Study of various estimates of the macroscopic tangent operator in the incremental homogenization of elastoplastic composites

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Micromechanics of particle-reinforced elasto-viscoplastic composites : Finite element simulations versus affine homogenization (2007, methodology): “Differences in the isotropisation method influence the concentration tensors at each phase and might have a considerable impact on the final result, as has been shown for the incremental formulation in elasto-plasticity ( Pierard and Doghri, 2006b ).”
Homogenization of elasto-(visco) plastic composites based on an incremental variational principle (2012, methodology): “For comparison, we also show results obtained with an incremental tangent method (Doghri and Ouaar, 2003; Pierard and Doghri, 2006b), labeled ‘‘Inc.Tgt’’ in the figures and briefly described in Appendix C.”