Homogenization schemes for aging linear viscoelastic matrix-inclusion composite materials with elongated inclusions

An extension of the Mori-Tanaka and Ponte Castañeda-Willis homogenization schemes for linear elastic matrix-inclusion composites with ellipsoidal inclusions to aging linear viscoelastic composites is proposed. To do so, the method of Sanahuja (2013) dedicated to spherical inclusions is generalized to ellipsoidal inclusions under the assumption of time-independent Poisson's ratio. The obtained time-dependent strains are successfully compared to those predicted by an existing method dedicated to time-shift aging linear viscoelasticity showing the consistency of the proposed approach. Moreover, full 3D numerical simulations on complex matrix-inclusion microstructures show that the proposed scheme accurately estimates their overall time-dependent strains. Finally, it is shown that an aspect ratio of aggregates in the range 0.3-3 has no significant influence on the time-dependent strains of composites with per-phase constitutive relations representative of a real concrete.