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• W2105965900 abstract "In the modeling of pressurized fractures using phase-field approaches, the irreversibility of crack growth is enforced through an inequality constraint on the temporal derivative of the phase-field function. In comparison to the classical case in elasticity , the presence of the pressure requires the additional constraint and makes the problem much harder to analyze. After temporal discretization , this induces a minimization problem in each time step over a solution dependent admissible set. To avoid solving the resulting variational inequality corresponding to the first order necessary conditions, a penalization approach is used, commonly, to remove the inequality constraint. It is well-known that for large penalty parameters the algorithm suffers from numerical instabilities in the solution process. Consequently, to avoid such a drawback, we propose an augmented Lagrangian algorithm for the discrete in time and continuous in space phase-field problems. The final set of equations is solved in a decoupled fashion. The proposed method is substantiated with several benchmark and prototype tests in two and three dimensions." @default.
• W2105965900 created "2016-06-24" @default.
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• W2105965900 date "2014-04-01" @default.
• W2105965900 modified "2023-10-04" @default.
• W2105965900 title "An augmented-Lagrangian method for the phase-field approach for pressurized fractures" @default.
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• W2105965900 doi "https://doi.org/10.1016/j.cma.2013.12.005" @default.
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