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

Abstract

In this paper, the incremental-secant mean-field homogenization (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 isotropization approximation required by the affine 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 MFH can thus be used to model a wide variety of composite material systems with a good accuracy.

Keywords:

• multiscale
• mean-field homogenization
• composites
• second statistical moments

Notes

No potential conflict of interest was reported by the authors.

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