A mathematical basis for strain-gradient plasticity theory. Part II: Tensorial plastic multiplier

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BASIC STRAIN GRADIENT PLASTICITY THEORIES WITH APPLICATION TO CONSTRAINED FILM DEFORMATION (2011, methodology): “…are presented for both the rate-independent formulation and the viscoplastic, rate-dependent formulation [Gudmundson 2004; Gurtin and Anand 2005; Fleck and Willis 2009b], with either full constraint on plastic flow at the platens (εP12 = ε P 11 = ε P 22 = ε P 33 = 0) or no constraint on plastic…”
Generalizing J2 flow theory: Fundamental issues in strain gradient plasticity (2012, methodology): “An unintended consequence of this new formulation has been highlighted by the work of Fleck and Willis [6], who formulated variational principles for incremental boundary value problems based on this class of theories.”
Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua (2010, methodology): “…theory has been provided by several authors (Forest et al., 2002; Gurtin and Anand, 2009; Fleck and Willis, 2009b) for models including the gradient of a scalar plastic measure, and (Forest and Sievert, 2003; Gurtin, 2003; Fleck and Willis, 2009a) for the gradient of the full plastic strain tensor.”