Predictive abilities of pseudodiscretization and pseudograin discretization schemes of the Mori–Tanaka homogenization, benchmarked against real and virtual RVEs

Abstract

In this article, the predictive abilities of two prevalent homogenization formulations, two-step Mori–Tanaka (MT–MT) and MT–Voigt are benchmarked using virtual representative volume element (RVE) involving full FE models and real RVE using prior published experimental data. MT–MT and MT–Voigt are interpreted as involving “pseudodiscretization” and “pseudograin discretization,” respectively. A comprehensive test campaign involving all possible permutations and combinations of modulus of inclusions and matrix (inclusions stiffer than the matrix and vice versa) and different loading types are conducted. The comparisons are done at three length scales: effective modulus, stresses in individual inclusions, stress distribution in the interphase, and strain at the onset of interphase debonding. Overall, both schemes have similar predictive capabilities for the effective modulus and phase average stress. The predictions of the stresses in the individual inclusions for complex RVEs with inclusions length and orientation distribution are correct as average trends but do not represent the full details of the FE-revealed strain scatter. Depending on the modulus mismatch, or loading direction, better predictions can be achieved by either MT–MT or MT–Voigt, even if the microstructure considered remains the same. The relative difference in the strain at the onset of debonding, predicted by MT–MT and MT–Voigt formulations, is about 10%. HIGHLIGHTS Two-step MT–MT and MT–Voigt are benchmarked against virtual and real RVEs Comparisons are done for all permutations of modulus mismatch and loading types Predictions are compared at three length scales: RVE, inclusions, and interphase