Phase-field model of brittle fracture in Reissner–Mindlin plates and shells

Kikis, Georgia; Ambati, Marreddy; Lorenzis, Laura De; Klinkel, Sven

doi:10.1016/j.cma.2020.113490

Cited by 24 publications

(14 citation statements)

References 63 publications

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“…Here, the condition was not examined, however, since the results obtained in the numerical examples in Sect. 4 were accurate and robust it is assumed that the condition is fulfilled. Nevertheless, in order to ensure the stability of the proposed mixed formulations in general, a mathematical verification of the condition should be carried out in future work.…”

Section: Hellinger-reissner Variational Formulationmentioning

confidence: 99%

“…The results are in general more accurate than for the following two approaches as it will be seen in Sect. 4.…”

Section: Advantagesmentioning

confidence: 99%

“…However, due to the discontinuity of the stress resultant fields, locking is not completely eliminated, as will be shown in Sect. 4.…”

Section: Discontinuous Approachmentioning

confidence: 99%

“…Since then, isogeometric analysis has been successfully implemented in structural mechanics and many other fields, e.g. in fluid mechanics [2], contact mechanics [3] and fracture mechanics [4].…”

Section: Introductionmentioning

confidence: 99%

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Two-field formulations for isogeometric Reissner–Mindlin plates and shells with global and local condensation

Kikis

Klinkel

2021

Comput Mech

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In this paper, mixed formulations are presented in the framework of isogeometric Reissner–Mindlin plates and shells with the aim of alleviating membrane and shear locking. The formulations are based on the Hellinger-Reissner functional and use the stress resultants as additional unknowns, which have to be interpolated in appropriate approximation spaces. The additional unknowns can be eliminated by static condensation. In the framework of isogeometric analysis static condensation is performed globally on the patch level, which leads to a high computational cost. Thus, two additional local approaches to the existing continuous method are presented, an approach with discontinuous stress resultant fields at the element boundaries and a reconstructed approach which is blending the local control variables by using weights in order to compute the global ones. Both approaches allow for a static condensation on the element level instead of the patch level. Various numerical examples are investigated in order to verify the accuracy and effectiveness of the different approaches and a comparison to existing elements that include mechanisms against locking is carried out.

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Section: Hellinger-reissner Variational Formulationmentioning

confidence: 99%

“…The results are in general more accurate than for the following two approaches as it will be seen in Sect. 4.…”

Section: Advantagesmentioning

confidence: 99%

“…However, due to the discontinuity of the stress resultant fields, locking is not completely eliminated, as will be shown in Sect. 4.…”

Section: Discontinuous Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Two-field formulations for isogeometric Reissner–Mindlin plates and shells with global and local condensation

Kikis

Klinkel

2021

Comput Mech

Self Cite

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“…A thermodynamically consistent formulation of the phase-field fracture model was proposed by [5], adopting an energetic cracking driving force definition. Since then, over the past decade, researchers have extended the work to thermo-mechanical problems at large strain [6], ductile failure [7,8], fracture in thin films [9], anisotropic fracture [10], fracture in fully/partially saturated porous media [11][12][13], hydrogen assisted cracking [14], dissolution-driven stress corrosion cracking [15], fracture and fatigue in shape-memory alloys [16], and brittle failure of Reisner-Mindlin plates [17] to cite a few. Finally, the phase-field model for fracture has also been used for the multi-scale finite element method [18][19][20], asymptotic homogenisation [21], and variationally consistent homogenisation [22].…”

Section: Introductionmentioning

confidence: 99%

Phase-field fracture irreversibility using the slack variable approach

Bharali¹,

Larsson²,

Jänicke³

2022

Preprint

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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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Phase-field model of brittle fracture in Reissner–Mindlin plates and shells

Cited by 24 publications

References 63 publications

Two-field formulations for isogeometric Reissner–Mindlin plates and shells with global and local condensation

Two-field formulations for isogeometric Reissner–Mindlin plates and shells with global and local condensation

Phase-field fracture irreversibility using the slack variable approach

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

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