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Bayesian model updating with finite element vs surrogate models: Application to a miter gate structural system
Bayesian finite element (FE) model updating using direct model evaluations of large-scale high-fidelity FE models is extremely computationally expensive. Surrogate models can be used as fast emulators of FE models to accelerate the model calibration process. The physics/mechanics-based FE models are still the underpinning behind the surrogate models. Here, this paper evaluates the loss in accuracy and the gain in computational time while performing Bayesian model updating by using surrogate model evaluations compared to using direct FE model evaluations. This evaluation is crucial before entirely relying on surrogate models in model updating for structural health monitoring (SHM) and damage prognosis (DP) purposes. This paper also demonstrates Bayesian updating and surrogate model construction of large-scale high-fidelity FE models of infrastructure systems. In this regard, the miter gate structural system is considered as the testbed structure. Three predominant damage modes (loss of contact between gate and wall, loss of thickness due to corrosion, and loss of tension in the diagonal rods) are considered for model updating purposes. Bayesian model updating is performed using direct FE evaluations by leveraging parallel computing. Two types of surrogates, namely polynomial chaos expansion (PCE) and Gaussian process regression (GPR), are developed for the miter gate. Model updating is performed again using the trained surrogate models, and the updating results are compared with their counterparts obtained using the direct FE evaluation results. The posterior distribution of the FE model parameters obtained using the trained surrogates are sufficiently accurate with respect to the posterior obtained utilizing the direct FE evaluations. In addition, an approximate 4-fold decrease in the computational time was observed when using surrogate model evaluations instead of direct FE evaluations for model updating.
A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM
Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. Here, the two primary approaches in the experimental mechanics community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, we conduct a series of test cases to assess both methods under practical challenges using a finite strain elastoplasticity model.
Digital image correlation and infrared thermography data for seven unique geometries of 304L stainless steel
Material Testing 2.0 (MT2.0) is a paradigm that advocates for the use of rich, full-field data, such as from digital image correlation and infrared thermography, for material identification. By employing heterogeneous, multi-axial data in conjunction with sophisticated inverse calibration techniques such as finite element model updating and the virtual fields method, MT2.0 aims to reduce the number of specimens needed for material identification and to increase confidence in the calibration results. To support continued development, improvement, and validation of such inverse methods—specifically for rate-dependent, temperature-dependent, and anisotropic metal plasticity models—we provide here a thorough experimental data set for 304L stainless steel sheet metal. The data set includes full-field displacement, strain, and temperature data for seven unique specimen geometries tested at different strain rates and in different material orientations. Commensurate extensometer strain data from tensile dog bones is provided as well for comparison. We believe this complete data set will be a valuable contribution to the experimental and computational mechanics communities, supporting continued advances in material identification methods.
Identification Uncertainty in Inverse Material Model Parameter Determination: A Sensitivity‐Based Decision Process for Load Path Selection
This research proposes a sensitivity-based framework for selecting the optimal prescribed loading path for a biaxial cruciform specimen. Optimality here is determined by the direction and magnitude of the prescribed displacement that minimizes the influence of random noise on the material model parameter identification. Using simulated experimental data based on finite element simulation, in this work, we identify the material model parameters of a Ludwik hardening model and plane stress implementation of the Hill-48 yield criterion using finite element model updating (FEMU). Our analysis reveals that the identification (or estimator) uncertainty of model parameters depends on the displacement boundary conditions (i.e., loading sequence) and the ground-truth value of the individual parameters. Optimal experimental design (OED) criteria based on the Fisher information matrix were investigated to mitigate indecision in the choice of optimal load path when the identification uncertainty of different material model parameters optimized at different load paths. The determinant of the Fisher information matrix was chosen here as the more useful metric due to its ability to capture uncertainty of the most influential material model parameters. The proposed framework demonstrates potential for real-time automated load step selection using scalar criteria derived prior to mechanical loading. The framework can be generalized to other geometries, boundary conditions and material models, allowing this procedure to be utilized for different experimental configurations and materials.
