Bayesian inversion for unified ductile phase-field fracture

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OriginalspracheEnglisch
Seiten (von - bis)943-980
Seitenumfang38
FachzeitschriftComputational mechanics
Jahrgang68
Ausgabenummer4
Frühes Online-Datum26 Aug. 2021
PublikationsstatusVeröffentlicht - Okt. 2021

Abstract

The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a sub-optimal calibration of plasticity- and fracture-related parameters for a large number of material properties. These parameters enter the system of partial differential equations as a forward model. In this work, we develop a step-wise Bayesian inversion framework for ductile fracture to provide accurate knowledge regarding the effective mechanical parameters. To this end, synthetic and experimental observations are used to estimate the posterior density of the unknowns. To model the ductile failure behavior of solid materials, we rely on the phase-field approach to fracture, for which we present a unified formulation that allows recovering different models on a variational basis. In the variational framework, incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. The overall formulation is revisited and extended to the case of anisotropic ductile fracture. Three different models are subsequently recovered by certain choices of parameters and constitutive functions, which are later assessed through Bayesian inversion techniques. To estimate the posterior density function of ductile material parameters, three common Markov chain Monte Carlo (MCMC) techniques are employed: (i) the Metropolis-Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, and (iii) ensemble Kalman filter combined with MCMC. To examine the computational efficiency of the MCMC methods, we employ the R-convergence tool.

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Bayesian inversion for unified ductile phase-field fracture. / Noii, Nima; Khodadadian, Amirreza; Ulloa, Jacinto et al.
in: Computational mechanics, Jahrgang 68, Nr. 4, 10.2021, S. 943-980.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Noii, N, Khodadadian, A, Ulloa, J, Aldakheel, F, Wick, T, François, S & Wriggers, P 2021, 'Bayesian inversion for unified ductile phase-field fracture', Computational mechanics, Jg. 68, Nr. 4, S. 943-980. https://doi.org/10.1007/s00466-021-02054-w
Noii N, Khodadadian A, Ulloa J, Aldakheel F, Wick T, François S et al. Bayesian inversion for unified ductile phase-field fracture. Computational mechanics. 2021 Okt;68(4):943-980. Epub 2021 Aug 26. doi: 10.1007/s00466-021-02054-w
Noii, Nima ; Khodadadian, Amirreza ; Ulloa, Jacinto et al. / Bayesian inversion for unified ductile phase-field fracture. in: Computational mechanics. 2021 ; Jahrgang 68, Nr. 4. S. 943-980.
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title = "Bayesian inversion for unified ductile phase-field fracture",
abstract = "The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a sub-optimal calibration of plasticity- and fracture-related parameters for a large number of material properties. These parameters enter the system of partial differential equations as a forward model. In this work, we develop a step-wise Bayesian inversion framework for ductile fracture to provide accurate knowledge regarding the effective mechanical parameters. To this end, synthetic and experimental observations are used to estimate the posterior density of the unknowns. To model the ductile failure behavior of solid materials, we rely on the phase-field approach to fracture, for which we present a unified formulation that allows recovering different models on a variational basis. In the variational framework, incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. The overall formulation is revisited and extended to the case of anisotropic ductile fracture. Three different models are subsequently recovered by certain choices of parameters and constitutive functions, which are later assessed through Bayesian inversion techniques. To estimate the posterior density function of ductile material parameters, three common Markov chain Monte Carlo (MCMC) techniques are employed: (i) the Metropolis-Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, and (iii) ensemble Kalman filter combined with MCMC. To examine the computational efficiency of the MCMC methods, we employ the R-convergence tool. ",
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AU - Noii, Nima

AU - Khodadadian, Amirreza

AU - Ulloa, Jacinto

AU - Aldakheel, Fadi

AU - Wick, Thomas

AU - François, Stijn

AU - Wriggers, Peter

N1 - Funding Information: N. Noii and F. Aldakheel were founded by the Priority Program DFG-SPP 2020 within its second funding phase. T. Wick and P. Wriggers were funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD, EXC 2122 (project number: 390833453).

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N2 - The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a sub-optimal calibration of plasticity- and fracture-related parameters for a large number of material properties. These parameters enter the system of partial differential equations as a forward model. In this work, we develop a step-wise Bayesian inversion framework for ductile fracture to provide accurate knowledge regarding the effective mechanical parameters. To this end, synthetic and experimental observations are used to estimate the posterior density of the unknowns. To model the ductile failure behavior of solid materials, we rely on the phase-field approach to fracture, for which we present a unified formulation that allows recovering different models on a variational basis. In the variational framework, incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. The overall formulation is revisited and extended to the case of anisotropic ductile fracture. Three different models are subsequently recovered by certain choices of parameters and constitutive functions, which are later assessed through Bayesian inversion techniques. To estimate the posterior density function of ductile material parameters, three common Markov chain Monte Carlo (MCMC) techniques are employed: (i) the Metropolis-Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, and (iii) ensemble Kalman filter combined with MCMC. To examine the computational efficiency of the MCMC methods, we employ the R-convergence tool.

AB - The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a sub-optimal calibration of plasticity- and fracture-related parameters for a large number of material properties. These parameters enter the system of partial differential equations as a forward model. In this work, we develop a step-wise Bayesian inversion framework for ductile fracture to provide accurate knowledge regarding the effective mechanical parameters. To this end, synthetic and experimental observations are used to estimate the posterior density of the unknowns. To model the ductile failure behavior of solid materials, we rely on the phase-field approach to fracture, for which we present a unified formulation that allows recovering different models on a variational basis. In the variational framework, incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. The overall formulation is revisited and extended to the case of anisotropic ductile fracture. Three different models are subsequently recovered by certain choices of parameters and constitutive functions, which are later assessed through Bayesian inversion techniques. To estimate the posterior density function of ductile material parameters, three common Markov chain Monte Carlo (MCMC) techniques are employed: (i) the Metropolis-Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, and (iii) ensemble Kalman filter combined with MCMC. To examine the computational efficiency of the MCMC methods, we employ the R-convergence tool.

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KW - MCMC techniques

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DO - 10.1007/s00466-021-02054-w

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SP - 943

EP - 980

JO - Computational mechanics

JF - Computational mechanics

SN - 0178-7675

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ER -

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