TY - JOUR

T1 - Modeling tensile failure of concrete considering multivariate correlated random fields of material parameters

AU - Hai, Lu

AU - Lyu, Meng Ze

N1 - 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.

PY - 2023/10

Y1 - 2023/10

N2 - 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.

AB - 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.

KW - Multivariate random field

KW - Phase field

KW - Probabilistic dependence

KW - Probability density evolution method (PDEM)

KW - Uncertainty characterization and propagation

UR - http://www.scopus.com/inward/record.url?scp=85172723526&partnerID=8YFLogxK

U2 - 10.1016/j.probengmech.2023.103529

DO - 10.1016/j.probengmech.2023.103529

M3 - Article

AN - SCOPUS:85172723526

VL - 74

JO - Probabilistic Engineering Mechanics

JF - Probabilistic Engineering Mechanics

SN - 0266-8920

M1 - 103529

ER -