A dissipation‐based arc‐length method for robust simulation of brittle and ductile failure

By Clemens V. Verhoosel, Joris J. C. Remmers, M. A. Gutiérrez. 2009

199 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c5b9491973a4df6cb5ff099220696adae38496f6

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In Biomedical Engineering

In Mechanics of Materials

Citations in the corpus

A level set based model for damage growth: The thick level set approach (2011, unknown): “[45].”
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).”
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].”
An isogeometric analysis approach to gradient damage models (2011, methodology): “A dissipation-based pathfollowing constraint [30] is used to trace the equilibrium path beyond the snapback point.”
A numerical assessment of phase-field models for brittle and cohesive fracture: Γ-Convergence and stress oscillations (2015, methodology): “Introducing an arc-length method to control theloading process as in Verhoosel et al.(2009) andMay et al.(2014), we can parameterise the external load vector asf̃ ext u = λ f̂ , with f̂ a normalised external force vector, andλ a load parameter.”
A phase-field formulation for dynamic cohesive fracture (2018, methodology): “In practice, we have employed penalty kernels in the range of γ = 10(2) − 10(5), which is consistent with those reported in Wheeler et al. (2014). In all cases, the monotonicity penalization is employed, whereas the threshold penalization is only employed in conjunction with the quasi-linear degrada”
Homogenization-based multiscale crack modelling: from micro diffusive damage to macro cracks (2011, background): “Macroscopic snapback can however be handled by, for instance, the energy-based arc-length control given in [36].”
Computational homogenization for adhesive and cohesive failure in quasi‐brittle solids (2010, methodology): “For generality, a dissipation-based arc-length control [24] has been used in this contribution.”