Homogenization of multi-coated inclusion-reinforced linear elastic composites with eigenstrains: application to the thermo-elastic behavior

Stephane Berbenni (1) , Mohammed Cherkaoui (2)

1 ENSAM
2 Mechanical Engineering

A new micromechanical approach for arbitrary multi-coated ellipsoidal elastic inclusions with general eigenstrains is developed. We start from the integral equation of the linear elastic medium with eigenstrains adopting the Green's function technique and we apply a "$(n+1)$-phase" model with a self-consistent condition to determine the homogenized behavior of multi-coated inclusion-reinforced composites. The effective elastic moduli and eigenstrains are obtained as well as the residual stresses through the local stress concentration equations. The effective eigenstrains are determined either with the concentration tensors here obtained by the present model, or, more classically, with Levin's formula. In order to assess our micromechanical model, some applications to the isotropic thermo-elastic behavior of composites with and without interphase are given. In particular, "$4$-phase" and "$3$-phase" models are derived for isotropic homothetic spherical inclusion-reinforced materials, and, the results are successfully compared to exact analytical solutions regarding the effective elastic moduli and the effective thermal expansion.

Mots clés: Physical Sciences

Stephane Berbenni, Mohammed Cherkaoui. Homogenization of multi-coated inclusion-reinforced linear elastic composites with eigenstrains: application to the thermo-elastic behavior. Philosophical Magazine, 2010, 90 (22), pp.3003-3026. ⟨10.1080/14786431003767033⟩. ⟨hal-00599234⟩