PSI - Issue 42

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ScienceDirect

Procedia Structural Integrity 42 (2022) 927–934 Structural Integrity Procedia 00 (2019) 000–000 Structural Integrity Procedia 00 (201 ) 000–000

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© 2022 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 the 23 European Conference on Fracture – ECF23 Abstract A computational model fracture in materials with inclusions is considered. The proposed model allows to predict crack initiation and growth in quasi-brittle materials. The inclusions cause that cracks may appear inside the matrix materials or along matrix inclusion interfaces. The model can treat them both using two internal variables in a form considered in damage mechanics so that crack formation process is a consequence of a material degradation. The first of the damage variables is defined at matrix-inclusion interfaces and it is related to by a thin degradable adhesive layer so that an adequate stress-strain relation is rendered as in common cohesive zone models. The second variable is defined in the structural domains, matrix plus inclusions, as a phase-field fracture variable which causes domain elastic properties degradation in a narrow material strip that results in a di ff use form of a crack. Both these damaging schemes are expressed in a unique quasi-static energy evolution process. The numerical solution approach is thus rendered from a variational form obtained by a staggered time-stepping procedure related to a separation of deformation variables from the damage ones, and by using sequential quadratic programming algorithms implemented within a MATLAB finite element code. The numerical simulations with the model include simplified structural and material elements with inclusions. 2020 The Authors. Published by Elsevier B.V. is is an open access article under the CC BY-NC-ND license (http: // creativec mmons.org / licenses / by-nc-nd / 4.0 / ) r-review under responsibility of 23 European Conference on F acture – ECF23 . Keywords: Phase-field fracture; Interface damage; Quadratic programming; Staggered approach 23 European Conference on Fracture – ECF23 A quasi-static computational model for interface and phase-field fracture in domains with inclusions Roman Vodicˇka a a Technical University of Kosˇice, Faculty of Civil Engineering, Vysokosˇkolska´ 4, 042 00 Kosˇice, Slovakia Abstract A computational model fracture in materials with inclusions is considered. The proposed model allows to predict crack initiation and growth in quasi-brittle materials. The inclusions cause that cracks may appear inside the matrix materials or along matrix inclusion interfaces. The model can treat them both using two internal variables in a form considered in damage mechanics so that crack formation process is a consequence of a material degradation. The first of the damage variables is defined at matrix-inclusion interfaces and it is related to by a thin degradable adhesive layer so that an adequate stress-strain relation is rendered as in common cohesive zone models. The second variable is defined in the structural domains, matrix plus inclusions, as a phase-field fracture variable which causes domain elastic properties degradation in a narrow material strip that results in a di ff use form of a crack. Both these damaging schemes are expressed in a unique quasi-static energy evolution process. The numerical solution approach is thus rendered from a variational form obtained by a staggered time-stepping procedure related to a separation of deformation variables from the damage ones, and by using sequential quadratic programming algorithms implemented within a MATLAB finite element code. The numerical simulations with the model include simplified structural and material elements with inclusions. © 2020 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 23 European Conference on Fracture – ECF23 . Keywords: Phase-field fracture; Interface damage; Quadratic programming; Staggered approach 23 European Conference on Fracture – ECF23 A quasi-static computational model for interface and phase-field fracture in domains with inclusions Roman Vodicˇka a a Technical University of Kosˇice, Faculty of Civil Engineering, Vysokosˇkolska´ 4, 042 00 Kosˇice, Slovakia

1. Introduction 1. Introduction

Cracks in materials together with those at material joints may form various motifs depending on the form of loading, geometrical description or constraints of the structure. Nevertheless, even for very similar exterior conditions the crack patterns may be di ff erent if the material is known to behave di ff erently, e.g., under tension and in shear. In relation to degradation processes, it is frequently explained by dependence of critical energy release rate on the mode of fracture. It is meant to incorporate this assumption into the present computational model. Cracks in materials together with those at material joints may form various motifs depending on the form of loading, geometrical description or constraints of the structure. Nevertheless, even for very similar exterior conditions the crack patterns may be di ff erent if the material is known to behave di ff erently, e.g., under tension and in shear. In relation to degradation processes, it is frequently explained by dependence of critical energy release rate on the mode of fracture. It is meant to incorporate this assumption into the present computational model.

∗ 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 © 2022 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 the 23 European Conference on Fracture – ECF23 10.1016/j.prostr.2022.12.117 2210-7843 © 2020 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 u der responsibility of 23 European Conference on Fracture – ECF23 . 2210-7843 © 2020 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 23 European Conference on Fracture – ECF23 .