Homogenization of discrete media

Authors
Citation
F. Pradel et K. Sab, Homogenization of discrete media, J PHYS IV, 8(P8), 1998, pp. 317-324
Citations number
6
Categorie Soggetti
Physics
Journal title
JOURNAL DE PHYSIQUE IV
ISSN journal
11554339 → ACNP
Volume
8
Issue
P8
Year of publication
1998
Pages
317 - 324
Database
ISI
SICI code
1155-4339(199811)8:P8<317:HODM>2.0.ZU;2-N
Abstract
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.