Framework using functional forms of hardening internal state variables in modeling elasto-plastic-damage behavior

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Numerical failure analysis of a stretch-bending test on dual-phase steel sheets using a phenomenological fracture model (2010, background): “Consequently, a family of continuum damage mechanics models has been developed under thermodynamic framework (Lemaitre, 1985; Chaboche, 1988a,b; Voyiadjis and Dorgan, 2007).”
Crystal Plasticity Finite Element Methods: in Materials Science and Engineering (2010, background): “Many have recognized that damage represented by D is not isotropic, and have introduced vectorial and tensorial modifications to this idea to simulate failure processes associated with crystallographic planes, intergranular fracture, or growth and distortion of voids (Brunig and Ricci, 2005; Luccion”
Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading – Part II: Ductile fracture (2012, methodology): “…damage, more complex CDM models featuring a tensorial (and hence direction sensitive) damage variable have been proposed (e.g. Brünig et al., 2008; Brünig and Gerke, 2011; Chow and Wang, 1987; Chow et al., 2001; Hammi and Horstemeyer, 2011; Menzel and Steinmann, 2001; Voyiadjis and Dorgan, 2007).”
Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications (2010, unknown): “[333] or Voyiadjis and Dorgan [334].”