Interpreting strain tensor data to characterize and monitor reservoirs for CO2 storage and other applications
Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and this has opened the door to new opportunities for characterization and monitoring. We have deployed strainmeters and then conducted injection well tests in an underlying reservoir at 530m depth. The resulting data indicated that the horizontal strain at shallow strainmeters (30 to 40m depth) was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 n/d over a few days. The signal at two strainmeters at shallow depth were consistent, although the magnitude of the horizontal strains were different reflecting the different radial directions from the well. The signal at a deep strainmeter deployed at reservoir depth was much different, with tensile vertical strains and compressive horizontal strains. These data can be interpreted by inverting poroelastic forward models developed using numerical and analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. This model is fast and can be inverted to estimate reservoir stiffness and geometry. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. The proxy model is periodically updated and refined using the finite element model to ensure accuracy. This approach significantly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. We have shown that the strain tensor in the caprock is sensitive to pressure in the reservoir, boundaries in the reservoir, and pressure in the caprock caused by leaks. These results indicate that coupling strain tensor data with inversion has the potential to help evaluate reservoirs during initial characterization, and to monitor them during the CO2 injection and storage process.
Updated Available Drawdowns for Big Hill SPR Caverns - Model Including the Caprock Fault
This report updates the estimated values of the baseline available drawdowns for the caverns at the Big Hill storage facility, and an updated table listing the available drawdowns. An updated finite element numerical analysis model, which included a fault in the caprock layers, was constructed and the daily data of actual wellhead pressures and oil-brine interfaces was used. The number of available drawdowns for each of the Big Hill SPR caverns is estimated using the new model. All caverns are predicted to have five available drawdowns remaining from a geomechanical perspective. BH-101 and 105 have a region of concern at the floor edge and/or sloping floor, where tensile and dilatant stresses are predicted to occur during each workover. The tensile state is predicted to occur because of the geometries of the edge and floor. Therefore, geomechanical examination for two caverns would be recommended after a drawdown leach. The well integrity of each cavern is not investigated in this report. The estimates for the number of baseline available drawdowns are subject to change in the future as the knowledge of physical phenomena at the sites, and the further development of the models of geomechanical behavior at the sites, evolve over time.
Characteristics of Fluid‐Solid Interaction Constitutive Models Within Poroelastodynamics at Higher Strain‐Rates and Large Deformations Implemented in 1D
The large deformation, mixed formulation, finite element (FE) modeling approach presented in Irwin et al. 2024 is extended herein to include improved constitutive models for representing dynamic solid-fluid interactions at higher strain rates (𝒪(10 2 −10 3 )s −1 ) and larger overpressure magnitudes (𝒪(10 2 )kPa) within a biphasic soft porous material using Theory of Porous Media (TPM) at finite strain. Specifically, these constitutive modeling improvements are the following: (i) a more physically robust constitutive model for pore fluid seepage velocity via inclusion of pore fluid viscous stress, and (ii) a modified deformation-dependent-permeability model and updated hyperelastic constitutive model better suited for handling larger volumetric compressions and extensions. The novelty of the present work is mainly the contribution (i): inclusion of pore fluid viscous stress at higher strain-rate and large deformations, which requires 𝐶 1 continuity in the weak formulation, accomplished by employing Hermite cubic interpolation functions within a mixed nonlinear poromechanical finite element formulation. In (ii), the model is updated to weakly enforce solid phase incompressibility, such that this assumption is not violated numerically, which provides improved numerical stability for achieving larger overpressure magnitudes on 𝒪(10 2 ) kPa, which were not achievable with the previous Kozeny–Carman model in Irwin et al. 2024. Also in (ii), the volumetric part of the solid skeleton free energy function is modified to ensure proper bounds on the solid skeleton Jacobian of deformation 𝐽 s related to incompressibility of the solid phase. Uniaxial strain, unidirectional flow examples at higher strain rates (𝒪(10 2 −10 3 )s −1 ) and larger deformations (up to 0.2 (or 20%) nominal axial strain) demonstrate the improved physical representation—and numerical stability—of these constitutive model improvements.
