Identification of Cosserat elastic overall media of quasi-periodic lattices

For a few years, the interest in architectured materials has grown since they enable to reach new zones of Ashby diagrams. Quasi-periodic lattices are a class of porous materials that appear locally disorganised but are highly deterministic, as shown by their sharp diffraction diagrams. Few studies on their mechanical behaviours have been done, but they seem to combine the advantages of foams and periodic lattices: isotropic behaviour and a better toughness. Their widespread use requires the ability to identify an equivalent medium, i.e a fictitious homogeneous medium having the same macroscopic behaviour. An appropriate behaviour law must be chosen. However, it has been shown that classical laws could be insufficient. The objective of this study is to identify the apparent Cauchy and Cosserat elastic parameters for different quasi-periodic patterns and determine which model is the most suitable.