Phase-field modeling of fracture in variably saturated porous media

Cajuhi, Tuanny; Sanavia, Lorenzo; Lorenzis, Laura De

doi:10.1007/s00466-017-1459-3

Cited by 88 publications

(48 citation statements)

References 36 publications

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“…The final step of the presented analysis is the derivation of the optimal lower bound for r (and, hence, for ρ). As before, we insert (56) into E S (α) in (51) and arrive at…”

Section: ρ-Penalization: Optimal Profile For the Linear Modelmentioning

confidence: 99%

“…We mention the papers by Del Piero et al [7], Lancioni and Royer-Carfagni [8], Amor et al [9], Freddi and Royer-Carfagni [10,11], Kuhn and Müller [12], Miehe et al [13,14], Pham et al [15], Borden [16], Borden et al [17], Vignollet et al [18], Mesgarnejad et al [19], Kuhn et al [20], Ambati et al [21], Strobl and Seelig [22], Weinberg and Hesch [23], Tanné et al [24], Sargado et al [25], Gerasimov et al [26], where various formulations are developed and validated. Recently, the framework has been also extended to ductile (elasto-plastic) fracture [27,28,29,30,31,32,33], fracture in films [34,35], shells [36,37,38,39], fracture under thermal loading [40,41,42], hydraulic fracture [43,44,45,46,47,48], fracture in porous media [49,50,51], anisotropic fracture [52,...…”

Section: Introductionmentioning

confidence: 99%

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On penalization in variational phase-field models of brittle fracture

Gerasimov

Lorenzis

2019

Computer Methods in Applied Mechanics and Engineering

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131

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Irreversible evolution is one of the central concepts as well as implementation challenges of both the variational approach to fracture by Francfort and Marigo (1998) and its regularized counterpart by Bourdin, Francfort and Marigo (2000and 2008, which is commonly referred to as a phase-field model of brittle fracture. Irreversibility of the crack phase-field imposed to prevent fracture healing leads to a constrained minimization problem, whose optimality condition is given by a variational inequality. In our study, the irreversibility is handled via penalization. Provided the penalty constant is well-tuned, the penalized formulation is a good approximation to the original one, with the advantage that the induced equality-based weak problem enables a much simpler algorithmic treatment. We propose an analytical procedure for deriving the optimal penalty constant, more precisely, its lower bound, which guarantees a sufficiently accurate enforcement of the crack phase-field irreversibility. Our main tool is the notion of the optimal phase-field profile, as well as the Γ-convergence result. It is shown that the explicit lower bound is a function of two formulation parameters (the fracture toughness and the regularization length scale) but is independent on the problem setup (geometry, boundary conditions etc.) and the formulation ingredients (degradation function, tension-compression split etc.). The optimally-penalized formulation is tested for two benchmark problems, including one with available analytical solution. We also compare our results with those obtained by using the alternative irreversibility technique based on the notion of the history field by .

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“…The final step of the presented analysis is the derivation of the optimal lower bound for r (and, hence, for ρ). As before, we insert (56) into E S (α) in (51) and arrive at…”

Section: ρ-Penalization: Optimal Profile For the Linear Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On penalization in variational phase-field models of brittle fracture

Gerasimov

Lorenzis

2019

Computer Methods in Applied Mechanics and Engineering

Self Cite

111

131

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show abstract

“…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]. Non-intrusive global/local approaches have also been applied to a quite large number of situations: the computation of the propagation of cracks in a sound model using the extended finite element method (XFEM) [37], the computation of assembly of plates introducing realistic non-linear 3D modeling of connectors [38], the extension to non-linear domain decomposition methods [39] and to explicit dynamics [40,41] with an application to the prediction of delamination under impact using Abaqus [42].…”

Section: Introductionmentioning

confidence: 99%

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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“…Only the quasi-static brittle fracture case is considered. The counterpart of the weak momentum equation in Eq: (20) for the quasistatic case with the FCM is…”

Section: Finite Cell Formulation For Phase-field Modeling Of Quasi-stmentioning

confidence: 99%

“…Similarly, the counterpart of the weak phasefield equation in Eq: (20) for the quasi-static case and the FCM is…”

Section: Finite Cell Formulation For Phase-field Modeling Of Quasi-stmentioning

confidence: 99%

Phase-field modeling of brittle fracture with multi-level hp-FEM and the finite cell method

et al. 2018

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sue by integrating a two-dimensional phase-field framework for brittle fracture with the finite cell method (FCM). The FCM based on high-order finite elements is a non-geometry-conforming discretization technique wherein the physical domain is embedded into a larger fictitious domain of simple geometry that can be easily discretized. This facilitates mesh generation for complex geometries and supports local refinement. Numerical examples including a comparison to a validation experiment illustrate the applicability of the multi-level hp-refinement and the FCM in the context of phase-field simulations.

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Phase-field modeling of fracture in variably saturated porous media

Cited by 88 publications

References 36 publications

On penalization in variational phase-field models of brittle fracture

On penalization in variational phase-field models of brittle fracture

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

Phase-field modeling of brittle fracture with multi-level hp-FEM and the finite cell method

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