Adaptive Numerical Simulation of a Phase-Field Fracture Model in Mixed Form Tested on an L-shaped Specimen with High Poisson Ratios

Publikation: Beitrag in Buch/Bericht/Sammelwerk/KonferenzbandAufsatz in KonferenzbandForschungPeer-Review

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  • Technische Universität Darmstadt
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OriginalspracheEnglisch
Titel des SammelwerksNumerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
Herausgeber/-innenFred J. Vermolen, Cornelis Vuik
Herausgeber (Verlag)Springer Science and Business Media Deutschland GmbH
Seiten1185-1193
Seitenumfang9
ISBN (elektronisch)978-3-030-55874-1
ISBN (Print)9783030558734
PublikationsstatusVeröffentlicht - 22 Aug. 2020
VeranstaltungEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 - Egmond aan Zee, Niederlande
Dauer: 30 Sept. 20194 Okt. 2019

Publikationsreihe

NameLecture Notes in Computational Science and Engineering
Band139
ISSN (Print)1439-7358
ISSN (elektronisch)2197-7100

Abstract

This work presents a new adaptive approach for the numerical simulation of a phase-field model for fractures in nearly incompressible solids. In order to cope with locking effects, we use a recently proposed mixed form where we have a hydro-static pressure as additional unknown besides the displacement field and the phase-field variable. To fulfill the fracture irreversibility constraint, we consider a formulation as a variational inequality in the phase-field variable. For adaptive mesh refinement, we use a recently developed residual-type a posteriori error estimator for the phase-field variational inequality which is efficient and reliable, and robust with respect to the phase-field regularization parameter. The proposed model and the adaptive error-based refinement strategy are demonstrated by means of numerical tests derived from the L-shaped panel test, originally developed for concrete. Here, the Poisson’s ratio is changed from the standard setting towards the incompressible limit ν → 0.5.

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Adaptive Numerical Simulation of a Phase-Field Fracture Model in Mixed Form Tested on an L-shaped Specimen with High Poisson Ratios. / Mang, Katrin; Walloth, Mirjam; Wick, Thomas et al.
Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Hrsg. / Fred J. Vermolen; Cornelis Vuik. Springer Science and Business Media Deutschland GmbH, 2020. S. 1185-1193 (Lecture Notes in Computational Science and Engineering; Band 139).

Publikation: Beitrag in Buch/Bericht/Sammelwerk/KonferenzbandAufsatz in KonferenzbandForschungPeer-Review

Mang, K, Walloth, M, Wick, T & Wollner, W 2020, Adaptive Numerical Simulation of a Phase-Field Fracture Model in Mixed Form Tested on an L-shaped Specimen with High Poisson Ratios. in FJ Vermolen & C Vuik (Hrsg.), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Lecture Notes in Computational Science and Engineering, Bd. 139, Springer Science and Business Media Deutschland GmbH, S. 1185-1193, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019, Egmond aan Zee, Niederlande, 30 Sept. 2019. https://doi.org/10.48550/arXiv.2003.09459, https://doi.org/10.1007/978-3-030-55874-1_118
Mang, K., Walloth, M., Wick, T., & Wollner, W. (2020). Adaptive Numerical Simulation of a Phase-Field Fracture Model in Mixed Form Tested on an L-shaped Specimen with High Poisson Ratios. In F. J. Vermolen, & C. Vuik (Hrsg.), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference (S. 1185-1193). (Lecture Notes in Computational Science and Engineering; Band 139). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.48550/arXiv.2003.09459, https://doi.org/10.1007/978-3-030-55874-1_118
Mang K, Walloth M, Wick T, Wollner W. Adaptive Numerical Simulation of a Phase-Field Fracture Model in Mixed Form Tested on an L-shaped Specimen with High Poisson Ratios. in Vermolen FJ, Vuik C, Hrsg., Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Springer Science and Business Media Deutschland GmbH. 2020. S. 1185-1193. (Lecture Notes in Computational Science and Engineering). doi: 10.48550/arXiv.2003.09459, 10.1007/978-3-030-55874-1_118
Mang, Katrin ; Walloth, Mirjam ; Wick, Thomas et al. / Adaptive Numerical Simulation of a Phase-Field Fracture Model in Mixed Form Tested on an L-shaped Specimen with High Poisson Ratios. Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Hrsg. / Fred J. Vermolen ; Cornelis Vuik. Springer Science and Business Media Deutschland GmbH, 2020. S. 1185-1193 (Lecture Notes in Computational Science and Engineering).
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abstract = "This work presents a new adaptive approach for the numerical simulation of a phase-field model for fractures in nearly incompressible solids. In order to cope with locking effects, we use a recently proposed mixed form where we have a hydro-static pressure as additional unknown besides the displacement field and the phase-field variable. To fulfill the fracture irreversibility constraint, we consider a formulation as a variational inequality in the phase-field variable. For adaptive mesh refinement, we use a recently developed residual-type a posteriori error estimator for the phase-field variational inequality which is efficient and reliable, and robust with respect to the phase-field regularization parameter. The proposed model and the adaptive error-based refinement strategy are demonstrated by means of numerical tests derived from the L-shaped panel test, originally developed for concrete. Here, the Poisson{\textquoteright}s ratio is changed from the standard setting towards the incompressible limit ν → 0.5.",
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N1 - Funding Information: Acknowledgments This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—392587580. It is part of the Priority Program 1748 (DFG SPP 1748) Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis.

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N2 - This work presents a new adaptive approach for the numerical simulation of a phase-field model for fractures in nearly incompressible solids. In order to cope with locking effects, we use a recently proposed mixed form where we have a hydro-static pressure as additional unknown besides the displacement field and the phase-field variable. To fulfill the fracture irreversibility constraint, we consider a formulation as a variational inequality in the phase-field variable. For adaptive mesh refinement, we use a recently developed residual-type a posteriori error estimator for the phase-field variational inequality which is efficient and reliable, and robust with respect to the phase-field regularization parameter. The proposed model and the adaptive error-based refinement strategy are demonstrated by means of numerical tests derived from the L-shaped panel test, originally developed for concrete. Here, the Poisson’s ratio is changed from the standard setting towards the incompressible limit ν → 0.5.

AB - This work presents a new adaptive approach for the numerical simulation of a phase-field model for fractures in nearly incompressible solids. In order to cope with locking effects, we use a recently proposed mixed form where we have a hydro-static pressure as additional unknown besides the displacement field and the phase-field variable. To fulfill the fracture irreversibility constraint, we consider a formulation as a variational inequality in the phase-field variable. For adaptive mesh refinement, we use a recently developed residual-type a posteriori error estimator for the phase-field variational inequality which is efficient and reliable, and robust with respect to the phase-field regularization parameter. The proposed model and the adaptive error-based refinement strategy are demonstrated by means of numerical tests derived from the L-shaped panel test, originally developed for concrete. Here, the Poisson’s ratio is changed from the standard setting towards the incompressible limit ν → 0.5.

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