Evaluation of machine learning and finite-element modeling methods for defect localization using demonstration vibration data
This brief report provides an update on FY24 efforts from the Acoustics team in the Instrumentation and Sensors technical area at Los Alamos National Laboratory to evaluate suitable data processing and modeling techniques for vibration-based defect localization.
Development and testing of a solar flux heating freeze recovery system for molten salt parabolic troughs
A major obstacle preventing commercialization of molten salt parabolic trough plants is freeze protection and recovery of the solar field. One of the most common nitrate salt compositions under consideration allows for solar field outlet temperatures up to 565°C and begins solidifying above 240°C. Using molten salt directly in the solar field can significantly reduce thermal energy storage costs and the higher temperature compared to oil heat transfer fluids can power a more efficient power cycle, but the very high freezing point is cause for concern. This work builds on a previous modeling effort investigating different methods for melting Solar Salt frozen in the solar field, which suggested the viability of a novel solar heating method to lower costs of the freeze protection system. In this work higher fidelity models are developed to better investigate the melting process with a more detailed 3D geometry which includes the insulated bellows. The thermal-fluid model of the melting process is updated to include temperature dependent density and data for solid phase properties. In addition, a finite element model is developed to resolve thermal stresses at the point with highest thermal gradients. Results with the new model confirm the viability of using controllable solar flux heating to thaw salt frozen in the solar field without damaging the receiver; however, the presence of non-illuminated sections significantly slows down the melting process. Solar heating simulations with pauses off-sun of 120 and 60 s require 18.5 and 11.9 h to melt salt from a night-time temperature of 10°C with 1000 W m2 DNI, which results in maximum thermal stresses of 48.2 and 53.5 MPa, respectively. Adding 150 W m−1 to the solar heating simulation with a 60 s pause off-sun decreases both the melt time and thermal stresses due to the more uniform heating, suggesting a combined heating method may be the best option.
Assessment of Buffer-IPyC Thermomechanical Debonding Behavior Using New Experiment Strength Data in BISON
TRIstructural ISOtropic (TRISO) single sub-millimeter-diameter nuclear fuel particle consists of a spherical fuel kernel surrounded by four coating layers. During reactor operation, the TRISO coating layers are subjected to irradiation-induced dimensional changes and the associated thermomechanical behavior of each layer. One of the observed behaviors is gap formation between the buffer and IPyC layer due to the porous buffer’s irradiation-induced shrinkage exceeding that of the IPyC layer. To predict TRISO thermomechanical performance, multi-physics models have been built that are continually updated and refined. The BISON code is a finite element-based nuclear fuel performance code that may be used for TRISO particle simulations. One of the recent additions to the BISON code is the ability to model the process of layer debonding. This paper will focus on the simulation results of the improved BISON debonding model that will utilize updated strengths measured from irradiated TRISO fuel particles. The new experimental strength data from micromechanical tests of irradiated TRISO fuel samples were exercised in the BISON simulations and compared to baseline strength data to assess their applicability in the models. This also includes updated buffer-IPyC bond strengths to simulate layer delamination. Based on current experimental observations it is noted that the buffer-IPyC separation occurs not exactly at the junction of these two layers, but more on the side of the buffer layer. This improved modeling approach using experimental strength data to characterize buffer-IPyC debonding and its potential subsequent cracking will be presented in the paper along with comparisons to available experimental observations.
Augmenting the Structural Dynamics Workflow to Reduce Development Times [Slides]
The structural dynamics workflow at LANL stands to be improved by implementing methods and techniques related to reduced-order finite-element modeling (FEM), pretest predictions, and FEM-test correlation and updating. The benefits of these industry-standard practices are demonstrated in this work. Software used for this project included Ansys 2023 R2 (Mechanical and Spaceclaim), Creo Parametric 8.0, MathCAD Prime 8.0, Matlab R2023b.
