Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “finite element methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,045 records · Page 58
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Application of the Continuum Damage Mechanics Wilshire-Cano-Stewart (WCS) Model

In this study, the applications of the continuum damage mechanics-based Wilshire-Cano-Stewart (WCS) model are explored to predict rupture time, minimum-creep-strain-rate (MCSR), damage, damage evolution, and creep deformation. Increase knowledge in manufacturing methods has pushed the limit of material science and the development of new materials. Conventional testing is required to qualify materials against creep which according to the ASME B&PV III code, 10,000+ hours of experiments are necessary for each heat before materials are put into service. This process is costly and not feasible for new materials. As an alternative, models have been employed to predict creep behaviors and reduce the amount of time necessary for material qualification. Many models have been developed to predict distinct creep behaviors and the question of which model is best remains. Amongst current models, the WCS model has emerge with the ability to predict multiple behaviors using an explicit analytical approach with the ability to predict long-term creep. In this study the novel continuum damage mechanics WCS is employed in multiple applications. The goals of the study are (a) to discuss and determine the framework of the WCS model and validated it mathematically and using parametric simulations, (b) applied the model to accelerated creep data to show the capabilities of the model with non-conventional data, and (c) applied a novel numerical method, the datum temperature method (DTM) to show the model extrapolations and interpolations capabilities with limited and reduce data sets. To accomplish these goals, data is gathered for alloy P91 and Inconel 718 to develop and post-audit validate the model. The benefits of using the WCS model is that it provides an explicit stress and temperature dependency ideal for extrapolations, the coupled equations are suitable for finite element analysis (FEA) implementation, and it follows an explicit calibration approach. The model also proves that it can be applied to accelerated testing data and using the DTM.

Cano, Jaime A↗
DOE OSTI2024

An Efficient Numerical Algorithm for Solving Coupled Time-Dependent Ginzburg-Landau Equation for Superconductivity and Elasticity

A decoupled finite element algorithm is developed for simulating the vortex dynamics on an elastic superconductor which couples the time-dependent Ginzburg- Landau equation with the complex-valued superconducting order parameter and the vector-valued magnetic potential, and the elasticity equation. We present an iterative algorithm for the decoupled system arising from the time and spatial discretization using a combination of preconditioner, algebraic multigrid method (AMG) and preconditioned conjugate gradient method (PCG). The iterative algorithm allows us to perform large-scale three-dimensional simulations of mesoscale pattern formation during superconducting phase transitions with arbitrary elastic boundary conditions. Here, the performance and efficiency of the algorithm are numerically verified by several benchmark problems, exhibiting up to two orders of magnitude improvement depending on the scale of discrete system compared to the exact solver.

Efficiency↗
DOE OSTI2022

NEAMS Technical Area Support in MOOSE

The Multiphysics Object-Oriented Simulation Environment (MOOSE) framework is a foundational capability used by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to create over 15 different simulation tools for advanced nuclear reactors. Due to this ubiquity, improvements to the framework in support of modeling and simulation goals are critical to the program. These improvements can take many forms, including optimization, improved user experience, streamlined application programming interfaces (APIs), parallelism, and new capabilities. The work transcribed in this report was conducted in direct support of the simulation tools and has already been deployed. The capabilities outlined in this report include a factor of 10^4 improvement in dependency resolution speed, sorting of user objects, ability to compute residuals and Jacobians together, transfer fixes, support for the mortar method in finite volume discretizations, addition of generalized advection schemes for fluid simulations, 10^2 speedup in some Griffin simulations due to a new matrix-only solve type, and much more.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

The effect of a transducer’s spatial averaging on an elastodynamic guided wave’s wavenumber spectrum

Elastodynamic guided waves propagate in an elastic solid which makes it difficult, if not impractical, to place a receiving transducer in the direct path of the propagating wave (as one would for an acoustic wave in a fluid medium). Thus, to account for this, receiving transducers are often placed on the surface of the solid waveguide such that the transducer surface is parallel to the wave propagation direction. This transducer orientation introduces spatial averaging, which causes the received signal to have an altered signal amplitude and mode bias. We investigate both of these effects and present a simple model from which we derive a scaling-ratio expression that describes the effects of spatial averaging. Furthermore, we then test its performance using finite-element simulations that incorporate “real-world” assumptions (e.g., transient waves, piezoelectric effects, etc.). The results from the simulations demonstrate that the scaling-ratio can characterize the effects resulting from spatial averaging. The scaling-ratio expression will be particularly useful when designing experiments involving high frequency (small wavelength) guided waves. Lastly, the proposed scaling-ratio expression could be applied to other sensing methods, like Laser Doppler Vibrometry (LDV) or piezoelectric waveguides with inter-digitated transducers, because of its generality. However, the authors are careful to note that the scaling-ratio expression is not intended as a replacement of multi-physics analysis or good experimental design, and the effects of spatial averaging should be avoided whenever possible.

