PSI - Issue 35

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ScienceDirect

Procedia Structural Integrity 35 (2022) 18–24 Structural Integrity Procedia 00 (2021) 000–000 Structural Integrity Procedia 00 (2021) 000–000

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© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of IWPDF 2021 Chair, Tuncay Yalçinkaya © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) r-review under responsibility of IWPDF 2021 Chair, Tuncay Yalc¸inkaya. Keywords: Elasto-plasticity; softening; localizing implicit gradient; ductile fracture Abstract As opposed to brittle fracture, the failure of ductile materials is preceded by severe plastic deformations. Microscopic mecha nisms i.e., void growth and coalescence result in macroscopic property degradation causing softening, localization, and finally macroscopic crack. This contribution focuses on softening in elasto-plasticity and its mesh-objective description using an implicit gradient type of non-local damage mechanics framework. As reported in several studies Geers et al. (1998), Poh and Sun (2017), artificial widening of localization zone is observed when conventional implicit gradient type regularization is used. To circumvent this non-physical artifact, localizing implicit gradient damage (LIGD) formulation that is motivated by higher order continuum arguments, is adopted, Poh and Sun (2017). As opposed to previous remedies to artificial widening of the localization zone, LIGD proposes an internal length scale that decreases with deformation. A two-field (displacement-non-local equivalent plastic strain) hexahedra and a three-field (displacement-pressure-non-local equivalent plastic strain) tetrahedra element are formulated and im plemented in commercial finite element software Abaqus through user element (UEL) subroutine. The e ff ectiveness of the approach is demonstrated by solving two numerical examples. © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of IWPDF 2021 Chair, Tuncay Yalc¸inkaya. Keywords: Elasto-plasticity; softening; localizing implicit gradient; ductile fracture 2nd International Workshop on Plasticity, Damage and Fracture of Engineering Materials Localizing Implicit Gradient Damage Based Treatment of Softening in Elasto-plasticity S. Yas¸ayanlar a , B. Kac¸maz a , ˙I. O¨ zdemir a, ∗ a I˙zmir Institute of Technology, Faculty of Engineering, Department of Civil Engineering, 35430, Urla, I˙zmir, Turkey Abstract As opposed to brittle fracture, the failure of ductile materials is preceded by severe plastic deformations. Microscopic mecha nisms i.e., void growth and coalescence result in macroscopic property degradation causing softening, localization, and finally macroscopic crack. This contribution focuses on softening in elasto-plasticity and its mesh-objective description using an implicit gradient type of non-local damage mechanics framework. As reported in several studies Geers et al. (1998), Poh and Sun (2017), artificial widening of localization zone is observed when conventional implicit gradient type regularization is used. To circumvent this non-physical artifact, localizing implicit gradient damage (LIGD) formulation that is motivated by higher order continuum arguments, is adopted, Poh and Sun (2017). As opposed to previous remedies to artificial widening of the localization zone, LIGD proposes an internal length scale that decreases with deformation. A two-field (displacement-non-local equivalent plastic strain) hexahedra and a three-field (displacement-pressure-non-local equivalent plastic strain) tetrahedra element are formulated and im plemented in commercial finite element software Abaqus through user element (UEL) subroutine. The e ff ectiveness of the approach is demonstrated by solving two numerical examples. 2nd International Workshop on Plasticity, Damage and Fracture of Engineering Materials Localizing Implicit Gradient Damage Based Treatment of Softening in Elasto-plasticity S. Yas¸ayanlar a , B. Kac¸maz a , ˙I. O¨ zdemir a, ∗ a I˙zmir Institute of Technology, Faculty of Engineering, Department of Civil Engineering, 35430, Urla, I˙zmir, Turkey

1. Introduction 1. Introduction

The ultimate failure of ductile materials is typically preceded by significant inelastic deformations and character istic softening. The numerical solutions (i.e. finite element) which are based on standard continuum damage-elasto plasticity formulations su ff er from mesh dependency in the sense that both the size and the direction of the localization zone depend on the resolution of the employed finite element mesh. In the limit (i.e. extremely fine resolutions), the dissipation due to damage tends to zero which is physically not consistent. The so-called regularization techniques have been formulated using non-local integral or gradient enhancements of specific variables reflecting the e ff ect of interactions between underlying micro failure processes, Bazant (1991). The ultimate failure of ductile materials is typically preceded by significant inelastic deformations and character istic softening. The numerical solutions (i.e. finite element) which are based on standard continuum damage-elasto plasticity formulations su ff er from mesh dependency in the sense that both the size and the direction of the localization zone depend on the resolution of the employed finite element mesh. In the limit (i.e. extremely fine resolutions), the dissipation due to damage tends to zero which is physically not consistent. The so-called regularization techniques have been formulated using non-local integral or gradient enhancements of specific variables reflecting the e ff ect of interactions between underlying micro failure processes, Bazant (1991).

∗ Corresponding author. Tel.: + 90-232-750-6810 ; fax: + 90-232-750-6801. E-mail address: izzetozdemir@iyte.edu.tr ∗ Corresponding author. Tel.: + 90-232-750-6810 ; fax: + 90-232-750-6801. E-mail address: izzetozdemir@iyte.edu.tr

2452-3216 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of IWPDF 2021 Chair, Tuncay Yal ç inkaya 10.1016/j.prostr.2021.12.043 2210-7843 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of IWPDF 2021 hair, Tuncay Yalc¸inkaya. 2210-7843 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of IWPDF 2021 Chair, Tuncay Yalc¸inkaya.