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

Research output: Chapter in book/report/conference proceedingConference contributionResearchpeer review

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  • Technische Universität Darmstadt
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Details

Original languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
EditorsFred J. Vermolen, Cornelis Vuik
PublisherSpringer Science and Business Media Deutschland GmbH
Pages1185-1193
Number of pages9
ISBN (electronic)978-3-030-55874-1
ISBN (print)9783030558734
Publication statusPublished - 22 Aug 2020
EventEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 - Egmond aan Zee, Netherlands
Duration: 30 Sept 20194 Oct 2019

Publication series

NameLecture Notes in Computational Science and Engineering
Volume139
ISSN (Print)1439-7358
ISSN (electronic)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.

Keywords

    Adaptive refinement, Error estimation, Finite elements, Incompressible solids, Mixed system, Phase-field fracture

ASJC Scopus subject areas

Cite this

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. ed. / Fred J. Vermolen; Cornelis Vuik. Springer Science and Business Media Deutschland GmbH, 2020. p. 1185-1193 (Lecture Notes in Computational Science and Engineering; Vol. 139).

Research output: Chapter in book/report/conference proceedingConference contributionResearchpeer 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 (eds), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Lecture Notes in Computational Science and Engineering, vol. 139, Springer Science and Business Media Deutschland GmbH, pp. 1185-1193, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019, Egmond aan Zee, Netherlands, 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 (Eds.), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference (pp. 1185-1193). (Lecture Notes in Computational Science and Engineering; Vol. 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, editors, Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Springer Science and Business Media Deutschland GmbH. 2020. p. 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. editor / Fred J. Vermolen ; Cornelis Vuik. Springer Science and Business Media Deutschland GmbH, 2020. pp. 1185-1193 (Lecture Notes in Computational Science and Engineering).
Download
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