  Lattice models for the second-order strain-gradient models of elasticity
theory are discussed. To combine the advantageous properties of two classes of
second-gradient models, we suggest a new lattice model that can be considered
as a discrete microstructural basis for gradient continuum models. It was
proved that two classes of the second-gradient models (with positive and
negative sign in front the gradient) can have a general lattice model as a
microstructural basis. To obtain the second-gradient continuum models we
consider a lattice model with the nearest-neighbor and next-nearest-neighbor
interactions with two different coupling constants. The suggested lattice model
gives unified description of the second-gradient models with positive and
negative signs of the strain gradient terms. The sign in front the gradient is
determined by the relation of the coupling constants of the nearest-neighbor
and next-nearest-neighbor interactions.
