Material such as granular media, beam assembly are easily seen as discrete
media. They look like geometrical paints linked together thanks to energeti
c expressions. Our purpose is to extand discrete kinematics to the one of a
n equivalent continuous material. First we explain how we build the localis
ation tool for periodic materials according to estimated continuum medium t
ype (classical Cauchy, and Cosserat media). Once the bridge built between d
iscrete and continuum media, we exhibit its application over two bidimensio
nal beam assembly structures : the honey comb and a structural reinforced v
ariation. The new behavior is then applied for the simple plan sheer proble
m in a Cosserat continuum and compared with the real discrete solution. By
the mean of this example, we establish the agreement of our new model with
real structures. The exposed method has a longer range than mechanics and c
an be applied to every discrete problems like electromagnetism in which rel
ationship between geometrical points can be summed up by an energetic funct
ion.