An augmented-Lagrangian method for the phase-field approach for pressurized fractures

By Mary F. Wheeler, Thomas Wick, Winnifried Wollner. 2014

307 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/0693b1d53fa5b57a7e3fd274053fe5e6d96cec19

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach (2015, methodology): “The configuration is the same as explained in [38] and illustrated in Figure 2.”
A phase-field formulation for dynamic cohesive fracture (2018, methodology): “We note that this approach is distinct from that of Wheeler et al. (2014), in which staggered iterations were used in an attempt to more closely capture the true equilibrium solution through an iterative procedure.”
Phase-field modeling of fluid-driven dynamic cracking in porous media (2019, background): “[45] extended the phase field model to porous media by introducing poroelastic terms into the energy functional.”
Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model (2016, background): “Keywords: Phase Field; Fluid Filled Fracture; Adaptive Finite Elements; Porous Media; PrimalDual Active Set”
On penalization in variational phase-field models of brittle fracture (2018, methodology): “The above P is the so-called Moreau-Yosida approximation of the indicator function IDαn−1 in (C), see [44] for details.”
Phase-field modeling of a fluid-driven fracture in a poroelastic medium (2015, methodology): “The crack irreversibility can be either treated via penalization using the parameter δ as it has been used for related problems of pressurized and fluid-filled fractures [17, 22]; or as recently proposed in [13], employing a robust primal-dual active set strategy that can be interpreted as a semi-sm”
A phase-field modeling approach of fracture propagation in poroelastic media (2018, background): “[19] rewrote the energy functional by including poroelastic terms and succeeded in extending the phase field model to porous media.”
The phase field method for geometric moving interfaces and their numerical approximations (2019, unknown): “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].”
A mixed-mode phase field fracture model in anisotropic rocks with consistent kinematics (2018, background): “[74], the non-iterative operator-split solver is faster than the monolithic counterpart.”
Crack nucleation in variational phase-field models of brittle fracture (2018, background): “They have been applied to a wide variety of fracture problems including fracture of ferro-magnetic and piezo-electric materials [1, 90], thermal and drying cracks [68, 22], or hydraulic fracturing [19, 89, 31, 91] to name a few.”