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A framework for polyconvex large strain phase-field methods to fracture / C. Hesch, A.J. Gil, R. Ortigosa, M. Dittmann, C. Bilgen, P. Betsch, M. Franke, A. Janz, K. Weinberg, Antonio Gil

Computer Methods in Applied Mechanics and Engineering, Volume: 317, Pages: 649 - 683

Swansea University Author: Antonio Gil

Abstract

Variationally consistent phase-field methods have been shown to be able to predict complex three-dimensional crack patterns. However, current computational methodologies in the context of large deformations lack the necessary numerical stability to ensure robustness in different loading scenarios. I...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa31628
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spelling 2017-02-01T09:05:50.0350441 v2 31628 2017-01-16 A framework for polyconvex large strain phase-field methods to fracture 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2017-01-16 CIVL Variationally consistent phase-field methods have been shown to be able to predict complex three-dimensional crack patterns. However, current computational methodologies in the context of large deformations lack the necessary numerical stability to ensure robustness in different loading scenarios. In this work, we present a novel formulation for finite strain polyconvex elasticity by introducing a new anisotropic split based on the principal invariants of the right Cauchy-Green tensor, which always ensures polyconvexity of the resulting strain energy function. The presented phase-field approach is embedded in a sophisticated isogeometrical framework with hierarchical refinement for three-dimensional problems using a fourth order Cahn-Hilliard crack density functional with higher-order convergence rates for fracture problems. Additionally, we introduce for the first time a Hu-Washizu mixed variational formulation in the context of phase-field problems, which permits the novel introduction of a variationally consistent stress-driven split. The new polyconvex phase-field fracture formulation guarantees numerical stability for the full range of deformations and for arbitrary hyperelastic materials. Journal Article Computer Methods in Applied Mechanics and Engineering 317 649 683 0045-7825 Finite deformations; Fracture mechanics; Isogeometric analysis; Phase-field; Polyconvexity 15 4 2017 2017-04-15 10.1016/j.cma.2016.12.035 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2017-02-01T09:05:50.0350441 2017-01-16T13:05:40.9539888 College of Engineering Engineering C. Hesch 1 A.J. Gil 2 R. Ortigosa 3 M. Dittmann 4 C. Bilgen 5 P. Betsch 6 M. Franke 7 A. Janz 8 K. Weinberg 9 Antonio Gil 0000-0001-7753-1414 10 0031628-16012017130647.pdf hesch2017.pdf 2017-01-16T13:06:47.3170000 Output 13264466 application/pdf Accepted Manuscript true 2018-01-09T00:00:00.0000000 false
title A framework for polyconvex large strain phase-field methods to fracture
spellingShingle A framework for polyconvex large strain phase-field methods to fracture
Antonio, Gil
title_short A framework for polyconvex large strain phase-field methods to fracture
title_full A framework for polyconvex large strain phase-field methods to fracture
title_fullStr A framework for polyconvex large strain phase-field methods to fracture
title_full_unstemmed A framework for polyconvex large strain phase-field methods to fracture
title_sort A framework for polyconvex large strain phase-field methods to fracture
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio, Gil
author Antonio, Gil
author2 C. Hesch
A.J. Gil
R. Ortigosa
M. Dittmann
C. Bilgen
P. Betsch
M. Franke
A. Janz
K. Weinberg
Antonio Gil
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 317
container_start_page 649
publishDate 2017
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2016.12.035
college_str College of Engineering
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hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
document_store_str 1
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description Variationally consistent phase-field methods have been shown to be able to predict complex three-dimensional crack patterns. However, current computational methodologies in the context of large deformations lack the necessary numerical stability to ensure robustness in different loading scenarios. In this work, we present a novel formulation for finite strain polyconvex elasticity by introducing a new anisotropic split based on the principal invariants of the right Cauchy-Green tensor, which always ensures polyconvexity of the resulting strain energy function. The presented phase-field approach is embedded in a sophisticated isogeometrical framework with hierarchical refinement for three-dimensional problems using a fourth order Cahn-Hilliard crack density functional with higher-order convergence rates for fracture problems. Additionally, we introduce for the first time a Hu-Washizu mixed variational formulation in the context of phase-field problems, which permits the novel introduction of a variationally consistent stress-driven split. The new polyconvex phase-field fracture formulation guarantees numerical stability for the full range of deformations and for arbitrary hyperelastic materials.
published_date 2017-04-15T03:51:30Z
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