A Method for Gradient Enhancement of Continuum Damage Models

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On the implementation of finite deformation gradient-enhanced damage models (2019, methodology): “The considered non-local, gradient-enhanced damage framework is based on the work by Waffenschmidt et al. [47], where, following a concept by Dimitrijević andHackl [8], the local free energy of the underlying material is enhanced by a non-local gradient term.”
A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts (2018, methodology): “In (29) each term is weighted by a damage function of the specific form (Dimitrijević and Hackl, 2008)”
Modelling large crack propagation: from gradient damage to cohesive zone models (2012, unknown): “…formulation of damage relies on the introduction of the Laplacian of the damage field inside the threshold function, see for instance Fremond and Nedjar (1996), Comi (1999), Lorentz and Andrieux (1999), Liebe et al. (2001), Dimitrijevic and Hackl (2008), Pham et al. (2010); it is described in Sect.”
A regularization framework for damage–plasticity models via gradient enhancement of the free energy (2011, background): “Following the work in [19, 20], which shares the same spirit with the so-called micromorphic approach presented in [21], it depends on newly introduced variables d (enhancing the damage parameter d) and P (enhancing the plastic softening parameter P) and their gradients, in addition to the selected ”