Assessment of computational fracture models using Bayesian method

authored by: K. M. Hamdia, M. A. Msekh, M. Silani, T. Q. Thai, P. R. Budarapu, T. Rabczuk
Abstract: We present a methodology to evaluate the uncertainty in several popular models for modelling damage and material failure, i.e. a gradient damage model, nonlocal model, phase field approach and cohesive zone model; the latter one is used in the context of the phantom node method though it can easily be used in the context of other computational methods for discrete fracture. The objective is to evaluate and compare the uncertainties in the current models and correlate them to practical observations. The Bayesian method is exploited to achieve this purpose based on experimental reference measurements. The developed methodology has been tested on mode-I fracture in concrete beams through well established three point bending test though other benchmark problems can be adopted for the comparison as well. The results from the current study are compared to the published experimental results. The methodology is implemented in three different steps. Firstly, a sensitivity analysis is performed to quantify the influence of uncertainties in the model parameters. Secondly, the coefficient of variation and average goodness of fit are calculated to evaluate the discrepancy of the predictions with respect to the corresponding measured experimental data. Finally, the posterior probability of models are updated to incorporate the uncertainties in both the model and the parameters, leading to an estimation of the model complexity. Based on the results, the gradient-enhanced damage is found to be the most probable model class with the lowest total model uncertainty. The present study can serve as a platform for future investigations on uncertainties associated with damage modelling and hence the concerned countermeasures.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Bauhaus-Universität Weimar
University of Babylon
Isfahan University of Technology
Indian Institute of Technology Bhubaneswar (IITBBS)
Ton Duc Thang University
Type: Article
Journal: Engineering fracture mechanics
Volume: 205
Pages: 387-398
No. of pages: 12
ISSN: 0013-7944
Publication date: 01.2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: General Materials Science, Mechanics of Materials, Mechanical Engineering
Electronic version(s): https://doi.org/10.1016/j.engfracmech.2018.09.019 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{568a579f9ebf4465b96108ae825eb27b,
title = "Assessment of computational fracture models using Bayesian method",
abstract = "We present a methodology to evaluate the uncertainty in several popular models for modelling damage and material failure, i.e. a gradient damage model, nonlocal model, phase field approach and cohesive zone model; the latter one is used in the context of the phantom node method though it can easily be used in the context of other computational methods for discrete fracture. The objective is to evaluate and compare the uncertainties in the current models and correlate them to practical observations. The Bayesian method is exploited to achieve this purpose based on experimental reference measurements. The developed methodology has been tested on mode-I fracture in concrete beams through well established three point bending test though other benchmark problems can be adopted for the comparison as well. The results from the current study are compared to the published experimental results. The methodology is implemented in three different steps. Firstly, a sensitivity analysis is performed to quantify the influence of uncertainties in the model parameters. Secondly, the coefficient of variation and average goodness of fit are calculated to evaluate the discrepancy of the predictions with respect to the corresponding measured experimental data. Finally, the posterior probability of models are updated to incorporate the uncertainties in both the model and the parameters, leading to an estimation of the model complexity. Based on the results, the gradient-enhanced damage is found to be the most probable model class with the lowest total model uncertainty. The present study can serve as a platform for future investigations on uncertainties associated with damage modelling and hence the concerned countermeasures.",
keywords = "Bayesian model, Damage modelling, Fracture mechanics, Model uncertainty, Sensitivity analysis",
author = "Hamdia, {K. M.} and Msekh, {M. A.} and M. Silani and Thai, {T. Q.} and Budarapu, {P. R.} and T. Rabczuk",
year = "2019",
month = jan,
doi = "10.1016/j.engfracmech.2018.09.019",
language = "English",
volume = "205",
pages = "387--398",
journal = "Engineering fracture mechanics",
issn = "0013-7944",
publisher = "Elsevier BV",
}