TY - CONF A1 - Jafari, Abbas A1 - Titscher, Thomas A1 - Chatzi, E. A1 - Unger, Jörg F. T1 - Variational Bayesian inference of damage in concrete material using spatially-dense data N2 - Numerical simulators, such as finite element models, have become increasingly capable of predicting the behaviour of structures and components owing to more sophisticated underlying mathematical models and advanced computing power. A common challenge lies, however, in calibrating these models in terms of their unknown/uncertain parameters. When measurements exist, this can be achieved by comparing the model response against measured data. Besides uncertain model parameters, phenomena like damage can give rise to further uncertainties; in particular, quasi-brittle materials, like concrete, experience damage in a heterogeneous manner due to various imperfections, e.g. in geometry and boundary conditions. This hardens an accurate prediction of the damaged behaviour of real structures that comprise such materials. In this study, which draws from a data-driven approach, we use the force-version of the finite element model updating method (FEMU-F) to incorporate measured displacements into the identification of the damage parameters, in order to cope with heterogeneity. In this method, instead of conducting a forward evaluation of the model and comparing the model response (displacements) against the data, we impose displacements to the model and compare the resulting force residuals with measured reaction forces. To account for uncertainties in the measurement of displacements, we endow this approach with a penalty term, which reflects the discrepancy between measured and imposed displacements, where the latter is assumed as unknown random variables to be identified as well. A Variational Bayesian approach is used as an approximating tool for computing posterior parameters. The underlying damage model considered in this work is a gradient-enhanced damage model. We first establish the identification procedure through two virtual examples, where synthetic data (displacements) are generated over a certain spatially-dense set of points over the domain. The procedure is then validated on an experimental case-study; namely a 3-point bending experiment with displacement measurements resulting from a digital image correlation (DIC) analysis. T2 - MSE 2022 CY - Online meeting DA - 27.09.2022 KW - Heterogeneity KW - Gradient damage KW - Model updating KW - Variational Bayesian KW - Concrete PY - 2022 AN - OPUS4-56625 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Jafari, Abbas A1 - Titscher, Thomas A1 - Chatzi, E. A1 - Unger, Jörg F. T1 - Stochastic parameter estimation of a gradient-enhanced damage material model of concrete using variational Bayesian inference N2 - A gradient-enhanced damage material model for concrete simulated by means of the finite element (FE) method is calibrated with respect to important parameters of the involved constitutive law by using the Variational Bayesian method. T2 - UNCECOMP - 4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering CY - Online meeting DA - 28.06.2021 KW - Stochastic model updating KW - Variational Bayesian KW - Gradient-enhanced damage KW - Concrete PY - 2021 AN - OPUS4-54034 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Jafari, Abbas A1 - Titscher, Thomas A1 - Chatzi, E. A1 - Unger, Jörg F. T1 - Variational Bayesian inference of a gradient-enhanced damage material model N2 - A finite element model is calibrated in terms of parameters of the constitutive law; namely the gradient damage model. The method of Variational Bayesian is used for this purpose. The study has been done based on synthetic data. T2 - YIC Young Investigators Conference CY - Online meeting DA - 07.07.2021 KW - Stochastic inference KW - Material model updating KW - Variational Bayesian KW - Gradient-enhanced damage PY - 2021 UR - https://yic2021.upv.es/ AN - OPUS4-54033 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Jafari, Abbas A1 - Vlachas, K. A1 - Chatzi, E. A1 - Unger, Jörg F. T1 - Bayesian finite element model updating using full-field measurements of displacements N2 - Finite element (FE) models are widely used to capture the mechanical behavior of structures. Uncertainties in the underlying physics and unknown parameters of such models can heavily impact their performance. Thus, to satisfy high precision and reliability requirements, the performance of such models is often validated using experimental data. In such model updating processes, uncertainties in the incoming measurements should be accounted for, as well. In this context, Bayesian methods have been recognized as a powerful tool for addressing different types of uncertainties. Quasi-brittle materials subjected to damage pose a further challenge due to the increased uncertainty and complexity involved in modeling crack propagation effects. In this respect, techniques such as Digital Image Correlation (DIC) can provide full-field displacement measurements that are able to reflect the crack path up to a certain accuracy. In this study, DIC-based full field measurements are incorporated into a finite element model updating approach, to calibrate unknown/uncertain