Validation simulations for the variational approach to fracture

Mesgarnejad, Ataollah; Bourdin, Blaise; Khonsari, M. M.

doi:10.1016/j.cma.2014.10.052

Cited by 169 publications

(92 citation statements)

References 55 publications

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“…The currently available phase-field formulations of brittle fracture encompass static and dynamic models. We mention the papers by Amor et al [7], Miehe et al [8,9], Kuhn and Müller [10], Pham et al [11], Borden et al [12], Mesgarnejad et al [13], Kuhn et al [14], Ambati et al [15], Wu et al [16], where various formulations are developed and validated. Recently, the framework has been also extended to ductile (elasto-plastic) fracture [17][18][19][20][21][22], pressurized fracture in elastic and porous media [23,24], fracture in films [25] and shells [26][27][28], and multi-field fracture [29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

“…is given by (13) and (14). Option 2 One preserves the representations (19) and (20), and, in contrast to (21), imposes only a weak continuity between λ C and λ L on .…”

Section: We Now Introduce Two Functions Onmentioning

confidence: 99%

“…Alternatively, staggered (also termed partitioned, or alternate minimization) solution scheme is widely used. This is based on decoupling of the strongly non-linear weak formulation into a system and then iterating between the equations [2][3][4][5][7][8][9][11][12][13]15,16]. The staggered scheme is proved to be robust, but typically has a very slow convergence behavior of the iterative solution process, see e.g.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A non-intrusive global/local approach applied to phase-field modeling of brittle fracture

Gerasimov

Noii

Allix

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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This paper aims at investigating the adoption of non-intrusive global/local approaches while modeling fracture by means of the phase-field framework. A successful extension of the non-intrusive global/local approach to this setting would pave the way for a wide adoption of phase-field modeling of fracture, already well established in the research community, within legacy codes for industrial applications. Due to the extreme difference in stiffness between the global counterpart of the zone to be analized locally and its actual response when undergoing extensive cracking, the main foreseen issues are robustness, accuracy and efficiency of the fixed point iterative algorithm which is at the core of the method. These issues are tackled in this paper. We investigate the convergence performance when using the native global/local algorithm and show that the obtained results are identical to the reference phase-field solution. We also equip the global/local solution update procedure with relaxation/acceleration techniques such as Aitken's 2 -method, the Symmetric Rank One and Broyden's methods and show that the iterative convergence can be improved significantly. Results indicate that Aitken's 2 -method is probably the most convenient choice for the implementation of the approach within legacy codes, as this method needs only tools already available for the so-called sub-modeling approach, a strategy routinely used in industrial contexts.

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Section: Introductionmentioning

confidence: 99%

“…is given by (13) and (14). Option 2 One preserves the representations (19) and (20), and, in contrast to (21), imposes only a weak continuity between λ C and λ L on .…”

Section: We Now Introduce Two Functions Onmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A non-intrusive global/local approach applied to phase-field modeling of brittle fracture

Gerasimov

Noii

Allix

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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“…The GPCG method is implemented in the parallel linear algebra library PETSc [24]. We also use this library for manipulation of sparse matrices and vectors, similarly to the previous work of [5,6]. It remains then to specify the temporal discretization method used for the u-problem.…”

Section: Numerical Implementationmentioning

confidence: 99%

“…The gradient damage model can thus be regarded as an elliptic regularization of the previous sharp-interface variational fracture model and the internal length serves as a purely numerical parameter which should be as small as possible. This is the interpretation undertaken among others by [3][4][5] where the gradient damage model is applied to drying, thin films debonding, and other fracture mechanics problems.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of dynamic brittle fracture via gradient damage models

Marigo

Guilbaud

et al. 2016

Adv. Model. and Simul. in Eng. Sci.

