PSI - Issue 80

ScienceDirect Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2025) 000–000 Procedia Structural Integrity 80 (2026) 501–508 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 (2025) 000–000 Structural Integrity Procedia 00 (2025) 000–000

© 2025 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 Ferri Aliabadi Abstract Computational analysis of fracture in elasto-plastic materials is considered. The computational model introduces internal variables to treat with the nonlinear phenomena: a plastic strain and a damage-like variable. The former includes also plastic kinematic hardening and is commonly initiated first. The latter enables to represent fracture by mechanical damage. Additionally, the damage parameter character is based on the theory of phase-field fracture which causes material elastic properties degradation only in a narrow material band which forms a di ff used crack. Both these internal variables together with a displacement field define a structure state inside a unique quasi-static energy evolution process which allows to formulate a novel computational approach in a variational form. The evolution is approximated by a staggered time stepping procedure related to a separation of strain variables, including the plastic strain, from the damage one. Both the strain solution and damage solution at each instant are resolved by non linear programming algorithms implemented in an in-house MATLAB computational code whose numerical treatment incorporates approximation by finite elements. The computations with the proposed model include a simplified material element which enables to assess mutual influences of plasticity and damage processes resulting in crack nucleation and propagation. Keywords: Phase-field fracture; Elasto-plastic material; Quasi-static crack propagation; Quadratic programming; Staggered approach Fracture, Damage and Structural Health Monitoring On Implementation of a Computational Approach of Phase-Field Fracture to Elasto-Plastic Materials Roman Vodicˇka a a Technical University of Kosˇice, Faculty of Civil Engineering, Vysokosˇkolska´ 4, 042 00 Kosˇice, Slovakia Abstract Computational analysis of fracture in elasto-plastic materials is considered. The computational model introduces internal variables to treat with the nonlinear phenomena: a plastic strain and a damage-like variable. The former includes also plastic kinematic hardening and is commonly initiated first. The latter enables to represent fracture by mechanical damage. Additionally, the damage parameter character is based on the theory of phase-field fracture which causes material elastic properties degradation only in a narrow material band which forms a di ff used crack. Both these internal variables together with a displacement field define a structure state inside a unique quasi-static energy evolution process which allows to formulate a novel computational approach in a variational form. The evolution is approximated by a staggered time stepping procedure related to a separation of strain variables, including the plastic strain, from the damage one. Both the strain solution and damage solution at each instant are resolved by non linear programming algorithms implemented in an in-house MATLAB computational code whose numerical treatment incorporates approximation by finite elements. The computations with the proposed model include a simplified material element which enables to assess mutual influences of plasticity and damage processes resulting in crack nucleation and propagation. Keywords: Phase-field fracture; Elasto-plastic material; Quasi-static crack propagation; Quadratic programming; Staggered approach Fracture, Damage and Structural Health Monitoring On Implementation of a Computational Approach of Phase-Field Fracture to Elasto-Plastic Materials Roman Vodicˇka a a Technical University of Kosˇice, Faculty of Civil Engineering, Vysokosˇkolska´ 4, 042 00 Kosˇice, Slovakia Abstract Computational analysis of fracture in elasto-plastic materials is considered. The computational model introduces internal variables to treat with the nonlinear phenomena: a plastic strain and a damage-like variable. The former includes also plastic kinematic hardening and is commonly initiated first. The latter enables to represent fracture by mechanical damage. Additionally, the damage parameter character is based on the theory of phase-field fracture which causes material elastic properties degradation only in a narrow material band which forms a di ff used crack. Both these internal variables together with a displacement field define a structure state inside a unique quasi-static energy evolution process which allows to formulate a novel computational approach in a variational form. The evolution is approximated by a staggered time stepping procedure related to a separation of strain variables, including the plastic strain, from the damage one. Both the strain solution and damage solution at each instant are resolved by non linear programming algorithms implemented in an in-house MATLAB computational code whose numerical treatment incorporates approximation by finite elements. The computations with the proposed model include a simplified material element which enables to assess mutual influences of plasticity and damage processes resulting in crack nucleation and propagation. Keywords: Phase-field fracture; Elasto-plastic material; Quasi-static crack propagation; Quadratic programming; Staggered approach www.elsevier.com / locate / procedia www.elsevier.com / locate / procedia Fracture, Damage and Structural Health Monitoring On Implementation of a Computational Approach of Phase-Field Fracture to Elasto-Plastic Materials Roman Vodicˇka a a Technical University of Kosˇice, Faculty of Civil Engineering, Vysokosˇkolska´ 4, 042 00 Kosˇice, Slovakia 1. Introduction 1. Introduction Damage and fracture are important concepts in mechanics of solid materials. If additionally the material is ductile, the degradation process involves additional inelastic process zones caused by plastic deformation close to the crack tip. Cumulating all such phenomena leads to loss of load bearing capacity of engineering structures and may result in catastrophic scenarios for them. Computational approaches for fracture suitable for a finite-element codes are frequently related to the variational fracture theory Francfort and Marigo (1998), which provided also the base for the phase-field fracture model formu lated in Bourdin et al. (2008); Miehe et al. (2010). The phase-field model introduces an internal parameter character ising degradation of strain energy. Its distribution defines crack path so that the actual location of discrete cracks is replaced by a distribution of narrow bands of a finite width of degraded material known as smear cracks. The width Damage and fracture are important concepts in mechanics of solid materials. If additionally the material is ductile, the degradation process involves additional inelastic process zones caused by plastic deformation close to the crack tip. Cumulating all such phenomena leads to loss of load bearing capacity of engineering structures and may result in catastrophic scenarios for them. Computational approaches for fracture suitable for a finite-element codes are frequently related to the variational fracture theory Francfort and Marigo (1998), which provided also the base for the phase-field fracture model formu lated in Bourdin et al. (2008); Miehe et al. (2010). The phase-field model introduces an internal parameter character ising degradation of strain energy. Its distribution defines crack path so that the actual location of discrete cracks is replaced by a distribution of narrow bands of a finite width of degraded material known as smear cracks. The width Damage and fracture are important concepts in mechanics of solid materials. If additionally the material is ductile, the degradation process involves additional inelastic process zones caused by plastic deformation close to the crack tip. Cumulating all such phenomena leads to loss of load bearing capacity of engineering structures and may result in catastrophic scenarios for them. Computational approaches for fracture suitable for a finite-element codes are frequently related to the variational fracture theory Francfort and Marigo (1998), which provided also the base for the phase-field fracture model formu lated in Bourdin et al. (2008); Miehe et al. (2010). The phase-field model introduces an internal parameter character ising degradation of strain energy. Its distribution defines crack path so that the actual location of discrete cracks is replaced by a distribution of narrow bands of a finite width of degraded material known as smear cracks. The width ∗ 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 © 2025 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 Ferri Aliabadi 10.1016/j.prostr.2026.02.048 2210-7843 c 2025 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 2025 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 2025 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.