parameters of an ansatz constitutive model. In contrast to the standard FEMU, where measured displacements are compared to the displacements from the FE model response, in the force-version of the standard FEMU, termed FEMU-F [1], displacements are applied as Dirichlet constraints. This enables the evaluation of the internal forces, which are then compared to measured external forces, thus quantifying the fulfillment of the momentum balance equation as a metric for the model discrepancy. In the present work, the FEMU-F approach is further equipped with a Bayesian technique that accounts for uncertainties in the measured displacements, as well. Via this modification, displacements are treated as unknown variables to be subsequently identified, while they are allowed to deviate from the measured values up to a certain measurement accuracy. To be able to identify many unknown variables; including constitutive parameters and the aforementioned displacements, the Variational Bayesian technique proposed in [2] is utilized as an approximative technique. A numerical example of a three-point bending case study is presented first to demonstrate the effectiveness of the proposed approach. The parameters of a gradient-enhanced damage material model [4] are identified using noisy synthetic data, and the effect of measurement noise is studied. The ability of the suggested approach on identifying constitutive parameters is then validated using real experimental data from a three-point bending test from [3]. The full field displacements required as input to the inference setup are extracted through a digital image correlation (DIC) analysis of the provided raw images. T2 - GACM-2023 - 10th GACM Colloquium on Computational Mechanics 2023 CY - Vienna, Austria DA - 10.09.2023 KW - Bayesian model updating KW - Full-field measurements KW - Gradient damage model PY - 2023 AN - OPUS4-58288 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Jafari, Abbas A1 - Chatzi, E. A1 - Unger, Jörg F. T1 - Bayesian updating of constitutive laws for Finite Element simulation using full field measurements N2 - Developed finite element (FE) models have been recognized as powerful tools for predicting the mechanical behaviour of engineered systems. As a prerequisite, those models need to be improved with respect to various uncertainties; most notably, concerning underlying physics assumptions and unknown parameters. This is very often accomplished by comparing the performance of a model (e.g. the model response) against available data measured from real experiments. Another challenge emerges in doing that, however, which is accounting for uncertainties of measured data. Bayesian methods have been widely considered and utilized as a suitable approach for coping with and quantifying the aforementioned uncertainties. Phenomena like damage - in particular in quasi-brittle materials - introduce further uncertainties due to the complexity underlying the crack propagation of phenomenon. This implies that, the fitting of a numerical model and an associated constitute law that can adequately describe such effects is non-trivial. The standard approach of finite element model updating (FEMU) is therefore modified to account for tracking of the crack propagation, as recorded during an experiment under increasing loading, via full field displacement measurements. The latter are fed as Dirichlet constraints to an available finite element model, leading to the evaluation of force residuals, which quantifies the accuracy of the model. This approach - which is known as FEMU-F (force-version of the standard FEMU) [1] - is here further equipped with a Bayesian technique, which accounts for the measurement uncertainties in the full field displacement. This is achieved by penalizing the discrepancy between the measured displacements and the modeled Dirichlet constraints, where the latter are considered as further unknowns. We specifically employ the Variational Bayesian technique, proposed in [2], as an approximating tool for the estimation of posterior parameters, including displacement variables that are allowed to deviate from the measurements. A Markov chain Monte Carlo (MCMC) is also used for sampling the posterior distribution of the unknown model parameters. The model updating procedure is first demonstrated through a numerically simulated example of threepoint bending, where the parameters of a gradient-enhanced damage material model [4] are identified in accordance with synthetic noisy data (displacements and reaction forces). For the validation, experimental data from a three-point bending test are used, where full field displacements are collected through a digital image correlation (DIC) analysis (raw data taken from [3]). The data is then used for the parameter identification of a gradient damage constitutive law, which is employed as an ansatz model T2 - 5th International Conference on Uncertainty Quantification inUNCECOMP 2023 - Computational Science and Engineering CY - Athens, Greece DA - 12.06.2023 KW - Bayesian model updating KW - Full field measurements KW - Gradient damage model PY - 2023 AN - OPUS4-58287 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -