A simplified implementation of a gradient-enhanced damage model with transient length scale effects

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Regularization of microplane damage models using an implicit gradient enhancement (2014, background): “For isotropic damage models, it is sufficient to apply the enhancement for a scalar valued quantity, such as the equivalent strain (Saroukhani et al., 2013), thus the extra degrees of freedom is limited to 1.”
Localizing gradient damage model with decreasing interactions (2017, methodology): “The original formulation of the strain-based transient gradient damage model requires an extra continuity equation in its implementation, but which has been reformulated to avoid this additional requirement [18].”