PSI - Issue 52

ScienceDirect Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2023) 000–000 Structural Integrity Procedia 00 (2023) 000–000 Available online at www.sciencedirect.com Available online at www.sciencedirect.com Available online at www.sciencedirect.com Available online at www.sciencedirect.com Procedia Structural Integrity 52 (2024) 583–593 Structural Integrity Procedia 00 (2023) 000–000

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© 2023 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 Professor Ferri Aliabadi Abstract Crack growth simulation using the mesh-free particle method has become more popular. One of the most used particle methods is the smoothed particle hydrodynamics (SPH). There are two crack modelling techniques in SPH using the particle deletion and interaction deletion frameworks. The particle deletion technique represents the crack by removing certain particles at the crack tip. Then, the crack growth path and the stress field around the crack tip can be observed. Another technique using particle interaction deletion uses a di ff erent approach. The crack is located between the particles, and the particle interaction that intersects the crack plane is removed. Then, the crack growth direction is analysed using the maximum principal plane direction, and the stress intensity factor is calculated using the J-integral method. One of the latest publications of SPH in the fracture mechanics area proposed a pseudo-spring-based SPH for fatigue crack growth simulation. The idea of the pseudo-spring is similar to the particle interaction deletion framework for crack modelling. In this research, a comparative study is performed to compare the performance of particle deletion and interaction deletion framework in handling crack growth problems using the updated Lagrangian SPH formulation. The study analyses the accuracy and simplicity of the crack growth modelling using the two frameworks. Keywords: Fatigue; Crack growth; Particle method; SPH Fracture, Damage and Structural Health Monitoring SPH Method for Crack Growth Modelling using Particle Deletion and Interaction Pair-based Framework Made Wiragunarsa a , Lavi Rizki Zuhal b, ∗ , Tatacipta Dirgantara a , Ichsan Setya Putra a a Lightweight Structure Research Group b Flight Physics Research Group Faculty of Mechanical and Aerospace Engineering, Institut Teknologi Bandung, Ganesha 10, Bandung 40132, Indonesia Abstract Crack growth simulation using the mesh-free particle method has become more popular. One of the most used particle methods is the smoothed particle hydrodynamics (SPH). There are two crack modelling techniques in SPH using the particle deletion and interaction deletion frameworks. The particle deletion technique represents the crack by removing certain particles at the crack tip. Then, the crack growth path and the stress field around the crack tip can be observed. Another technique using particle interaction deletion uses a di ff erent approach. The crack is located between the particles, and the particle interaction that intersects the crack plane is removed. Then, the crack growth direction is analysed using the maximum principal plane direction, and the stress intensity factor is calculated using the J-integral method. One of the latest publications of SPH in the fracture mechanics area proposed a pseudo-spring-based SPH for fatigue crack growth simulation. The idea of the pseudo-spring is similar to the particle interaction deletion framework for crack modelling. In this research, a comparative study is performed to compare the performance of particle deletion and interaction deletion framework in handling crack growth problems using the updated Lagrangian SPH formulation. The study analyses the accuracy and simplicity of the crack growth modelling using the two frameworks. Keywords: Fatigue; Crack growth; Particle method; SPH Fracture, Damage and Structural Health Monitoring SPH Method for Crack Growth Modelling using Particle Deletion and Interaction Pair-based Framework Made Wiragunarsa a , Lavi Rizki Zuhal b, ∗ , Tatacipta Dirgantara a , Ichsan Setya Putra a a Lightweight Structure Research Group b Flight Physics Research Group Faculty of Mechanical and Aerospace Engineering, Institut Teknologi Bandung, Ganesha 10, Bandung 40132, Indonesia Abstract Crack growth simulation using the mesh-free particle method has become more popular. One of the most used particle methods is the smoothed particle hydrodynamics (SPH). There are two crack modelling techniques in SPH using the particle deletion and interaction deletion frameworks. The particle deletion technique represents the crack by removing certain particles at the crack tip. Then, the crack growth path and the stress field around the crack tip can be observed. Another technique using particle interaction deletion uses a di ff erent approach. The crack is located between the particles, and the particle interaction that intersects the crack plane is removed. Then, the crack growth direction is analysed using the maximum principal plane direction, and the stress intensity factor is calculated using the J-integral method. One of the latest publications of SPH in the fracture mechanics area proposed a pseudo-spring-based SPH for fatigue crack growth simulation. The idea of the pseudo-spring is similar to the particle interaction deletion framework for crack modelling. In this research, a comparative study is performed to compare the performance of particle deletion and interaction deletion framework in handling crack growth problems using the updated Lagrangian SPH formulation. The study analyses the accuracy and simplicity of the crack growth modelling using the two frameworks. Keywords: Fatigue; Crack growth; Particle method; SPH The behavior of fatigue crack propagation in mechanical structures is often complex. Various methods have been employed to analyse these phenomena, including mesh-free and finite element methods, with X-FEM being the most popular approach. However, commercial X-FEM methods have di ffi culty solving the cracks merging problem. As an alternative to overcome the cumbersome of the FEM, mesh-free based on particle discretisation was developed. Smoothed particle hydrodynamics (SPH) which was reported in Lucy [1997], Gingold and Monaghan [1997], is a mesh-free method initially used in