Augmenting the Structural Dynamics Workflow to Reduce Development Times
The success of future systems development at Los Alamos National Laboratory (LANL) depends, in part, on the ability to make informed decisions quickly. This is particularly true when asked to perform structural-mechanical analyses across many design alternatives. To help reduce development time, techniques in reduced-order finite-element modeling (FEM), pretest predictions, and FEM-test correlation and updating were demonstrated in the fiscal year (FY) 23 Technology and Demonstration Project (TED): Augmenting the Structural Dynamics Workflow to Reduce Development Times. This report expands on the TED project final report, LA-UR-34022.
Assessment of buffer-IPyC thermomechanical debonding behavior using new experimental strength data in BISON
TRIstructural ISOtropic (TRISO) fuel is a nuclear fuel commonly used in High Temperature Gas-cooled Reactors (HTGRs). A single sub-millimeter-diameter TRISO fuel particle consists of a spherical fuel kernel surrounded by four coating layers: a low-density pyrocarbon buffer layer, an inner pyrolytic carbon (IPyC) layer, a silicon carbide (SiC) layer, and an outer pyrolytic carbon (OPyC) layer. The kernel is commonly made of UO2 or a mixture of uranium carbide and uranium oxide (UCO). During reactor operation, the TRISO coating layers are subjected to irradiation-induced dimensional changes and the associated thermomechanical behavior of each layer. One of the observed behaviors is gap formation between the buffer and IPyC layer due to the porous buffer’s irradiation-induced shrinkage exceeding that of the IPyC layer. Not all irradiated particles will experience buffer-IPyC gap formation. The debonding may be partial, or it may be nearly total. However, from post-irradiation examination of UCO TRISO fuels irradiated as part of the Advanced Gas Reactor (AGR) Fuel Development and Qualification Program, it was concluded that partial buffer-IPyC debonding was the most common type of buffer-IPyC interaction. To predict TRISO thermomechanical performance, multi-physics models have been built that are being continually updated and refined. The BISON code is a finite element-based nuclear fuel performance code that may be used for 1D, 2D, and 3D TRISO particle simulations. This code is used to calculate fuel temperature, kernel swelling, buffer densification, thermal and irradiation creep, fracture, and fission gas production and release. One of the recent additions to the BISON code is the ability to model the process of layer debonding. This paper will focus on the simulation results of the improved BISON debonding model that will utilize updated strengths measured from irradiated AGR TRISO fuel particles. The new experimental strength data from micromechanical tests of irradiated TRISO fuel samples were exercised in the BISON simulations and compared to baseline strength data to assess their applicability in the models. This also includes updated buffer-IPyC bond strengths to simulate layer delamination. Based on current experimental observations it is noted that the buffer-IPyC separation occurs not exactly at the junction of these two layers, but more on the side of the buffer layer. That observation is also implemented in the TRISO interface debonding model. This improved modeling approach using experimental strength data to characterize buffer-IPyC debonding and its potential subsequent cracking will be presented in the paper along with comparisons to available experimental observations.
