A phase-field crack model based on a directional strain decomposition and a stress-driven Crack-Opening Indicator

Luo, Chenyi; Chen, Lin; Huang, Yu

doi:10.1016/j.cma.2021.113928

Cited by 7 publications

(5 citation statements)

References 35 publications

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“…The work of Ref. [6] shows that the two splits yield similar results in both the tensile and the shear tests but have difficulties in describing cracking under more complex stress states [26,27]. Without loss of generality, we herein take the volumetric and deviatoric split [4].…”

Section: A Phase-field Model Of Brittle Fracturementioning

confidence: 99%

Fast staggered schemes for the phase-field model of brittle fracture based on the fixed-stress concept

Luo

2023

Computer Methods in Applied Mechanics and Engineering

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Section: A Phase-field Model Of Brittle Fracturementioning

confidence: 99%

Fast staggered schemes for the phase-field model of brittle fracture based on the fixed-stress concept

Luo

2023

Computer Methods in Applied Mechanics and Engineering

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“…In the commonly adopted staggered algorithm for solving phase field models, Equations ( 36) and ( 37) are alternatively solved in every loading step until convergence is achieved based on the selected criterion. However, when solving the displacement field 𝑢 with a fixed phase field 𝑑, the tangent stiffness term In this paper, the hybrid formulation proposed by Ambati et al 48 is used to avoid the iterations required in solving Equation (36), which simplifies Equation (39) to…”

Section: Endmentioning

confidence: 99%

“…In their model, the cracking direction is the same as that obtained from the macroscopic Mohr–Coulomb strength theory. To accurately simulate material behaviors in the post‐fracture stage, Luo et al 36 . presented a phase‐field model with a directional strain decomposition to consider the crack surface normal and a stress‐driven crack opening indicator to distinguish the opening and closure of pre‐cracks.…”

Section: Introductionmentioning

confidence: 99%

“…In their model, the cracking direction is the same as that obtained from the macroscopic Mohr-Coulomb strength theory. To accurately simulate material behaviors in the post-fracture stage, Luo et al 36 presented a phase-field model with a directional strain decomposition to consider the crack surface normal and a stress-driven crack opening indicator to distinguish the opening and closure of pre-cracks. Steinke et al 37 discussed in detail the spatial orientation of the potential crack surface and the issue of internal locking and lateral phase-field evolution due to local orientation misalignment.…”

Section: Introductionmentioning

confidence: 99%

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A phase‐field formulation based on an extended F‐criterion for rock fracture

Sun,

Lu,

Wang

et al. 2023

Num Anal Meth Geomechanics

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In this paper a phase‐field formulation based on an extended F‐criterion (the normalized strain energy release rate criterion) is proposed to simulate tensile‐compressive‐shear rock fractures. By applying the F‐criterion, the phase‐field crack‐driving energy decomposition is determined by a direction search which maximizes the local fracture dissipation. In compressive‐shear states, the computation is supplemented by an explicitly expressed confinement‐dependent mode‐II fracture energy release rate, and the cracking angle is determined by both the fracture energy and strain states. The hybrid formulation and alternate minimization algorithm are adopted for the numerical examples in this paper. Fractures for rock and rock‐like specimens subjected to compression demonstrate the ability of the present model in capturing tensile‐compressive‐shear rock fracture behaviors.

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“…The work of [6] shows that both splits yield similar results in both the tensile and the shear tests. Although both splits have their difficulties in describing cracking under complex stress states [19,20], we take the volumetric and deviatoric (VD) split from [4] in the following discussion. The proposed staggered scheme in this paper should be easily extended to the phase field model with other splits, e.g., spectral decomposition.…”

Section: Phase Field Model For Brittle Fracturementioning

confidence: 99%

Fast staggered schemes for the phase-field model of brittle fracture based on the fixed-stress concept

Luo¹

2022

Preprint

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Phase field models are promising to tackle various fracture problems where a diffusive crack is introduced and modeled using the phase variable. Owing to the non-convexity of the energy functional, the derived partial differential equations are usually solved in a staggered manner. However, this method suffers from a low convergence rate, and a large number of staggered iterations are needed, especially at the fracture nucleation and propagation. In this study, we propose novel staggered schemes, which are inspired by the fixed-stress split scheme in poromechanics. By fixing the stress when solving the damage evolution, the displacement increment is expressed in terms of the increment of the phase variable. The relation between these two increments enables a prediction of the displacement and the active energy based on the increment of the phase variable. Thus, the maximum number of staggered iterations is reduced, and the computational efficiency is improved. We present three staggered schemes by fixing the first invariant, second invariant, or both invariants of the stress, denoted by S1, S2, and S3 schemes. The performance of the schemes is then verified by comparing with the standard staggered scheme through three benchmark examples, i.e., tensile, shear, and L-shape panel tests. The results exhibit that the force-displacement relations and the crack patterns computed using the fast schemes are consistent with the ones based on the standard staggered scheme. Moreover, the proposed S1 and S2 schemes can largely reduce the maximum number of staggered iterations and total CPU time in all benchmark tests. The S2 scheme performs comparably except in the shear test, where the underlying assumption is violated in the region close to the crack.

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A phase-field crack model based on a directional strain decomposition and a stress-driven Crack-Opening Indicator

Cited by 7 publications

References 35 publications

Fast staggered schemes for the phase-field model of brittle fracture based on the fixed-stress concept

Fast staggered schemes for the phase-field model of brittle fracture based on the fixed-stress concept

A phase‐field formulation based on an extended F‐criterion for rock fracture

Fast staggered schemes for the phase-field model of brittle fracture based on the fixed-stress concept

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