An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals

By R. Masson, M. Bornert, Pierre Suquet, A. Zaoui. 2000

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Homogenization of elasto-(visco) plastic composites based on an incremental variational principle (2012, background): “The affine formulation of Masson et al. (2000) is an interesting alternative to Hill’s formulation (see also (Zaoui, 2002)).”
Multiscale modeling of plasticity based on embedding the viscoplastic self-consistent formulation in implicit finite elements (2012, methodology): “Depending on the linearization assumption, M(r) and _eoðrÞ can be chosen differently.2 For instance, making use of the affine linearization (Masson et al., 2000): MðrÞ ¼ n _co X k mkðrÞ mkðrÞ skðrÞo mkðrÞ : r0ðrÞ skðrÞo !n 1 ð16Þ _eoðrÞ ¼ ð1 nÞ _co X k mkðrÞ : r0ðrÞ skðrÞo !n sgnðmkðrÞ : r0ðrÞÞ…”
Micromechanical modeling of coupled viscoelastic–viscoplastic composites based on an incrementally affine formulation (2013, neutral): “, 1987) and affine (Masson et al., 2000) approaches.”
Crystal Plasticity Finite Element Methods: in Materials Science and Engineering (2010, background): “(1982), Peirce, Asaro, and Needleman (1983), Asaro and Needleman (1985) Becker (1991), Becker et al.”