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Damage-driven strain localisation in networks of fibres: A computational homogenisation approach

Felipe Figueredo Rocha, Pablo Javier Blanco, Pablo Javier Sánchez, Eduardo de Souza Neto De Souza Neto Orcid Logo, Raúl Antonino Feijóo

Computers & Structures, Volume: 255, Start page: 106635

Swansea University Author: Eduardo de Souza Neto De Souza Neto Orcid Logo

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Abstract

In many applications, such as textiles, fibreglass, paper and several kinds of biological fibrous tissues, the main load-bearing constituents at the micro-scale are arranged as a fibre network. In these materials, rupture is usually driven by micro-mechanical failure mechanisms, and strain localisat...

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Published in: Computers & Structures
ISSN: 0045-7949
Published: Elsevier BV 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa57435
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spelling 2021-08-19T16:21:21.6936144 v2 57435 2021-07-22 Damage-driven strain localisation in networks of fibres: A computational homogenisation approach 91568dee6643b7d350f0d5e8edb7b46a 0000-0002-9378-4590 Eduardo de Souza Neto De Souza Neto Eduardo de Souza Neto De Souza Neto true false 2021-07-22 CIVL In many applications, such as textiles, fibreglass, paper and several kinds of biological fibrous tissues, the main load-bearing constituents at the micro-scale are arranged as a fibre network. In these materials, rupture is usually driven by micro-mechanical failure mechanisms, and strain localisation due to progressive damage evolution in the fibres is the main cause of macro-scale instability. We propose a strain-driven computational homogenisation formulationbased on Representative Volume Element (RVE), within a framework in which micro-scale fibre damage can lead to macro-scale localisation phenomena. The mechanical stiffness considered here for the fibrous structure system is due to: i) an intra-fibre mechanism in which each fibre is axially stretched, and as a result, it can suffer damage; ii) an inter-fibre mechanism in which the stiffness results from the variation of the relative angle between pairs of fibres. The homogenised tangent tensor, which comes from the contribution of these two mechanisms, is required to detect the so-called bifurcation point at the macro-scale, through the spectral analysis of the acoustic tensor. This analysis can precisely determine the instant at which the macro-scale problem becomes ill-posed. At such a point, the spectral analysis provides information about the macro-scale failure pattern (unit normal and crack-opening vectors). Special attention is devoted to present the theoretical fundamentals rigorously in the light of variational formulations for multi-scale models. Also, the impact of a recent derived more general boundary condition for fibre networks is assessed in the context of materials undergoing softening. Numerical examples showing the suitability of the present methodology are also shown and discussed. Journal Article Computers & Structures 255 106635 Elsevier BV 0045-7949 Computational homogenisation, Fibrous materials, Strain localisation, Regularised damage model 15 10 2021 2021-10-15 10.1016/j.compstruc.2021.106635 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2021-08-19T16:21:21.6936144 2021-07-22T08:56:42.9838924 College of Engineering Engineering Felipe Figueredo Rocha 1 Pablo Javier Blanco 2 Pablo Javier Sánchez 3 Eduardo de Souza Neto De Souza Neto 0000-0002-9378-4590 4 Raúl Antonino Feijóo 5 57435__20441__d69ea7ba09f84cdfad9a8bde3adc099c.pdf 57435.pdf 2021-07-22T08:58:32.1584494 Output 9782631 application/pdf Version of Record true ©2021 The Authors. This is an open access article under the CC BY license true eng http://creativecommons.org/licenses/by/4.0/
title Damage-driven strain localisation in networks of fibres: A computational homogenisation approach
spellingShingle Damage-driven strain localisation in networks of fibres: A computational homogenisation approach
Eduardo de Souza Neto De Souza Neto
title_short Damage-driven strain localisation in networks of fibres: A computational homogenisation approach
title_full Damage-driven strain localisation in networks of fibres: A computational homogenisation approach
title_fullStr Damage-driven strain localisation in networks of fibres: A computational homogenisation approach
title_full_unstemmed Damage-driven strain localisation in networks of fibres: A computational homogenisation approach
title_sort Damage-driven strain localisation in networks of fibres: A computational homogenisation approach
author_id_str_mv 91568dee6643b7d350f0d5e8edb7b46a
author_id_fullname_str_mv 91568dee6643b7d350f0d5e8edb7b46a_***_Eduardo de Souza Neto De Souza Neto
author Eduardo de Souza Neto De Souza Neto
author2 Felipe Figueredo Rocha
Pablo Javier Blanco
Pablo Javier Sánchez
Eduardo de Souza Neto De Souza Neto
Raúl Antonino Feijóo
format Journal article
container_title Computers & Structures
container_volume 255
container_start_page 106635
publishDate 2021
institution Swansea University
issn 0045-7949
doi_str_mv 10.1016/j.compstruc.2021.106635
publisher Elsevier BV
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 In many applications, such as textiles, fibreglass, paper and several kinds of biological fibrous tissues, the main load-bearing constituents at the micro-scale are arranged as a fibre network. In these materials, rupture is usually driven by micro-mechanical failure mechanisms, and strain localisation due to progressive damage evolution in the fibres is the main cause of macro-scale instability. We propose a strain-driven computational homogenisation formulationbased on Representative Volume Element (RVE), within a framework in which micro-scale fibre damage can lead to macro-scale localisation phenomena. The mechanical stiffness considered here for the fibrous structure system is due to: i) an intra-fibre mechanism in which each fibre is axially stretched, and as a result, it can suffer damage; ii) an inter-fibre mechanism in which the stiffness results from the variation of the relative angle between pairs of fibres. The homogenised tangent tensor, which comes from the contribution of these two mechanisms, is required to detect the so-called bifurcation point at the macro-scale, through the spectral analysis of the acoustic tensor. This analysis can precisely determine the instant at which the macro-scale problem becomes ill-posed. At such a point, the spectral analysis provides information about the macro-scale failure pattern (unit normal and crack-opening vectors). Special attention is devoted to present the theoretical fundamentals rigorously in the light of variational formulations for multi-scale models. Also, the impact of a recent derived more general boundary condition for fibre networks is assessed in the context of materials undergoing softening. Numerical examples showing the suitability of the present methodology are also shown and discussed.
published_date 2021-10-15T04:13:34Z
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