New mean-field homogenization schemes for the constitutive modelling of the elastic and elastoplastic deformation behavior of multi-phase materials

In this study, a new class of mean-field homogenization (MFH) models were developed based on the underlying concepts of the direct and inverse Mori-Tanaka and Lielens MFH schemes. The proposed models were employed to predict the elastic and elastoplastic constitutive responses for a range of representative multi-phase materials, including polymer- and metal-matrix composites and a dual-phase steel. To evaluate the performance of the developed MFH models in the elastic region, their predictions for the elastic constants of graphite-reinforced epoxy, Al2O3 -reinforced AA7075, and TiB2-reinforced AISI 1045 steel with different ellipsoidal-inclusion shapes and volume fractions were compared with the results of unit-cell finite element method (FEM) simulations under uniaxial-tension loading. For the plastic region, the proposed MFH models were coupled with various linearization approaches, including the first-order secant-based and tangent-based schemes, to estimate the flow behavior of DP590 steel in uniaxial tension. The MFH predictions were shown to compare favorably with the results of unit-cell FEM simulations and experiment. Moreover, the predictive ability of the developed models for both elastic and plastic responses was assessed via comparisons with the approximations of the self-consistent and Mori-Tanaka MFH models. The results showed that the proposed MFH models can describe the elastic and elastoplastic behavior of heterogeneous materials with different constituent volume fractions as well as or better than conventional MFH models.