Journal ArticleDOI
An augmented-Lagrangian method for the phase-field approach for pressurized fractures
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TLDR
This work proposes an augmented Lagrangian algorithm for the discrete in time and continuous in space phase-field problems and states that for large penalty parameters the algorithm suffers from numerical instabilities in the solution process.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2014-04-01. It has received 228 citations till now. The article focuses on the topics: Augmented Lagrangian method & Variational inequality.read more
Citations
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Crack nucleation in variational phase-field models of brittle fracture
TL;DR: In this paper, the authors use U-and V-notches to show that the nucleation load varies smoothly from that predicted by a strength criterion to that of a toughness criterion when the strength of the stress concentration or singularity varies.
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A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach
TL;DR: In this paper, a primal-dual active set strategy is proposed to enforce crack irreversibility as a constraint, which can be identified as a semi-smooth Newton method, and the active set iteration is merged with the Newton iteration for solving the fully-coupled nonlinear partial differential equation discretized using finite elements.
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Phase field modeling of fracture in multi-physics problems. Part III. Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media
Christian Miehe,Steffen Mauthe +1 more
TL;DR: In this article, a macroscopic framework is proposed for a continuum phase field modeling of fracture in porous media, which provides a rigorous geometric approach to a diffusive crack modeling based on the introduction of a constitutive balance equation for a regularized crack surface and its modular linkage to a Darcy-Biot type bulk response of hydro-poro-elasticity.
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A phase-field modeling approach of fracture propagation in poroelastic media
TL;DR: In this paper, a phase field model for fracture in poroelastic media is proposed, where the fracture propagation is driven by the elastic energy where the phase field is used as an interpolation function to transit fluid property from the intact medium to the fully broken one.
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Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model
TL;DR: Robust and efficient numerical algorithms for pressure-driven and fluid-driven settings in which the focus relies on mesh adaptivity in order to save computational cost for large-scale 3D applications are developed.
References
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Journal ArticleDOI
The Phenomena of Rupture and Flow in Solids
TL;DR: In this article, the authors investigated the effect of surface scratches on the mechanical strength of solids, and some general conclusions were reached which appear to have a direct bearing on the problem of rupture, from an engineering standpoint, and also on the larger question of the nature of intermolecular cohesion.
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A finite element method for crack growth without remeshing
TL;DR: In this article, a displacement-based approximation is enriched near a crack by incorporating both discontinuous elds and the near tip asymptotic elds through a partition of unity method.
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The Partition of Unity Method
Ivo Babuška,Jens Markus Melenk +1 more
TL;DR: In this article, a new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved, which can therefore be more efficient than the usual finite element methods.
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Revisiting brittle fracture as an energy minimization problem
TL;DR: In this paper, a variational model of quasistatic crack evolution is proposed, which frees itself of the usual constraints of that theory : a preexisting crack and a well-defined crack path.
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Multiplier and gradient methods
TL;DR: The main purpose of this paper is to suggest a method for finding the minimum of a functionf(x) subject to the constraintg(x)=0, which consists of replacingf byF=f+λg+1/2cg2, and computing the appropriate value of the Lagrange multiplier.