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Background: Gradient damage models can be acknowledged as a unified framework of dynamic brittle fracture. As a phase-field approach to fracture, they are gaining popularity over the last few years in the computational mechanics community. This paper concentrates on a better understanding of these models. We will highlight their properties during the initiation and propagation phases of defect evolution. Methods: The variational ingredients of the dynamic gradient damage model are recalled. Temporal discretization based on the Newmark-β scheme is performed. Several energy release rates in gradient damage models are introduced to bridge the link from damage to fracture. Results and discussion: An antiplane tearing numerical experiment is considered. It is found that the phase-field crack tip is governed by the asymptotic Griffith's law. In the absence of unstable crack propagation, the dynamic gradient damage model converges to the quasi-static one. The defect evolution is in quantitative accordance with the linear elastic fracture mechanics predictions. Conclusion: These numerical experiments provide a justification of the dynamic gradient damage model along with its current implementation, when it is used as a phase-field model for complex real-world dynamic fracture problems.

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A coupled phase-field and reactive-transport framework for fracture propagation in poroelastic media

Clavijo

Addassi

Finkbeiner

et al. 2022

Preprint

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We present a novel approach to model hydro-chemo-mechanical responses in rock formations subject to fracture propagation within chemically active rock formations. The framework developed integrates the mechanisms of reactive transport, fluid flow and transport in porous media, and phasefield modelling of fracture propagation in poroelastic media. The solution approach integrates the geochemical package PHREEQC with a finite-element open-source platform, FEniCs. The PHREEQC solver is used to calculate the localized chemical reaction, including solid dissolution/precipitation. The resulting solid weakening by chemical damage is estimated from the reaction-induced porosity change. The proposed coupled model was verified with previous numerical results and applied to a synthetic case exhibiting hydraulic fracturing enhanced with chemical damage. Simulation results suggest that mechanical failure could be accelerated in the presence of ongoing chemical processes due to rock weakening and porosity changes, allowing the nucleation, growth, and development of fractures.Modeling the chemo-mechanical responses in porous media is of interest to several disciplines in engineering and science, including underground storage of carbon dioxide (CO 2 ) in reactive rock formations 1-5 , CO 2 injection for enhanced oil and gas recovery [6][7][8][9] , well stimulation 10 , concrete durability [11][12][13][14] , geothermal recovery [15][16][17] , and long term storage of hazardous waste [18][19][20] , among others. The physical and chemical processes involved govern mineral formations, such as dissolution and precipitation in metamorphic and sedimentary rocks and the resulting reaction-driven fracture propagation. Proper modeling of the impact of mineral reactions and the associated mechanical response of subsurface rocks is, therefore, crucial [21][22][23][24][25] .Various modeling approaches have been proposed in the literature to simulate the complex dynamics of mechanical failure, particularly fracture propagation combined with other fluid/rock processes such as diffusion, advection, and chemical reactions in rock formations [21][22][23] . For a fluid-solid system, fractures provide hydraulic pathways for fluid flow, allowing the progress of the reaction front. Bringedal et al. 26 proposed a model for dissolution and precipitation in porous media using an evolving interface between the fluid and solid, where physical and chemical properties vary smoothly. This diffusive fluid-solid interface models the transition between the fluid and the mineral phases. According to Bringedal et al. 26 , the solution of the second-order Allen-Cahnlike partial differential equation defines the dissolution and precipitation profile in the system. Schuler et al. 23 developed a chemo-mechanical phase-field model to study dissolution-assisted fracture development. Ogata et al. 22 developed a fluid flow and mass transport model for rock fractures using a coupled thermal-hydraulicmechanical-chemical framework. The proposed formulation requires introduc...

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Validation simulations for the variational approach to fracture

Cited by 169 publications

References 55 publications

A non-intrusive global/local approach applied to phase-field modeling of brittle fracture

A non-intrusive global/local approach applied to phase-field modeling of brittle fracture

Numerical investigation of dynamic brittle fracture via gradient damage models

A coupled phase-field and reactive-transport framework for fracture propagation in poroelastic media

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