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

Abstract
An imbricated finite element technique has been recently developed in the context of multiscale inelastic analysis of composite structures. The constitutive equations in the classical overall inelastic analysis are replaced by a lower level finite element analysis within the periodic homogenization framework. All the physics of the problem, included in the local elastoviscoplastic and damage equations, is written for constituents at the microscale. Contrarily to more classical approaches, the two scales are coupled, the local behavior being integrated in-situ and in real time. This method is extended to take into account the case of material having an intrinsic length by coupling a Cosserat continuum at the macroscopic scale and a Cauchy continuum at the lower scale. This kind of modeling allows: (i) to easily build non-linear behavior for high oder mechanical theories (Cosserat, 2nd grade material, etc. . . ) and (ii) to treat some cases which can not be handled by classical theories, such as "coarse grains" composite materials.