PSI - Issue 74

Jiří Vala et al. / Procedia Structural Integrity 74 (2025) 91–98

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J.Vala & V.Koza´k / Structural Integrity Procedia 00 (2025) 000–000

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theory, cf. Vala and Rek (2023). Furhter motivations for the research in the near future with significant engineering applications can be sees in coupling of mechanical and thermal processes, including those active on elevated or high temperature. The previous part of the conclusion is rather devoted to mathematical aspects of modelling viscous problems. But for our presentation of the creep growth, when illustrative example is dedicated to power creep, the reader will be struck by the question of the correct critical value of the J ˙integral and its possible value when the failure mechanism changes from intercrystalline to transcrystalline. It can be said due to dominance of secondary creep, the decisive fail ure for model material is intercrystalline. Only in the very short final episode the tertiary creep occurs and then changes the critical value of J ˙ integral. The traction separation law used was close to exponential; it would be interesting to model the grain structure of the material as a composite with the e ff ect of pulling out individual grains. Acknowledgement This study has been supported from the project of specific university research at Brno University of Technology No. FAST-S-25-8850. References Al Janaideh, M., Krejcˇ´ı, P., Monteiro, G. A., 2024. “Memory reduction of rate-dependent Prandtl–Ishlinskiˇı compensators in applications on high-precision motion systems.” Physica B: Condensed Matter 677, 415595 / 1–16. Arruda, M. R. T., Pacheco, J.; Castro, L. M. S., Julio, E., 2023. A modified Mazars damage model with energy regularization. Theoretical and Applied Fracture Mechanics 124, 108129 / 1–22. Bazˇant, Z. P., 2019. “Design of quasibrittle materials and structures to optimize strength and scaling at probability tail: an apercu.” Proceedings of the Royal Society of London A 475, 20180617 / 1–30. Belytschko, T., Gracie, R., Ventura, G. A ., 2009. “A review of extended / generalized finite element methods for material modeling.” Modelling and Simulation in Materials Science and Engineering 17, 043001–31. Bre´zis, H., 1968. “E´ quations et ine´quations non-line´aires dans les espaces vectoriel en dualite´.” Annales de l’Institute Fourier 18, 115–176. Brust, F. W., Atluri, S. N., 1986. “Studies on creep crack growth using the ˙ T ∗ -integral.” Engineering Fracture Mechanics 23, 551–574. Bu¨hler, I., Salomon, D. A., 2017. Functional Analysis. Eidgeno¨ssische Technische Hochschule, Zu¨rich. Chen, Z., Liu, D., Liao, M., 2024. “Computations of J -integral and T ∗ -integral in elastic-plastic fracture by the quadrature element method.” Theoretical and Applied Fracture Mechanics 130, 104252 / 1–12. Cianchi, A., Maz’ya, V. G., 2016. “Sobolev inequalities in arbitrary domains.” Advances in Mathematics 293, 644–696. Dra´bek, P., Milota, I., 2013. Methods of Nonlinear Analysis. Birkha¨user, Basel. Eringen, A. C., 2002. Nonlocal Continuum Field Theories. Springer, New York. Giry, C., Dufour, F., Mazars, J., 2011. “Stress-based nonlocal damage model.” International Journal of Solids and Structures 48, 3431–3443. Han, J., Vitek, V., Srolovitz, D. J., 2017. “The grain-boundary structural unit model redux.” Acta Materialia 133, 186–199. Havla´sek, P., Grassl, P., M. Jira´sek, M., 2016. “Analysis of size e ff ect on strength of quasi-brittle materials using integral-type nonlocal models.” Engineering Fracture Mechanics 157, 72–85. Jiang, R., Kauranen, A., 2015. “Korn inequality on irregular domains.” Journal of Mathematical Analysis and Applications 426, 41–59. Koza´k, V., Chlup, Z., Padeˇlek, P., Dlouhy´, I., 2017. “Prediction of traction separation law of ceramics using iterative finite element method.” Solid State Phenomena 258, 186–189. Koza´k, V., Vala, J., 2024. “Prediction of the high temperature crack propagation in the AISI 304L steel using the cohesive approach.” Proceedings of 28th Thermophysics in Dalesˇice (Czech Republic, 2023). AIP Conference Proceedings 3126, 020011 / 1–7. Koza´k V., Vala, J., 2025. Some peculiarities of using the extended finite element method in modelling the damage behaviour of fibre-reinforced composites. Materials 18, 1787 / 1–16 Kro¨mer, S., Kruzˇ´ık, M., Morandotti, M., Zappale, E., 2024. “Measure-valued structured deformations.” Journal of Nonlinear Science 34, 100 / 1–33. Kruzˇ´ık, M., Roub´ıcˇek, T., 2019. Mathematical Methods in Continuum Mechanics of Solids. Springer, Cham. Le´ger, S., Pepin, A., 2016. “An updated Lagrangian method with error estimation and adaptive remeshing for very large deformation elasticity problems: The three-dimensional case.” Computer Methods in Applied Mechanics and Engineering 309, 1–18. Liu, G., Guo, J., Bao, Y., 2022. “Convergence investigation of XFEM enrichment schemes for modeling cohesive cracks.” Mathematics 10, 383–17. Lu, G., Chen, J., Ren, Y., 2024. “New insights into fracture and cracking simulation of quasi-brittle materials based on the NMMD model.” Computer Methods in Applied Mechanics and Engineering 432, 117347 / 1–29. Neˇmec, I., Vala, J., Sˇ tekbauer, H., Jedlicˇka, M., Burkart, D., 2022. “On a new computational algorithm for impacts of elastic bodies.” Proceedings of 21st Programs and Algorithms of Numerical Mathematics (PANM) in Hejnice (Czech Republic, 2021), 133–148. Institute of Mathematics CAS, Prague. Papenfuß, Ch., 2020. Continuum Thermodynamics and Constitutive Theory. Springer, Berlin. Pike, M. G., Oskay, C., 2015. “XFEM modeling of short microfiber reinforced composites with cohesive interfaces.” Finite Elements in Analysis and Design 106, 16 / 1–31.

Roub´ıcˇek, T., 2005. Nonlinear Partial Di ff erential Equations with Applications. Birkha¨user, Basel. Steinhauser, M. O., 2008. Computational Multiscale Modelling of Fluids and Solids. Springer, Berlin.