astrophysics, which replaces the mesh with a set of particles to model the physical domain. Several improvements have been made to reduce the zero energy mode, tensile instability, and boundary e ff ect using artificial viscosity Monaghan [1994], artificial stress Monaghan [2000], and corrected SPH formulation Chen and Beraun [2000], Bonet and Lok [1998]. In computational solid mechanics, SPH has been successfully Fracture, Damage and Structural Health Monitoring SPH Method for Crack Growth Modelling using Particle Deletion and Interaction Pair-based Framework Made Wiragunarsa a , Lavi Rizki Zuhal b, ∗ , Tatacipta Dirgantara a , Ichsan Setya Putra a a Lightweight Structure Research Group b Flight Physics Research Group Faculty of Mechanical and Aerospace Engineering, Institut Teknologi Bandung, Ganesha 10, Bandung 40132, Indonesia Abstract Crack growth simulation using the mesh-free particle method has become more popular. One of the most used particle methods is the smoothed particle hydrodynamics (SPH). There are two crack modelling techniques in SPH using the particle deletion and interaction deletion frameworks. The particle deletion technique represents the crack by removing certain particles at the crack tip. Then, the crack growth path and the stress field around the crack tip can be observed. Another technique using particle interaction deletion uses a di ff erent approach. The crack is located between the particles, and the particle interaction that intersects the crack plane is removed. Then, the crack growth direction is analysed using the maximum principal plane direction, and the stress intensity factor is calculated using the J-integral method. One of the latest publications of SPH in the fracture mechanics area proposed a pseudo-spring-based SPH for fatigue crack growth simulation. The idea of the pseudo-spring is similar to the particle interaction deletion framework for crack modelling. In this research, a comparative study is performed to compare the performance of particle deletion and interaction deletion framework in handling crack growth problems using the updated Lagrangian SPH formulation. The study analyses the accuracy and simplicity of the crack growth modelling using the two frameworks. Keywords: Fatigue; Crack growth; Particle method; SPH 1. Introduction The behavior of fatigue crack propagation in mechanical structures is often complex. Various methods have been employed to analyse these phenomena, including mesh-free and finite element methods, with X-FEM being the most popular approach. However, commercial X-FEM methods have di ffi culty solving the cracks merging problem. As an alternative to overcome the cumbersome of the FEM, mesh-free based on particle discretisation was developed. Smoothed particle hydrodynamics (SPH) which was reported in Lucy [1997], Gingold and Monaghan [1997], is a mesh-free method initially used in astrophysics, which replaces the mesh with a set of particles to model the physical domain. Several improvements have been made to reduce the zero energy mode, tensile instability, and boundary e ff ect using artificial viscosity Monaghan [1994], artificial stress Monaghan [2000], and corrected SPH formulation Chen and Beraun [2000], Bonet and Lok [1998]. In computational solid mechanics, SPH has been successfully Fracture, Damage and Structural Health Monitoring SPH Method for Crack Growth Modelling using Particle Deletion and Interaction Pair-based Framework Made Wiragunarsa a , Lavi Rizki Zuhal b, ∗ , Tatacipta Dirgantara a , Ichsan Setya Putra a a Lightweight Structure Research Group b Flight Physics Research Group Faculty of Mechanical and Aerospace Engineering, Institut Teknologi Bandung, Ganesha 10, Bandung 40132, Indonesia 1. Introduction 1. Introduction The behavior of fatigue crack propagation in mechanical structures is often complex. Various methods have been employed to analyse these phenomena, including mesh-free and finite element methods, with X-FEM being the most popular approach. However, commercial X-FEM methods have di ffi culty solving the cracks merging problem. As an alternative to overcome the cumbersome of the FEM, mesh-free based on particle discretisation was developed. Smoothed particle hydrodynamics (SPH) which was reported in Lucy [1997], Gingold and Monaghan [1997], is a mesh-free method initially used in astrophysics, which replaces the mesh with a set of particles to model the physical domain. Several improvements have been made to reduce the zero energy mode, tensile instability, and boundary e ff ect using artificial viscosity Monaghan [1994], artificial stress Monaghan [2000], and corrected SPH formulation Chen and Beraun [2000], Bonet and Lok [1998]. In computational solid mechanics, SPH has been successfully The behavior of fatigue crack propagation in mechanical structures is often complex. Various methods have been employed to analyse these phenomena, including mesh-free and finite element methods, with X-FEM being the most popular approach. However, commercial X-FEM methods have di ffi culty solving the cracks merging problem. As an alternative to overcome the cumbersome of the FEM, mesh-free based on particle discretisation was developed. Smoothed particle hydrodynamics (SPH) which was reported in Lucy [1997], Gingold and Monaghan [1997], is a mesh-free method initially used in astrophysics, which replaces the mesh with a set of particles to model the physical domain. Several improvements have been made to reduce the zero energy mode, tensile instability, and boundary e ff ect using artificial viscosity Monaghan [1994], artificial stress Monaghan [2000], and corrected SPH formulation Chen and Beraun [2000], Bonet and Lok [1998]. In computational solid mechanics, SPH has been successfully ∗ Corresponding author: Lavi Rizki Zuhal E-mail address: lavi.zuhal@itb.ac.id Structural Integrity Procedia 00 (2023) 000–000 www.elsevier.com / locate / procedia 1. Introduction

∗ Corresponding author: Lavi Rizki Zuhal E-mail address: lavi.zuhal@itb.ac.id ∗ Corresponding author: Lavi Rizki Zuhal E-mail address: lavi.zuhal@itb.ac.id

2210-7843 .

2452-3216 © 2023 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 Professor Ferri Aliabadi 10.1016/j.prostr.2023.12.058 2210-7843 . ∗ Corresponding author: Lavi Rizki Zuhal E-mail address: lavi.zuhal@itb.ac.id 2210-7843 . 2210-7843 .