Macroscopic modelling of structured materials: Relationship between orthotropic Cosserat continuum and rigid elements

The macroscopic modelling of in-plane elastic behaviour of composite solids made with regular orthotropic texture is the object of the present study. At the macro-scale, the effect of heterogeneity can be included by adopting an homogenisation toward a generalised continuum on which specific finite element codes are based. As an alternative, a specific rigid element approach has been recently proposed [Casolo, S., 2004. Modelling in-plane micro-structure of masonry walls by rigid elements. International Journal of Solids and Structures 41(13), 3625–3641] based on a discrete mechanistic formulation. This paper presents a sequel of such research, and expounds the theoretical relationship between the orthotropic Cosserat continuum and the proposed rigid elements. Then, referring to two different masonry-like textures, the constitutive parameters of the corresponding Cosserat continuum and of the rigid element model are calculated. Numerical analyses compare their performance, and display the impact of the composite texture in the case of a concentrated load. The capability to discern the behaviour of different structured materials at the macro-scale is pointed out by observing how the local rotation of the blocks and the consequent different deformation of vertical and horizontal joints have influence on the strain field maps.