pyNuMAD v.0.1
SAND2024-08606O The pyNuMAD software is used for managing wind turbine blade model data. pyNuMAD specializes in defining the geometry, materials, and boundary conditions for structural analysis of wind turbine blades. This includes loading in data files and providing an interface for users to make updates to the model. The software also features meshing functionality, which takes the blade model and creates a shell or brick mesh for use in finite element analysis. A typical user workflow might be: load in blade information from a yaml file, make adjustments to the blade properties, update the blade based on the adjustments, create a mesh of the blade, export this blade to another software for structural analysis. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
Modeling of High-Temperature Corrosion of Zirconium Alloys Using the eXtended Finite Element Method (X-FEM)
Oxidation modeling in modern nuclear fuel performance codes is currently limited by the lack of coupling with mechanics, thus preventing proper description of how high-temperature oxidation impacts mechanical properties. This is mostly due to the fact that the finite difference formalism adopted in corrosion models is incompatible with the direct coupling with mechanics in the finite element modeling employed in modern nuclear fuel performance codes. In this study, a physically based zirconium alloy corrosion model called the Coupled-Current Charge Compensation (C4) model, which was initially developed for operating temperature conditions, has been updated to include high-temperature corrosion in order to provide additional critical information (e.g., oxygen concentration profile) under loss-of-coolant accident (LOCA) conditions—information lacking in existing empirical models. The C4 model was implemented in the MOOSE finite-element framework developed at Idaho National Laboratory, enabling it to be used in the BISON nuclear fuel performance code based on the MOOSE framework. To precisely track the different interfaces at a relatively low computational cost, the eXtended Finite Element Method (X-FEM) was applied in MOOSE. The model’s results were compared to those of existing empirical models as well as metallographic analysis of high-temperature oxidized Zircaloy-4 coupons. Oxygen diffusivities in the a and ß phases resulting from this comparison closely agree with those found in the literature. The C4 model implemented with X-FEM in MOOSE now has the capability to accurately predict oxide, oxygen-stabilized a, and prior ß phase layer growth kinetics under isothermal exposure at high temperature (1000–1500°C). Furthermore, in contrast with the empirical models, the C4 model accounts for the finite thickness of the fuel cladding. It can predict the oxygen concentration profile evolution through the whole cladding, enabling evaluation of the remaining ductile thickness—a crucial variable for modeling the mechanical behavior of the fuel cladding under LOCA. Furthermore, this implementation allows direct coupling with mechanics, at a low computing cost, using finite-element-based nuclear fuel performance codes such as BISON.
A finite element formulation for deformation twinning induced strain localization in polycrystal magnesium alloys
Deformation twinning induces shear strain localization in hexagonal close-packed crystals and is critical for the material’s ductility and failure. Cracks often occur at twin-twin or twin-grain boundary intersections and propagate along twin bands. However, most crystal plasticity models for deformation twinning are based on a “pseudo-slip” approach and do not capture the localized deformation associated with the formation of each discrete twin band. The few exceptions are discrete twin models that involve very complex numerical algorithms and are often compromised in accuracy due to the numerical convergence. These factors make the discrete twin models hard to adopt. This paper proposes a modification to the conventional finite element weak form, to fully incorporate a twin-induced heterogeneous deformation that does not depend on the “pseudo-slip” assumption. The model starts by splitting the deformation gradient into elastic-slip-twinning components. The twin-induced deformation gradient component is computed separately by solving a microstructural evolution problem and then implemented into finite element weak form by constructing a global “twin-force” vector. The constitutive update (e.g., in the user-defined material subroutine, or UMAT, for ABAQUS) therefore avoids dealing with the twinning and recovers to the form of a regular slip-based crystal plasticity model. The results presented here indicate that the twin-induced strain localization and the associated stress-reversal phenomena near the twin band were naturally captured in the model, which was validated against an in-situ synchrotron X-ray micro-diffraction experiment.
Method and apparatus for shape-based energy analysis of solids
A computer-readable medium stores instructions including storing a model of a physical structure and defining a mesh for the model. The mesh includes finite elements, each defined by a respective set of edges. The instructions include, for each finite element, identifying a governing differential equation and a set of complementary functions that exactly satisfy the governing differential equation. The instructions include determining an applied physical stimulus for the physical structure. The instructions include generating an energy optimization model that minimizes a difference between internal energy and external energy of the finite elements in response to the applied physical stimulus. The model includes a matrix of respective scalar multipliers for the complementary functions for each finite element. The instructions include transforming the matrix and calculating a physical parameter of interest. The instructions include, in response to the physical parameter not satisfying a design parameter, updating the model of the physical structure.