Homogenization of discrete media

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.