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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 Orcid Logo

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

Swansea University Author: Antonio Gil Orcid Logo

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 2017-04-15T03:43:29Z
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