Modeling tensile failure of concrete considering multivariate correlated random fields of material parameters

verfasst von: Lu Hai, Meng Ze Lyu
Abstract: This paper presents a novel approach for modeling the tensile failure of quasi-brittle materials by incorporating a multivariate random field to represent material parameters in the phase field model. The aim is to characterize and propagate uncertainties in the behaviors of materials, taking into account the spatial variability and probabilistic dependence. Copula theory is employed to investigate the probability distributions and dependence configuration of the parameters. The proposed framework combines the generation approach for the multivariate random field with the phase field model, resulting in a complete numerical analysis methodology. The governing equations of the deterministic phase field model for quasi-brittle solids are outlined, followed by a description of the multivariate random field for quasi-brittle media and its uncertainty characterization procedure using copula theory. A numerical approach for generating samples of the multivariate random field is introduced. The numerical analysis procedure for the tensile fracture of concrete is presented, and the effects of material uncertainties on failure patterns and macroscopic responses are discussed. The results demonstrate that the developed methodology effectively captures the random damage and fracture processes in concrete specimens. The interaction between the correlation length of the random field and the characteristic length scale of the phase field significantly influences the probabilistic characteristics of the random responses. The research findings emphasize the importance of determining the correlation length values accurately. This study contributes to the field of structural reliability analysis by providing a comprehensive framework for modeling the stochastic behavior of quasi-brittle materials. The integration of a multivariate random field and copula theory allows for the realistic representation of material uncertainties and their probabilistic dependence. The proposed methodology, combined with the probability density evolution method (PDEM), offers a powerful tool for analyzing and predicting the probabilistic evolution of material behaviors under tensile loading conditions.
Organisationseinheit(en): Institut für Kontinuumsmechanik
Externe Organisation(en): Ocean University of China
Tongji University
Typ: Artikel
Journal: Probabilistic Engineering Mechanics
Band: 74
ISSN: 0266-8920
Publikationsdatum: 10.2023
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Statistische und nichtlineare Physik, Tief- und Ingenieurbau, Kernenergie und Kernkraftwerkstechnik, Physik der kondensierten Materie, Luft- und Raumfahrttechnik, Meerestechnik, Maschinenbau
Elektronische Version(en): https://doi.org/10.1016/j.probengmech.2023.103529 (Zugang: Geschlossen)
: Details im Forschungsportal „Research@Leibniz University“

BibTeX

@article{2073aebfe788426db10818eb53e9e823,
title = "Modeling tensile failure of concrete considering multivariate correlated random fields of material parameters",
abstract = "This paper presents a novel approach for modeling the tensile failure of quasi-brittle materials by incorporating a multivariate random field to represent material parameters in the phase field model. The aim is to characterize and propagate uncertainties in the behaviors of materials, taking into account the spatial variability and probabilistic dependence. Copula theory is employed to investigate the probability distributions and dependence configuration of the parameters. The proposed framework combines the generation approach for the multivariate random field with the phase field model, resulting in a complete numerical analysis methodology. The governing equations of the deterministic phase field model for quasi-brittle solids are outlined, followed by a description of the multivariate random field for quasi-brittle media and its uncertainty characterization procedure using copula theory. A numerical approach for generating samples of the multivariate random field is introduced. The numerical analysis procedure for the tensile fracture of concrete is presented, and the effects of material uncertainties on failure patterns and macroscopic responses are discussed. The results demonstrate that the developed methodology effectively captures the random damage and fracture processes in concrete specimens. The interaction between the correlation length of the random field and the characteristic length scale of the phase field significantly influences the probabilistic characteristics of the random responses. The research findings emphasize the importance of determining the correlation length values accurately. This study contributes to the field of structural reliability analysis by providing a comprehensive framework for modeling the stochastic behavior of quasi-brittle materials. The integration of a multivariate random field and copula theory allows for the realistic representation of material uncertainties and their probabilistic dependence. The proposed methodology, combined with the probability density evolution method (PDEM), offers a powerful tool for analyzing and predicting the probabilistic evolution of material behaviors under tensile loading conditions.",
keywords = "Multivariate random field, Phase field, Probabilistic dependence, Probability density evolution method (PDEM), Uncertainty characterization and propagation",
author = "Lu Hai and Lyu, {Meng Ze}",
note = "Funding Information: Financial supports from China Postdoctoral Science Foundation (Grant No. 2023M732669 ) and Shanghai Post-doctoral Excellence Program (Grant No. 2022558 ) are highly appreciated. Prof. Jian-Bing Chen at Tongji University is greatly appreciated for the helpful comments. ",
year = "2023",
month = oct,
doi = "10.1016/j.probengmech.2023.103529",
language = "English",
volume = "74",
journal = "Probabilistic Engineering Mechanics",
issn = "0266-8920",
publisher = "Elsevier Ltd.",
}