abstract
- This study addresses the estimation of the effective thermoelastic properties of hierarchical composites whose coating phase is not a homogeneous material but their properties result from a lower-scale heterogeneous microstructure. A reiterated semi-analytical homogenization framework is proposed for a three-phase composite formed by a central spherical inclusion, an equivalent shell, and an external matrix. The shell is first obtained from a periodic multiphase composite containing ellipsoidal inclusions, whose equivalent anisotropic thermoelastic properties are determined through a first homogenization step and subsequently used as the coating phase in a second homogenization problem. In this way, the proposed model differs from previous two-phase semi-analytical approaches by coupling two successive homogenization levels and transferring the anisotropy generated at the shell scale to the overall coated-inclusion composite. The governing equations for local problems on a unit cell are derived via asymptotic homogenization and solved using the finite element method. The full periodic unit cell is reduced to one-eighth of the original cell by exploiting its geometric symmetry together with the parity of the local fields, whereby the periodic boundary conditions are transformed into equivalent mixed boundary conditions. This reduction assumes a periodic microstructure and material properties that are even functions with respect to the local coordinate system centered on the unit cell. The methodology is first validated for a two-phase composite reinforced by spherical inclusions through comparison with classical variational bounds and is subsequently applied to investigate the influence of the shell microstructure and the radius of the central spherical inclusion on the effective elastic, thermal-stress, thermal-expansion, and thermal-conductivity coefficients. The numerical implementation is carried out in COMSOL Multiphysics to compute the effective thermoelastic coefficients.