Phase field modeling of brittle fracture in an Euler–Bernoulli beam accounting for transverse part-through cracks

Lai, Wenyu; Gao, Jianmei; Li, Yihuan; Arroyo, Marino; Shen, Yongxing

doi:10.1016/j.cma.2019.112787

Cited by 28 publications

(9 citation statements)

References 25 publications

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“…45 However, the application of the phase-field approach to model cracks along the thickness direction of shells has been given very limited attention up until now. To the author's best knowledge, except two contributions, 46,47 all of the aforementioned models consider the phase-field to be constant along the thickness direction of shells argued for with their slenderness. Thereby, these models are exclusively able to represent cracks which do not vary along the thickness direction.…”

Section: Introductionmentioning

confidence: 99%

Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

Ambati

Heinzmann

Seiler

et al. 2022

Numerical Meth Engineering

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The prediction of fracture in thin-walled structures is decisive for a wide range of applications. Modeling methods such as the phase-field method usually consider cracks to be constant over the thickness which, especially in load cases involving bending, is an imperfect approximation. In this contribution, fracture phenomena along the thickness direction of structural elements (plates or shells) are addressed with a phase-field modeling approach. For this purpose, a new, so called "mixed-dimensional" model is introduced, which combines structural elements representing the displacement field in the two-dimensional shell midsurface with continuum elements describing a crack phase-field in the three-dimensional solid space. The proposed model uses two separate finite element discretizations, where the transfer of variables between the coupled twoand three-dimensional fields is performed at the integration points which in turn need to have corresponding geometric locations. The governing equations of the proposed mixed-dimensional model are deduced in a consistent manner from a total energy functional with them also being compared to existing standard models. The resulting model has the advantage of a reduced computational effort due to the structural elements while still being able to accurately model arbitrary through-thickness crack evolutions as well as partly along the thickness broken shells due to the continuum elements. Amongst others, the higher accuracy as well as the numerical efficiency of the proposed model are tested and validated by comparing simulation results of the new model to those obtained by standard models using numerous representative examples.

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Section: Introductionmentioning

confidence: 99%

Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

Ambati

Heinzmann

Seiler

et al. 2022

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…The advantages include obviating the need for explicitly tracking the crack path geometry, and the ability to predict crack nucleation and bifurcation without extra criterion. The method has since been applied to fracture modeling in Euler-Bernoulli beams [5], thin shells [6], composite materials [7,8], cement-based materials [9], layered structures [10], and CO 2 fracturing [11].…”

Section: Introductionmentioning

confidence: 99%

A manifold learning approach to accelerate phase field fracture simulations in the representative volume element

2020

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The multiscale simulation of heterogeneous materials is a popular and important subject in solid mechanics and materials science due to the wide application of composite materials. However, the classical FE 2 (finite element 2) scheme can be costly, especially when the microproblem is nonlinear. In this paper, we consider the case when the microproblem is the phase field formulation for fracture. We adopt the locally linear embedding (LLE) manifold learning approach, a method for non-linear dimension reduction, to extract the manifold that contains a collection of phase-field-represented initial microcrack patterns in the representative volume element (RVE). Then the output data corresponding to any other microcrack pattern, e.g., the evolved phase field at a fixed load, can be accurately reconstructed using the learned manifold with minimum computation. The method has two features: a minimum number of parameters for the scheme, and an input-specific error bar. The latter feature enables an adaptive strategy for any new input on whether to use the proposed, less expensive reconstruction, or to use an accurate but costly high-fidelity computation instead.

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“…The advantages include obviating the need for explicitly tracking the crack path geometry, and the ability to predict crack nucleation and bifurcation without extra criterion. The method has since been applied to fracture modeling in Euler-Bernoulli beams [5], thin shells [6], composite materials [7,8], cementbased materials [9], layered structures [10], and CO 2 fracturing [11]. However, solving the equations arising from the phase field method for fracture can be costly.…”

Section: Introductionmentioning

confidence: 99%

A Manifold Learning Approach to Accelerate Phase Field Fracture Simulations in the Representative Volume Element

Liu,

Weng,

Shen

2020

Preprint

Self Cite

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The multiscale simulation of heterogeneous materials is a popular and important subject in solid mechanics and materials science due to the wide application of composite materials. However, the classical FE 2 (finite element 2 ) scheme can be costly, especially when the microproblem is nonlinear. In this paper, we consider the case when the microproblem is the phase field formulation for fracture. We adopt the locally linear embedding (LLE) manifold learning approach, a method for non-linear dimension reduction, to extract the manifold that contains a collection of phase-fieldrepresented initial microcrack patterns in the representative volume element (RVE). Then the output data corresponding to any other microcrack pattern, e.g., the evolved phase field at a fixed load, can be accurately reconstructed using the learned manifold with minimum computation. The method has two features: a minimum number of parameters for the scheme, and an input-specific error bar. The latter feature enables an adaptive strategy for any new input on whether to use the proposed, less expensive reconstruction, or to use an accurate but costly high-fidelity computation instead.

show abstract

Phase field modeling of brittle fracture in an Euler–Bernoulli beam accounting for transverse part-through cracks

Cited by 28 publications

References 25 publications

Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

A manifold learning approach to accelerate phase field fracture simulations in the representative volume element

A Manifold Learning Approach to Accelerate Phase Field Fracture Simulations in the Representative Volume Element

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