An incremental-secant mean-field homogenisation method with second statistical moments for elasto-plastic composite materials

In this paper, the incremental-secant mean-field homogenisation (MFH) scheme recently developed by the authors is extended to account for second statistical moments. The incremental-secant MFH method possesses several advantages compared to other MFH methods. Indeed the method can handle non-proportional and non-monotonic loadings, while the instantaneous stiffness operators used in the Eshelby tensor are naturally isotropic, avoiding the isotropisation approximation required by the affne and incremental-tangent methods.
Moreover, the incremental-secant MFH formalism was shown to be able to account for material softening when extended to include a non-local damage model in the matrix phase, thus enabling an accurate simulation of the onset and evolution of damage across the scales.
In this work, by accounting for a second statistical moment estimation of the current yield stress in the composite phases, the plastic flow computation allows capturing with a better accuracy the plastic yield in the composite material phases, which in turn improves the accuracy of the predictions, mainly in the case of short fibre composite materials. The incremental-secant mean-field-homogenisation (MFH) can thus be used to model a wide variety of composite material systems with a good accuracy.