shown that the 1-D micropolar
model leads to the exact 2-D lattice response in the absence of boundary
effects even when the length of the 1-D beam (macrostructure) equals that of
the 2-D unit cell (microstructure), that is, when L=l.
