Details
| Original language | English |
|---|---|
| Pages (from-to) | 943-980 |
| Number of pages | 38 |
| Journal | Computational mechanics |
| Volume | 68 |
| Issue number | 4 |
| Early online date | 26 Aug 2021 |
| Publication status | Published - Oct 2021 |
Abstract
Keywords
- (An)isotropic ductile materials, Bayesian inference, MCMC techniques, Phase-field fracture
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational mechanics, Vol. 68, No. 4, 10.2021, p. 943-980.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Bayesian inversion for unified ductile phase-field fracture
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).
PY - 2021/10
Y1 - 2021/10
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.
KW - (An)isotropic ductile materials
KW - Bayesian inference
KW - MCMC techniques
KW - Phase-field fracture
UR - http://www.scopus.com/inward/record.url?scp=85113611628&partnerID=8YFLogxK
U2 - 10.1007/s00466-021-02054-w
DO - 10.1007/s00466-021-02054-w
M3 - Article
VL - 68
SP - 943
EP - 980
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 4
ER -