PSI - Issue 61

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ScienceDirect

Procedia Structural Integrity 61 (2024) 138–147 Structural Integrity Procedia 00 (2024) 000–000 Structural Integrity Procedia 00 (2024) 000–000

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3rd International Workshop on Plasticity, Damage and Fracture of Engineering Materials (IWPDF 2023) Formulation of a Bilinear Traction-Separation Interface Law in 3rd International Workshop on Plasticity, Damage and Fracture of Engineering Materials (IWPDF 2023) Formulation of a Bilinear Traction-Separation Interface Law in

Boundary Elements with Homogenization Ahmet Arda Akay a, ∗ , Serdar Go¨ktepe b , Ercan Gu¨rses a Boundary Elements with Homogenization Ahmet Arda Akay a, ∗ , Serdar Go¨ktepe b , Ercan Gu¨rses a

a Department of Aerospace Engineering, Middle East Technical University, Dumlupınar Bulvarı 1, C¸ ankaya, Ankara, 06800, Tu¨rkiye b Department of Civil Engineering, Middle East Technical University, Dumlupınar Bulvarı 1, C¸ ankaya, Ankara, 06800, Tu¨rkiye a Department of Aerospace Engineering, Middle East Technical University, Dumlupınar Bulvarı 1, C¸ ankaya, Ankara, 06800, Tu¨rkiye b Department of Civil Engineering, Middle East Technical University, Dumlupınar Bulvarı 1, C¸ ankaya, Ankara, 06800, Tu¨rkiye

© 2024 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 the scientific committee of IWPDF 2023 Chairman Abstract Similar to most conventional composite materials, the interface is generally the weakest part of nanocomposites. For this rea son, the behavior of the reinforcement-matrix interface is critical for determining the strength of nanocomposites. Especially in nanocomposites, if no special precautions are taken, the matrix consisting of nano-reinforcements and polymer chains are bound to each other by weak van der Waals interactions and electrostatic interactions. As a result, in most nanocomposites under loading, damage first begins as a separation at the interface. This study focuses on a key aspect of modeling polymer nanocomposites: the interface between the inclusion and the matrix. First, the alternative boundary conditions of homogenization are presented and then implemented into the boundary element method. Afterward, a bilinear interface law between inclusion and matrix is defined in the boundary element-based homogenization method. The homogenized stress response of a heterogeneous Representative Volume Element (RVE) undergoing debonding is compared with numerical studies from the literature. RVEs, including both single and multi-inclusions, are studied. Comparisons are made with the studies related to the modeling interfaces using micromechanics and Mori-Tanaka-based approaches, and boundary element method-based approaches. A good agreement is observed between results. © 2024 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 the scientific committee of IWPDF 2023. Keywords: Boundary element method; homogenization; bilinear traction-seperation interface law; uniform traction boundary condition; linear displacement boundary condition; periodic displacement boundary condition Abstract Similar to most conventional composite materials, the interface is generally the weakest part of nanocomposites. For this rea son, the behavior of the reinforcement-matrix interface is critical for determining the strength of nanocomposites. Especially in nanocomposites, if no special precautions are taken, the matrix consisting of nano-reinforcements and polymer chains are bound to each other by weak van der Waals interactions and electrostatic interactions. As a result, in most nanocomposites under loading, damage first begins as a separation at the interface. This study focuses on a key aspect of modeling polymer nanocomposites: the interface between the inclusion and the matrix. First, the alternative boundary conditions of homogenization are presented and then implemented into the boundary element method. Afterward, a bilinear interface law between inclusion and matrix is defined in the boundary element-based homogenization method. The homogenized stress response of a heterogeneous Representative Volume Element (RVE) undergoing debonding is compared with numerical studies from the literature. RVEs, including both single and multi-inclusions, are studied. Comparisons are made with the studies related to the modeling interfaces using micromechanics and Mori-Tanaka-based approaches, and boundary element method-based approaches. A good agreement is observed between results. © 2024 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 the scientific committee of IWPDF 2023. Keywords: Boundary element method; homogenization; bilinear traction-seperation interface law; uniform traction boundary condition; linear displacement boundary condition; periodic displacement boundary condition

1. Introduction 1. Introduction

The boundary element method is a strong alternative to the finite element method (FEM) for linear problems with stress concentrations that require greater precision. The most important advantage of the boundary element method is that only the discretization of the boundary is su ffi cient to solve the entire domain, rather than the discretization of the whole volume, Brebbia and Dominguez (1992). In the problems of heterogeneous domains having very small The boundary element method is a strong alternative to the finite element method (FEM) for linear problems with stress concentrations that require greater precision. The most important advantage of the boundary element method is that only the discretization of the boundary is su ffi cient to solve the entire domain, rather than the discretization of the whole volume, Brebbia and Dominguez (1992). In the problems of heterogeneous domains having very small

∗ Corresponding author. Tel.: + 90-554-307-5277 E-mail address: aakay@metu.edu.tr ∗ Corresponding author. Tel.: + 90-554-307-5277 E-mail address: aakay@metu.edu.tr

2452-3216 © 2024 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 the scientific committee of IWPDF 2023 Chairman 10.1016/j.prostr.2024.06.019 2210-7843 © 2024 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 the scientific committee of IWPDF 2023. 2210-7843 © 2024 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 the scientific committee of IWPDF 2023.