Energy release control for numerical simulations of failure in quasi‐brittle solids

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Coupled-volume multi-scale modelling of quasi-brittle material (2008, methodology): “Another possible procedure to control snap-back behaviour has been introduced by [Gutiérrez, 2004].”
A phantom node formulation with mixed mode cohesive law for splitting in laminates (2009, methodology): “For details of this method we refer to the work by Gutiérrez (2004) and Verhoosel et al. (2008). As usual in arclength methods, a constraint equation is added to the system of equations that is solved iteratively.”
A simplified implementation of a gradient-enhanced damage model with transient length scale effects (2013, methodology): “Conventional displacement control is used to compute the equilibrium path in the elastic regime, whereas a dissipation-based arc-length method [10] is employed thereupon so that any 0 50 100 start end 0 5”
A dissipation‐based arc‐length method for robust simulation of brittle and ductile failure (2009, unknown): “For the simulation of damage evolution, a natural choice is to use a constraint based on the rate of energy dissipation [8].”
Phase-field models for brittle and cohesive fracture (2014, unknown): “Approximation of the ﬁeld variables and their derivatives as results in a nonlinear set of equations which can be linearised and solved using a Newton–Raphson iterative scheme, again enhanced by the dissipation-based arc-length method [14, 21].”