Sequential Bayesian Inference of the GTN Damage Model Using Multimodal Experimental Data

Abstract

Reliable parameter identification in ductile damage models remains challenging because the salient physics of damage progression are localized to small regions in material responses, and their signatures are often diluted in specimen-level measurements. Here, we propose a sequential Bayesian Inference (BI) framework for the calibration of the Gurson-Tvergaard-Needleman (GTN) model using multimodal experimental data (i.e., the specimen-level force-displacement (F-D) measurements and the spatially resolved digital image correlation (DIC) strain fields). This calibration approach builds on a previously developed two-step BI framework that first establishes a low-computational-cost emulator for a physics-based simulator (here, a finite element model incorporating the GTN material model) and then uses the experimental data to sample posteriors for the material model parameters using the Transitional Markov Chain Monte Carlo (T-MCMC). A central challenge to the successful application of this BI framework to the present problem arises from the high-dimensional representations needed to capture the salient features embedded in the F-D curves and the DIC fields. In this paper, it is demonstrated that Principal Component Analysis (PCA) provides low-dimensional representations that make it possible to apply the BI framework to the problem. Most importantly, it is shown that the sequence in which the BI is applied has a dramatic influence on the results obtained. Specifically, it is observed that applying BI first on F-D curves and subsequently on the DIC fields produces improved estimates of the GTN parameters. Possible causes for these observations are discussed in this paper, using AA6111 aluminum alloy as a case study.

Figures (17)

• Figure 1: Sequential Bayesian Inference framework comparing two update sequences. Each sequence provides both final posteriors and intermediate single-update results for evaluating individual data stream contributions to GTN parameter estimation.
• Figure 2: Specimen geometry and speckle pattern: (a) Tensile specimen geometry with central hole designed for multiaxial loading and strain localization, (b) full gauge section view and (c) magnified view demonstrating speckle size distribution and contrast quality.
• Figure 3: Stereoscopic DIC experimental setup showing dual-camera configuration with specimen positioning. The rigid mounting frame ensures stable camera positioning throughout the test duration.
• Figure 4: FE model configuration: (a) Voxelized mesh showing uniform element distribution around the central hole geometry with 0.17 mm characteristic element size, and (b) boundary conditions showing the symmetry plane, vertically fixed bottom nodes, and a displacement-controlled loading condition matching the experimental setup.
• Figure 5: (a) F-D curves from 400 FE simulations. Point $Y$ is the intersection with a line from the origin having slope $95\%$ of the initial elastic slope; the corresponding displacement $d_Y$ is marked. (b) Strain-field examples with different levels of strain concentration.