A phase-field description for pressurized and non-isothermal propagating fractures

Abstract

In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws between a porous medium and the fracture. The resulting model is augmented with thermodynamical arguments and then analyzed from a mechanical perspective. The numerical solution is based on a robust semi-smooth Newton approach in which the linear equation systems are solved with a generalized minimal residual method and algebraic multigrid preconditioning. The proposed modeling and algorithmic developments are substantiated with different examples in two-and three dimensions. We notice that for some of these configurations manufactured solutions can be constructed, allowing for a careful verification of our implementation. Furthermore, crack-oriented predictor-corrector adaptivity and a parallel implementation are used to keep the computational cost reasonable. Snapshots of iteration numbers show an excellent performance of the nonlinear and linear solution algorithms. Lastly, for some tests, a computational analysis of the effects of strain-energy splitting is performed, which has not been undertaken to date for similar phase-field settings involving pressure, fluids or non-isothermal effects.

An adaptive global–local approach for phase-field modeling of anisotropic brittle fracture

“…In the case of elastic cracks, it can be shown that the phase field satisfies 0 ≤ d ≤ 1. When additional physics are included for instance a fluid inside the fracture [74] or non-isothermal effects [79], the energy functional must be modified to cope with negative values of d. Hence in order to allow for future extensions, we work in the remainder of this paper with d + rather than d. A detailed discussion is provided in [74][Section 3].…”

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

“…The following three-dimensional research studies using PF are available: formation and growth of echelon cracks [164], pressure vessel simulation [158], single-edge notched shear test [162], cube with rigid spherical inclusion under tension [157], Kalthoff Winkler experiment [157], bolted plate compared against experimental results [161], simple shear tests of thoracic aorta with anisotropic failure compared against experimental results [163], random nucleation sites [159], L-shaped specimen [160,233], tension test of cube with spherical inclusion [112], bending of Hopkinson bar [363], and Sneddon/Lowengrub benchmark [146,217,237], and non-isothermal pressurized fractures [364].…”

A Bayesian estimation method for variational phase-field fracture problems

“…The computational costs can be high, specifically when an appropriate estimation is required inside multi-physics frameworks, see e.g. [ 3 , 26 – 28 ]. Using Bayesian inversion, we strive to solve such problems with a coarser mesh and fit the parameters.…”

“…Therefore, sufficiently small length-scales are computationally demanding. To date, the focus in such cases was on local mesh adaptivity and parallel computing in order to reduce the computational cost significantly; see for instance [3][4][5][6][7][8][9][10][11]. Another recent approach is a global-local technique in which parts of the domain are solved with a simplified approach [12,13] that also aims to reduce the computational cost.…”