A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach

By Timo Heister, Mary F. Wheeler, Thomas Wick. 2015

425 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0344bf9312ac661a6484fff6c1d206e392978057

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Phase-field modeling of fluid-driven dynamic cracking in porous media (2019, background): “However, in recent years, a lot of work has been done on quasi-monolithic (explicit convexification) [48] and fully monolithic methods [59, 60].”
Transfer learning enhanced physics informed neural network for phase-field modeling of fracture (2019, methodology): “The two fields could either be solved simultaneously using the monolithic-solution scheme [18, 19] or they could be solved one at a time using the staggered-solution scheme [13, 14].”
Coupled phase-field and plasticity modeling of geological materials: From brittle fracture to ductile flow (2018, background): “[117]) in conjunction with an internal variable projection scheme for plasticity modeling (e.”
A phase-field modeling approach of fracture propagation in poroelastic media (2018, methodology): “[21] were then enhanced using adaptive element schemes by [23].”
An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation (2020, methodology): “Since the first introduction of the method, numerous open-source implementations were proposed [32,33,39,44].”
The phase field method for geometric moving interfaces and their numerical approximations (2019, methodology): “One may further incorporate other features to model ductile fracture [14, 324] and fluid-filled fracture [423], and utilize various discretization techniques, see recent discussions in [253, 446].”
On penalization in variational phase-field models of brittle fracture (2018, background): “Alternatively, the so-called monolithic approach which treats arguments simultaneously manifests major iterative convergence issues of the Newton-Raphson procedure due to non-convexity [59, 61, 62, 63];”
Phase-field modeling of a fluid-driven fracture in a poroelastic medium (2015, methodology): “Compute active set Ak (see Remark 6 and [13]).”
Goal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity (2016, methodology): “A remedy has been presented in [30] in which a predictor-corrector scheme has been applied in order to ensure the ‘correct’ size of ε > h at each time step of a propagating fracture with high mesh resolution.”
Modified Newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation (2017, methodology): “Consulting our computational experiences from [32, 73] in which we designed a very efficient and robust method by neglecting the cross-term block, we conjecture that the most critical term is the off-diagonal contribution”
Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model (2016, background): “(40)”