PSI - Issue 74

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ScienceDirect

Procedia Structural Integrity 74 (2025) 91–98 Structural Integrity Procedia 00 (2025) 000–000 Structural Integrity Procedia 00 (2025) 000–000

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© 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 the responsibility of Libor Pantělejev Abstract Reversible i) viscoelastic deformation of material samples or engineering structures, caused by external mechanical, thermal, etc. loads, quite di ff erent under tension and compression in many cases, is accompanied by irreversible ii) damage, starting with the formation of micro-fractured zones and continued with the initiation of propagation of macroscopic cracks. A su ffi ciently simple, but still interesting model problem covering both i) and ii), motivated by the behaviour of cementitious composites, as fibre-reinforced concrete, is presented in this contribution, together with proper verification of existence of its weak solutions and convergence of appropriate sequences of approximate solutions in finite-dimensional spaces. This is based on the method of discretization in time, on the smeared damage relying on the Eringen regularization and on the extended finite element method, covering macroscopic cracking, open to possible generalizations in several directions. © 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) 11th International Conference on Materials Structure and Micromechanics of Fracture Viscoelastic deformation with damage of quasi-brittle composites: mathematical and computational issues Jiˇr´ı Vala a, ∗ , Vladislav Koza´k a a Brno University of Technology, Faculty of Civil Engineering, Institute of Mathematics and Descriptive Geometry, Veverˇ´ı 331 / 95, 602 00 Brno, Czech Republic Abstract Reversible i) viscoelastic deformation of material samples or engineering structures, caused by external mechanical, thermal, etc. loads, quite di ff erent under tension and compression in many cases, is accompanied by irreversible ii) damage, starting with the formation of micro-fractured zones and continued with the initiation of propagation of macroscopic cracks. A su ffi ciently simple, but still interesting model problem covering both i) and ii), motivated by the behaviour of cementitious composites, as fibre-reinforced concrete, is presented in this contribution, together with proper verification of existence of its weak solutions and convergence of appropriate sequences of approximate solutions in finite-dimensional spaces. This is based on the method of discretization in time, on the smeared damage relying on the Eringen regularization and on the extended finite element method, covering macroscopic cracking, open to possible generalizations in several directions. © 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) 11th International Conference on Materials Structure and Micromechanics of Fracture Viscoelastic deformation with damage of quasi-brittle composites: mathematical and computational issues Jiˇr´ı Vala a, ∗ , Vladislav Koza´k a a Brno University of Technology, Faculty of Civil Engineering, Institute of Mathematics and Descriptive Geometry, Veverˇ´ı 331 / 95, 602 00 Brno, Czech Republic

Peer-review under responsibility of the scientific committee of Libor Panteˇlejev. Keywords: Quasi-brittle composites; viscoelasticity; damage; computational modelling. PACS: 62.20.mt, 46.50. + a, 46.35. + z, 02.30.Jr. 2020MSC: 74R10, 65M06, 65M60. Peer-review under responsibility of the scientific committee of Libor Panteˇlejev. Keywords: Quasi-brittle composites; viscoelasticity; damage; computational modelling. PACS: 62.20.mt, 46.50. + a, 46.35. + z, 02.30.Jr. 2020MSC: 74R10, 65M06, 65M60.

1. Introduction Numerical models for the stress and strain analysis of quasi-brittle composites, as introduced by Sumi (2014) and Sun et al. (2021), e. g. of cementitious composites like fibre-reinforced concrete, should cover both formation of micro-fractured zones and initiation and propagation of macroscopic cracks. Both these processes are irreversible, unlike an elastic, viscoelastic, etc. deformation, considered in an initial stage of related material samples or engineer ing structures usually. Moreover, quite di ff erent behaviour of such materials under tension and compression cannot be avoided. Usually macroscopic cracks are analysed using some extended, generalized or similar finite element technique (XFEM, GFEM, etc. algorithms), whose substantial progress in the last two decades can be documented on Belytchko et al. (2009), Wang et al. (2024) and Koza´k and Vala (2025). Unlike this approach, the study of micro- 1. Introduction Numerical models for the stress and strain analysis of quasi-brittle composites, as introduced by Sumi (2014) and Sun et al. (2021), e. g. of cementitious composites like fibre-reinforced concrete, should cover both formation of micro-fractured zones and initiation and propagation of macroscopic cracks. Both these processes are irreversible, unlike an elastic, viscoelastic, etc. deformation, considered in an initial stage of related material samples or engineer ing structures usually. Moreover, quite di ff erent behaviour of such materials under tension and compression cannot be avoided. Usually macroscopic cracks are analysed using some extended, generalized or similar finite element technique (XFEM, GFEM, etc. algorithms), whose substantial progress in the last two decades can be documented on Belytchko et al. (2009), Wang et al. (2024) and Koza´k and Vala (2025). Unlike this approach, the study of micro-

∗ Corresponding author. Tel.: + 420-54114-7602. E-mail address: vala.j@fce.vutbr.cz ∗ Corresponding author. Tel.: + 420-54114-7602. E-mail address: vala.j@fce.vutbr.cz

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 the responsibility of Libor Pantělejev 10.1016/j.prostr.2025.10.039 2210-7843 © 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 the scientific committee of Libor Panteˇlejev. 2210-7843 © 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 the scientific committee of Libor Panteˇlejev.