Numerical and analytical estimation of the ageing linear viscoelastic behavior of a two-phase composite with expansive inclusions

We investigate the behavior of a two-phase composite consisting of an inclusive elastic phase and an ageing linear viscoelastic matrix (ALVE) experiencing an expansion of the inclusions or equivalently a differential dilation of both phases. We propose, based on an analogy with thermoviscoelasticity, to estimate the macroscopic mechanical properties of the composite and to determine its overall free strains and macroscopic coefficient of expansion. Numerically, 3D cubic specimens are generated with spherical or polyhedral inclusion shapes. Finite element simulations are then performed, allowing to calculate the macroscopic strains generated by the expansions, as well as the moduli at different time of loading. The effect of the inclusions shape on both local and macroscopic behavior are also studied. Analytically, a methodology suitable for estimating the overall behavior of composite materials in an ALVE context is applied, and extended to the case of ageing linear thermoviscoelasticity. Specifically, the macroscopic effects of the expansion of inclusions assumed as spherical are determined via the dilation coefficient, and obtained by a semi-explicit homogenization procedure. Finally, numerical and analytical results are compared in terms of macroscopic response and mechanical properties at different ages, and for various ageing and expansion functions.