Field statistics in linear viscoelastic composites and polycrystals

• Estimates for the effective response of linear viscoelastic composites.
• Estimates for the statistics of the stress field within the phases of the composite.
• Application to two-phase particulate composites and polycrystalline materials.

The aim of this study is to estimate the effective response, as well as the statistics of the fields (average and fluctuations per phase) in linear viscoelastic heterogeneous materials. To this effect, a variational method based on a rate variational principle (RVP) has recently been introduced by the authors in which, at each time step, the stress or strain fields are approximated by those of a linear thermoelastic comparison composite. In the present study, a different derivation of this estimate is proposed, based on a simple approximation of the stress field along the time steps. The present study also explores the accuracy of the RVP model by comparing its predictions with reference results, either in closed form (for specific two-phase particulate composites) or obtained by full-field simulations (FFT method) for 2D polycrystals. A differential equation for the second moment of the stress field in the individual phases of two-phase particulate composites is given for the first time. These comparisons show that the RVP model delivers a very accurate estimate of the effective behavior as well as of the statistics of the local fields in two-phase particulate composites. For polycrystalline materials subjected to monotonic loading, the effective behavior and the statistics of the local fields are well predicted. The agreement is less accurate for cycling loadings.