A transition scheme from diffusive to discrete crack topologies at finite strain during the course of a staggered iterative procedure

Han, Jike; Shintaku, Yuichi; Moriguchi, Shuji; Terada, Kenjiro

doi:10.1002/nme.7169

Cited by 6 publications

(4 citation statements)

References 89 publications

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“…Algorithm 2 presents an overview of the moving circle algorithm, 63 which possesses the feature of nonlocal damage and determines new explicit crack tips while updating discrete cracks.…”

Section: Appendix a Explicit Crack Tip Determination Techniquementioning

confidence: 99%

“…Algorithm 1 presents an overview of the enhanced staggered iterative algorithm to realize the transition from diffusive to discrete cracks. This algorithm was originally developed for quasi‐static crack propagation problems by Han et al 63 but can be applied to dynamic problems without much modification. Note that the algorithm takes advantage of both the PFM and the strong discontinuity of the FCM, allowing a discrete crack path to propagate and even curve within a short time interval under the finite strain framework.…”

Section: Spatial and Temporal Discretizationsmentioning

confidence: 99%

“…Otherwise, the necessity of updating explicit crack tips is checked before proceeding to the next FC‐based staggered iteration

k+1

. This algorithm is benefit for the diffusive‐discrete crack transition within the quasi‐static framework, as demonstrated in Han et al, 63 since the crack may penetrate multiple elements in one time step. In contrast, in general, a certain time length (or time steps) is needed for the dynamic crack propagation, and the crack rarely evolves significantly within a single time increment.…”

Section: Spatial and Temporal Discretizationsmentioning

confidence: 99%

“…These studies have each presented unique transition algorithms, but most of them can be considered to follow the same approach of connecting the crack tips determined at two consecutive times by straight lines, as depicted in Figure 1A. Inspired by these studies, Han et al 63 proposed a transition scheme within the finite strain framework, by which even a curved crack path that evolves significantly within a single time increment can be successfully captured; see Figure 1B.…”

Section: Introductionmentioning

confidence: 99%

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Crack phase‐field enhanced finite cover method for dynamic fracture at finite strain

Han,

Hirayama,

Shintaku

et al. 2023

Numerical Meth Engineering

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SummaryThis study presents an enhancement of the diffusive‐discrete crack transition scheme (10.1002/nme.7169) to describe dynamic fracture at finite strain. In the enhanced scheme, the crack initiation, propagation, and bifurcation processes are determined from an energy minimization problem based on crack phase‐field theory, and the predicted diffusive crack is replaced by the discrete representation using the finite cover method. In the meantime, numerical damping is introduced to maintain computational stability and avoid distortion of the physical mesh in the finite cover context. By taking advantage of the features of the diffusive‐discrete crack transition scheme, the proposed approach enables us to stably simulate a series of dynamic fracture events involving crack initiation at an arbitrary location, propagation, and bifurcation in arbitrary directions, arbitrary divisions of an original object into multiple portions, and independent motions of divided portions. After spatial and temporal discretizations by the finite cover method and the Newmark method are described, as well as the simulation algorithm of the enhanced finite cover‐based staggered iterative procedure for dynamic fracture, several representative numerical examples are presented to demonstrate the performance and capabilities of the developed approach.

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“…Algorithm 2 presents an overview of the moving circle algorithm, 63 which possesses the feature of nonlocal damage and determines new explicit crack tips while updating discrete cracks.…”

Section: Appendix a Explicit Crack Tip Determination Techniquementioning

confidence: 99%

Section: Spatial and Temporal Discretizationsmentioning

confidence: 99%

“…Otherwise, the necessity of updating explicit crack tips is checked before proceeding to the next FC‐based staggered iteration

k+1

Section: Spatial and Temporal Discretizationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Crack phase‐field enhanced finite cover method for dynamic fracture at finite strain

Han,

Hirayama,

Shintaku

et al. 2023

Numerical Meth Engineering

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A diffusive‐discrete crack transition scheme for ductile fracture at finite strain

Han,

Shintaku,

Moriguchi

et al. 2024

Numerical Meth Engineering

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SummaryThis study presents a diffusive‐discrete crack transition scheme for stably conducting ductile fracture simulations within a finite strain framework. In the developed scheme, the crack initiation and propagation processes are determined according to an energy minimization problem based on crack phase‐field theory, and the predicted diffusive path is transformed to a discrete representation using the finite cover method during the staggered iterative scheme. In particular, for stably conducting ductile fracture simulations, three computational techniques, the staggered iterative configuration update technique, the subincremental damage update technique, and the crack opening stabilization technique, are introduced. The first and second techniques can be used regardless of whether discrete cracks are considered, and the third technique is specialized for diffusive‐discrete crack transition schemes. Accordingly, ductile fracture simulations with the developed scheme rarely encounter troublesome problems such as oscillations in the displacement field and severe distortion of finite elements that can lead to divergence of calculations. After the crack phase‐field model for ductile fractures is formulated and discretized, the numerical algorithms for realizing the diffusive‐discrete crack transition while maintaining computational stability are explained. Several representative numerical examples are presented to demonstrate the performance and capabilities of the developed approach.

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From ductile damage to unilateral contact via a point-wise implicit discontinuity

Daneshyar,

Herrmann,

Kollmannsberger

2023

Comput Mech

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Ductile damage models and cohesive laws incorporate the material plasticity entailing the growth of irrecoverable deformations even after complete failure. This unrealistic growth remains concealed until the unilateral effects arising from the crack closure emerge. We address this issue by proposing a new strategy to cope with the entire process of failure, from the very inception in the form of diffuse damage to the final stage, i.e. the emergence of sharp cracks. To this end, we introduce a new strain field, termed discontinuity strain, to the conventional additive strain decomposition to account for discontinuities in a continuous sense so that the standard principle of virtual work applies. We treat this strain field similar to a strong discontinuity, yet without introducing new kinematic variables and nonlinear boundary conditions. In this paper, we demonstrate the effectiveness of this new strategy at a simple ductile damage constitutive model. The model uses a scalar damage index to control the degradation process. The discontinuity strain field is injected into the strain decomposition if this damage index exceeds a certain threshold. The threshold corresponds to the limit at which the induced imperfections merge and form a discrete crack. With three-point bending tests under pure mode I and mixed-mode conditions, we demonstrate that this augmentation does not show the early crack closure artifact which is wrongly predicted by plastic damage formulations at load reversal. We also use the concrete damaged plasticity model provided in Abaqus commercial finite element program for our comparison. Lastly, a high-intensity low-cycle fatigue test demonstrates the unilateral effects resulting from the complete closure of the induced crack.

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A transition scheme from diffusive to discrete crack topologies at finite strain during the course of a staggered iterative procedure

Cited by 6 publications

References 89 publications

Crack phase‐field enhanced finite cover method for dynamic fracture at finite strain

Crack phase‐field enhanced finite cover method for dynamic fracture at finite strain

A diffusive‐discrete crack transition scheme for ductile fracture at finite strain

From ductile damage to unilateral contact via a point-wise implicit discontinuity

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