A thermodynamically motivated implicit gradient damage framework and its application to brick masonry cracking

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Localizing gradient damage model with decreasing interactions (2017, methodology): “Note that the same damage model as [26] was developed in [31] by requiring that the second law of thermodynamics be satisfied only in a global sense.”
A Method for Gradient Enhancement of Continuum Damage Models (2008, unknown): “The first one is based on an energy-release rate threshold condition and corresponds to the model of Simo and Ju (1987): φd := q − r1 ≤ 0 (19) ḋ = κ̇ (20) and the second one is based on the energy-release rate of the positive strains and distinguishes between the material response in tension and com”
Micromorphic Approach for Gradient Elasticity, Viscoplasticity, and Damage (2009, methodology): “Such a framework has been sketched in the reference Peerlings et al. 2004 where a quadratic potential similar to Eq.”
Mixed variational principles and robust finite element implementations of gradient plasticity at small strains (2013, background): “A thermodynamic foundation was given later in [25, 34] in the context of a micromorphic theory.”