Numerical simulations of inelastic mechanical behavior of heterogeneous quasibrittle material are essential in a number of engineering areas. Specifically in civil engineering they are applied in assessment of critical buildings and infrastructure made of concrete. Robust high-fidelity models require detailed information about material composition which makes them computationally prohibitive. The projects solves this burden by state of the art techniques using machine learning combined with homogenization and domain decomposition. The heart of the project is advanced physically constrained machine learning surrogate capable to locally replace material response. Such artificial intelligence will be used to emulate behavior of (i) spherical representative volume element in the asymptotic expansion homogenization and (ii) regions tiling the decomposed domain. For such goal the homogenization will be equipped with auxiliary modes accounting for strain localization and the domain decomposition will be improved by reduced order modeling of the communication between individual regions.

Keywords
mechanical behavior;heterogeneity;fracture;strain localization;homogenization;domain decomposition;surrogate;machine learning

Key words in Czech
mechanické chování;heterogenita;lom;lokalizace deformace;homogenizace;doménová dekompozice;náhradní model;strojové učení

24-11845S

English

Eliáš Jan, prof. Ing., Ph.D. - principal person responsible
Bednář Michal - fellow researcher
Blažíček František - fellow researcher
Dajčar Jan, Bc. - fellow researcher
Fleischerová Beáta, Ing. - fellow researcher
Hadačová Michaela, Bc. - fellow researcher
Halíková Dana - fellow researcher
Ivánová Andrea, Bc. - fellow researcher
Krejčí Eliška - fellow researcher
Křížek Michael, Bc. - fellow researcher
Novák Lukáš, doc. Ing., Ph.D. - fellow researcher
Omelka František, Bc. - fellow researcher
Raisinger Jan, Ing. - fellow researcher
Ryšavý Martin, Ing. - fellow researcher
Sadílek Václav, Ing., Ph.D. - fellow researcher
Sedláková Monika - fellow researcher
Středulová Monika, M.Sc. - fellow researcher
Svoboda Daniel, Bc. - fellow researcher
Špetla Jan, Bc. - fellow researcher
Trýsková Martina - fellow researcher

Institute of Structural Mechanics
- responsible department (27.3.2023 - not assigned)
Institute of Structural Mechanics
- beneficiary (1.1.2023 - 31.12.2026)

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SHARMA, H.; NOVÁK, L.; SHIELDS, M. Polynomial chaos expansion for operator learning. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2026, vol. 453, iss. 1, p. 1-15.
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RAISINGER, J.; ZHANG, Q.; BOLANDER, J.; ELIÁŠ, J. Exploring Induced Heterogeneity in Elastic Discrete Mechanical Models. IA-FraMCoS, 2025. p. 1.
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ELIÁŠ, J.; MARTINÁSEK, J.; LE, J. Application of J-Integral to a Random Elastic Medium. Journal of applied mechanics, 2025, vol. 92, iss. 3, p. 031006-1 (031006-6 p.)
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ELIÁŠ, J.; CUSATIS, G. Do discrete fine-scale mechanical models with rotational degrees of freedom homogenize into a Cosserat or a Cauchy continuum?. Journal of the Mechanics and Physics of Solids, 2026, vol. 207, iss. 1, p. 1-22.
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LALE, E.; ELIÁŠ, J.; YU, K.; TROEMNER, M.; STŘEDULOVÁ, M.; KHOURY, J.; XUE, T.; KOUTROMANOS, I.; FASCETTI, A.; AYHAN, B.; CHEN, B.; LUZIO, G.; LYU, Y.; PATHIRAGE, M.; PIJAUDIER-CABOT, G.; SHEN, L.; TASORA, A.; YANG, L.; ZHONG, J.; CUSATIS, G. Lattice Discrete Particle Model (LDPM): Comparison of Various Time Integration Solvers and Implementations. International journal for numerical and analytical methods in geomechanics, 2026, vol. 50, iss. 8, p. 3468-3488.
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ELIÁŠ, J.; CUSATIS, G. Asymptotic Homogenization of Discrete Models With Rotational Degrees of Freedom. IA-FraMCoS, 2025. p. 1.
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RAISINGER, J.; NOVÁK, L.; ELIÁŠ, J. Data-Driven Prediction of Stress Response for Inelastic Discrete RVE. 2025. p. 169.ISBN: 978-80-86246-96-3.
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Responsibility: Eliáš Jan, prof. Ing., Ph.D.