An approximate multiscale model for aging viscoelastic materials exhibiting time-dependent Poisson's ratio

A multi-scale homogenization scheme is proposed to estimate the time-dependent strains of fiber-reinforced concrete. This material is modeled as an aging linear viscoelastic composite material featuring ellipsoidal inclusions embedded in a viscoelastic cementitious matrix characterized by a time-dependent Poisson's ratio. To this end, the homogenization scheme proposed in Lavergne et al. [1] is adapted to the case of a time-dependent Poisson's ratio and it is successfully validated on a non-aging material computed in the Fourier domain. Finally, the new extended estimates of the time-dependent strains of fiber-reinforced concrete are compared to the experimental measurements of Chern and Young [2] and the effects of the volume fraction and aspect ratio of the steel fibers on the time-dependent strains of fiber-reinforced concrete are investigated.