Bayesian inversion for unified ductile phase-field fracture

authored by: Nima Noii, Amirreza Khodadadian, Jacinto Ulloa, Fadi Aldakheel, Thomas Wick, Stijn François, Peter Wriggers
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.
Organisation(s): Institute of Continuum Mechanics
Institute of Applied Mathematics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
External Organisation(s): KU Leuven
Type: Article
Journal: Computational mechanics
Volume: 68
Pages: 943-980
No. of pages: 38
ISSN: 0178-7675
Publication date: 10.2021
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): http://arxiv.org/abs/2104.11114v1 (Access: Open)
https://doi.org/10.1007/s00466-021-02054-w (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{190d9b5c22014b20936e509e5734e714,
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. ",
keywords = "(An)isotropic ductile materials, Bayesian inference, MCMC techniques, Phase-field fracture",
author = "Nima Noii and Amirreza Khodadadian and Jacinto Ulloa and Fadi Aldakheel and Thomas Wick and Stijn Fran{\c c}ois and Peter Wriggers",
note = "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{\textquoteright}s Excellence Strategy within the Cluster of Excellence PhoenixD, EXC 2122 (project number: 390833453).",
year = "2021",
month = oct,
doi = "10.1007/s00466-021-02054-w",
language = "English",
volume = "68",
pages = "943--980",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "4",
}