Multiscale non linear FE2 analysis of composite structures: Fiber size effects

An imbricated finite element technique has been recently developed in the c ontext of multiscale inelastic analysis of composite structures. The consti tutive equations in the classical overall inelastic analysis are replaced b y a lower level finite element analysis within the periodic homogenization framework. All the physics of the problem, included in the local elastovisc oplastic and damage equations, is written for constituents at the microscal e. Contrarily to more classical approaches, the two scales are coupled, the local behavior being integrated in-situ and in real time. This method is e xtended to take into account the case of material having an intrinsic lengt h by coupling a Cosserat continuum at the macroscopic scale and a Cauchy co ntinuum at the lower scale. This kind of modeling allows: (i) to easily bui ld non-linear behavior for high oder mechanical theories (Cosserat, 2nd gra de material, etc...) and (ii) to treat some cases which can not be handled by classical theories, such as "coarse grains" composite materials.