Modeling the effective elastic behavior of composites: a mixed finite element and homogenisation approach

To make possible the Finite Element computation of Representative Volume Elements (RVE) of composites with a complex microstructure, we first propose to mesh the volume independently of the considered microstructure. Homogeneous elastic properties are then given to the elements whose behavior is ill-defined (different phases in the same element) while a polarization is homogeneously applied to these so-called 'interphase elements' to control the corresponding error. New bounds are derived by optimizing the polarisation. When interphase elements are given extreme elastic properties these bounds yield satisfying results in both cases of a unit cell as well as a concrete RVE.