A coupled elastoplastic damage model for geomaterials

By M. Salari, S. Saeb, K. Willam, S. Patchet, R. Carrasco. 2004

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Computational applications of a coupled plasticity-damage constitutive model for simulating plain concrete fracture (2010, background): “[13,16,23,29–31,33,34,44,53,65,69,70,79,81,82]), where the effective stress is defined as the average micro-scale stress acting on the undamaged material between micro-defects.”
An elastic plastic damage formulation for concrete: Application to elementary tests and comparison with an isotropic damage model (2006, background): “[39], Lee and Fenves [24], Faria et al.”
Bouc–Wen-Type Models with Stiffness Degradation: Thermodynamic Analysis and Applications (2008, methodology): “The formalism of the loading function fD, as well as the pseudo-potential φ ∗ D = IfD≤0 , can be used to express the damage evolution (Lemaitre and Chaboche, 1990; Salari et al., 2004; Nedjar, 2001; Frémond, 2002).”
Coupled damage and plasticity models derived from energy and dissipation potentials (2007, background): “As observed by Simo and Ju (1987), and supported in the above, this means that the strain equivalence is naturally associated with strain-based formulation and the stress equivalence corresponds to a stress-spaced formulation.”