PSI - Issue 52

ScienceDirect Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2023) 000–000 Procedia Structural Integrity 52 (2024) 242–251 Available online at www.sciencedirect.com Available online at www.sciencedirect.com Available online at www.sciencedirect.com

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Structural Integrity Procedia 00 (2023) 000–000 Structural Integrity Procedia 00 (2023) 000–000

© 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 A computational model is stated to study dynamic crack propagation in quasi-brittle materials exposed to time-dependent loading conditions. Under such conditions, inertial e ff ects of structural components play an important role in modelling crack propagation problems. The computational model is proposed within the theory of smeared cracks which use damage-like internal variables. Here, fracture considers phase-field damage which gives rise to a material degradation in a narrow material strip defining the smeared crack. Based on the energy formulation using the Lagrangian of the system, the proposed computational approach in troduces a staggered scheme adopted to solve the coupled system and providing it in a variational form within the time stepping procedure. The numerical data are obtained by quadratic programming algorithms implemented together with a finite element code. Keywords: Phase-field fracture; Dynamic crack propagation; Quadratic programming; Staggered approach Fracture, Damage and Structural Health Monitoring A Computational approach of Dynamic Quasi-Brittle Fracture Using a Phase-Field Model Roman Vodicˇka a a Technical University of Kosˇice, Faculty of Civil Engineering, Vysokosˇkolska´ 4, 042 00 Kosˇice, Slovakia Abstract A computational model is stated to study dynamic crack propagation in quasi-brittle materials exposed to time-dependent loading conditions. Under such conditions, inertial e ff ects of structural components play an important role in modelling crack propagation problems. The computational model is proposed within the theory of smeared cracks which use damage-like internal variables. Here, fracture considers phase-field damage which gives rise to a material degradation in a narrow material strip defining the smeared crack. Based on the energy formulation using the Lagrangian of the system, the proposed computational approach in troduces a staggered scheme adopted to solve the coupled system and providing it in a variational form within the time stepping procedure. The numerical data are obtained by quadratic programming algorithms implemented together with a finite element code. Keywords: Phase-field fracture; Dynamic crack propagation; Quadratic programming; Staggered approach Fracture, Damage and Structural Health Monitoring A Computational approach of Dynamic Quasi-Brittle Fracture Using a Phase-Field Model Roman Vodicˇka a a Technical University of Kosˇice, Faculty of Civil Engineering, Vysokosˇkolska´ 4, 042 00 Kosˇice, Slovakia Abstract A computational model is stated to study dynamic crack propagation in quasi-brittle materials exposed to time-dependent loading conditions. Under such conditions, inertial e ff ects of structural components play an important role in modelling crack propagation problems. The computational model is proposed within the theory of smeared cracks which use damage-like internal variables. Here, fracture considers phase-field damage which gives rise to a material degradation in a narrow material strip defining the smeared crack. Based on the energy formulation using the Lagrangian of the system, the proposed computational approach in troduces a staggered scheme adopted to solve the coupled system and providing it in a variational form within the time stepping procedure. The numerical data are obtained by quadratic programming algorithms implemented together with a finite element code. Keywords: Phase-field fracture; Dynamic crack propagation; Quadratic programming; Staggered approach Damage, degradation and eventually fracture of a material are significant concepts in solid mechanics. Even if these phenomena are solved quasi-statically, they provide satisfactory agreement with real behaviour of structures in such models. Nevertheless, if the processes tend to be fast, the inertial e ff ect may substantially modify the response of the structural components and in such a way also modify cracks and their formation processes. Anyhow, any information, including those of crack propagation, in real structures may be transfered only at a finite speed. Therefore, dynamic crack propagation should be taken into account in more complex computational models of fracture. Many brittle fracture computational approaches suitable for a finite-element implementation, are related or directly founded on the work Francfort and Marigo (1998), which formulated the problem variationally in terms of strain en ergy in domains and surface energy of arisen cracks related to Gri ffi th’s concept of crack propagation. To facilitate the solution of the problem with unknown location of discrete cracks, a rearrangement of the fracture mechanisms was proposed to define a concept of smear cracks which does not define the crack as a place of a material discontinuity. It works with an internal variable instead which di ff uses the flaw locus to have a finite width and the crack is than seen as a narrow band of the material. One of such concepts includes the phase-field model (PFM) of fracture, which can www.elsevier.com / locate / procedia www.elsevier.com / locate / procedia Fracture, Damage and Structural Health Monitoring A Computational approach of Dynamic Quasi-Brittle Fracture Using a Phase-Field Model Roman Vodicˇka a a Technical University of Kosˇice, Faculty of Civil Engineering, Vysokosˇkolska´ 4, 042 00 Kosˇice, Slovakia 1. Introduction 1. Introduction Damage, degradation and eventually fracture of a material are significant concepts in solid mechanics. Even if these phenomena are solved quasi-statically, they provide satisfactory agreement with real behaviour of structures in such models. Nevertheless, if the processes tend to be fast, the inertial e ff ect may substantially modify the response of the structural components and in such a way also modify cracks and their formation processes. Anyhow, any information, including those of crack propagation, in real structures may be transfered only at a finite speed. Therefore, dynamic crack propagation should be taken into account in more complex computational models of fracture. Many brittle fracture computational approaches suitable for a finite-element implementation, are related or directly founded on the work Francfort and Marigo (1998), which formulated the problem variationally in terms of strain en ergy in domains and surface energy of arisen cracks related to Gri ffi th’s concept of crack propagation. To facilitate the solution of the problem with unknown location of discrete cracks, a rearrangement of the fracture mechanisms was proposed to define a concept of smear cracks which does not define the crack as a place of a material discontinuity. It works with an internal variable instead which di ff uses the flaw locus to have a finite width and the crack is than seen as a narrow band of the material. One of such concepts includes the phase-field model (PFM) of fracture, which can Damage, degradation and eventually fracture of a material are significant concepts in solid mechanics. Even if these phenomena are solved quasi-statically, they provide satisfactory agreement with real behaviour of structures in such models. Nevertheless, if the processes tend to be fast, the inertial e ff ect may substantially modify the response of the structural components and in such a way also modify cracks and their formation processes. Anyhow, any information, including those of crack propagation, in real structures may be transfered only at a finite speed. Therefore, dynamic crack propagation should be taken into account in more complex computational models of fracture. Many brittle fracture computational approaches suitable for a finite-element implementation, are related or directly founded on the work Francfort and Marigo (1998), which formulated the problem variationally in terms of strain en ergy in domains and surface energy of arisen cracks related to Gri ffi th’s concept of crack propagation. To facilitate the solution of the problem with unknown location of discrete cracks, a rearrangement of the fracture mechanisms was proposed to define a concept of smear cracks which does not define the crack as a place of a material discontinuity. It works with an internal variable instead which di ff uses the flaw locus to have a finite width and the crack is than seen as a narrow band of the material. One of such concepts includes the phase-field model (PFM) of fracture, which can ∗ Corresponding author. Tel.: + 421-55-602-4388. E-mail address: roman.vodicka@tuke.sk 1. Introduction

∗ Corresponding author. Tel.: + 421-55-602-4388. E-mail address: roman.vodicka@tuke.sk ∗ Corresponding author. Tel.: + 421-55-602-4388. E-mail address: roman.vodicka@tuke.sk

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.2023.12.025 2210-7843 c 2023 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 Professor Ferri Aliabadi. 2210-7843 c 2023 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 Professor Ferri Aliabadi. 2210-7843 c 2023 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 Professor Ferri Aliabadi.