PSI - Issue 68

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

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Procedia Structural Integrity 68 (2025) 32–38

European Conference on Fracture 2024 Boundary element method for 3D fracture mechanics analysis in quasicrystal solids under thermal loading Roman Kushnir a , Heorhiy Sulym a , Iaroslav Pasternak b, *, Vitalii Kozelko b a Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Naukova Str. 3-b, 79060 Lviv, Ukraine b Lesya Ukrainka Volyn National University, Voli Avenue 13, 43025 Lutsk, Ukraine Abstract This study presents a boundary element approach for analyzing 3D cracks in thermoelastic quasicrystals. The approach uses compact notations, combining phonon and phason fields into extended vectors and tensors, simplifying the equilibrium equations. Boundary integral equations are derived for heat conduction and thermoelasticity, avoiding the need for volume discretization. Special methods are employed to evaluate integrals and determine stress intensity factors at the crack front. © 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 ECF24 organizers Keywords: quasicrystal; thermoelastic; anisotropic; phonon-phason coupling 1. Introduction Modern instrumentation and aerospace engineering are increasingly adopting non-traditional materials with unique properties that offer distinctive responses to external forces. These materials, such as quasicrystals, are particularly suited for the development of innovative technologies, which is why their properties and potential applications have been actively researched over the past few decades (Fan, 2016). Quasicrystals, discovered in 1982, display mechanical behaviors significantly different from traditional materials, prompting the development of a separate theory of elasticity for these materials (Fan, 2016; Fan et al., 2022). This theory accounts for the interaction between phonon European Conference on Fracture 2024 Boundary element method for 3D fracture mechanics analysis in quasicrystal solids under thermal loading Roman Kushnir a , Heorhiy Sulym a , Iaroslav Pasternak b, *, Vitalii Kozelko b a Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Naukova Str. 3-b, 79060 Lviv, Ukraine b Lesya Ukrainka Volyn National University, Voli Avenue 13, 43025 Lutsk, Ukraine Abstract This study presents a boundary element approach for analyzing 3D cracks in thermoelastic quasicrystals. The approach uses compact notations, combining phonon and phason fields into extended vectors and tensors, simplifying the equilibrium equations. Boundary integral equations are derived for heat conduction and thermoelasticity, avoiding the need for volume discretization. Special methods are employed to evaluate integrals and determine stress intensity factors at the crack front. © 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 ECF24 organizers Keywords: quasicrystal; thermoelastic; anisotropic; phonon-phason coupling 1. Introduction Modern instrumentation and aerospace engineering are increasingly adopting non-traditional materials with unique properties that offer distinctive responses to external forces. These materials, such as quasicrystals, are particularly suited for the development of innovative technologies, which is why their properties and potential applications have been actively researched over the past few decades (Fan, 2016). Quasicrystals, discovered in 1982, display mechanical behaviors significantly different from traditional materials, prompting the development of a separate theory of elasticity for these materials (Fan, 2016; Fan et al., 2022). This theory accounts for the interaction between phonon © 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 ECF24 organizers

* Corresponding author. Tel.: +380973016819. E-mail address: iaroslav.pasternak@vnu.edu.ua * Corresponding author. Tel.: +380973016819. E-mail address: iaroslav.pasternak@vnu.edu.ua

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 ECF24 organizers 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 ECF24 organizers

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 ECF24 organizers 10.1016/j.prostr.2025.06.019