2DFFT↗
DOE OSTI2022

Finite-volume pionless effective field theory for few-nucleon systems with differentiable programming

Finite-volume pionless effective field theory provides an efficient framework for the extrapolation of nuclear spectra and matrix elements calculated at finite volume in lattice QCD to infinite volume, and to nuclei with larger atomic number. In this work, it is demonstrated how this framework may be implemented via a set of correlated Gaussian wave functions optimized using differentiable programming and via solution of a generalized eigenvalue problem. This approach is shown to be significantly more efficient than a stochastic implementation of the variational method based on the same form of correlated Gaussian wave functions, yielding comparably accurate representations of the ground-state wave functions with an order of magnitude fewer terms. The efficiency of representation allows such calculations to be extended to larger systems than in previous work. Further, the method is demonstrated through calculations of the binding energies of nuclei with atomic number A ϵ {2,3,4} in finite volume, matched to lattice QCD calculations at quark masses corresponding to m π = 806 MeV, and infinite-volume effective field theory calculations of A ϵ {2,3,4,5,6} systems based on this matching.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Structural modeling and validation of laminated stacks in magnetic gearing applications

Laminated structures are commonly employed in magnetic gears based on their ability to direct magnetic flux, while inhibiting eddy currents. Unfortunately, the stiffness of the laminated structure is much lower than a solid part, which can lead to unacceptable deflections, given the large magnetic forces and small air gaps in magnetic gears. Finite element analysis of laminations to accurately predict these deflections can be computationally expensive due to the small elements needed to model the thin lamination dimensions. These analyses also have some uncertainty due to the assignment of bonding stiffness. This paper presents a means of accurately modelling the deflection of a laminated stack with reduced complexity and computational time, which is compared to experimental results. Here, the resulting methods are then used to assess the magnetic and mechanical advantages of different designs for the modulating pieces of a magnetic gear.

42 ENGINEERING↗
DOE OSTI2023

A probabilistic-phase field model for the fracture of brittle materials

Abstract We develop a computational method to determine the failure probability of brittle materials under general mechanical loading conditions. The method is a combination of two parts: (1) numerical simulations of materials with multiple cracks using phase field theory, where the complete fracture process is viewed as ‘damage percolation’ along critical paths or clusters of cracks, rather than the traditional weak-link failure mechanism of Weibull, and (2) an extension of the Batdorf statistical theory of fracture to finite domains, where it is implemented within the finite element framework. The results of phase-field simulations at the ‘percolation threshold’ are used as failure data in the Batdorf theory to determine the overall probability of failure. The input to this approach is the size distribution of cracks in a pristine material. An example is shown, where alumina samples that were previously tested by Abe and coworkers (Abeet al2003J. Am. Ceram. Soc.861019–21) in four-point loading are compared to the results of our numerical simulations. The approach developed here has the advantage of being extendable to more complex thermomechanical loading.

Materials Science↗
DOE OSTI2020

Mechanism-Based Energy Regularization in Computational Modeling of Quasibrittle Fracture

Abstract Quasibrittle materials are featured by a strain-softening constitutive behavior under many loading scenarios, which could eventually lead to localization instability. It has long been known that strain localization would result in spurious mesh sensitivity in finite element (FE) simulations. Previous studies have shown that, for the case of fully localized damage, the mesh sensitivity can be mitigated through energy regularization of the material constitutive law. However, depending on the loading configuration and structural geometry, quasibrittle structures could exhibit a complex damage process, which involves both localized and diffused damage patterns at different stages of loading. This study presents a generalized energy regularization method that considers the spatial and temporal evolution of damage pattern. The method introduces a localization parameter, which describes the local damage pattern. The localization parameter governs the energy regularization of the constitutive model, which captures the transition from diffused to localized damage during the failure process. The method is cast into an isotropic damage model, and is further extended to rate-dependent behavior. The energy regularization scheme is directly incorporated into the kinetics of damage growth. The model is applied to simulate static and dynamic failures of ceramic specimens. It is shown that the present model is able to effectively mitigate the spurious mesh sensitivity in FE simulations of both types of failure. The present analysis demonstrates the essential role of mechanism-based energy regularization of constitutive relation in FE simulations of quasibrittle fracture.

Mechanics↗
DOE OSTI2024

R-Adaptivity to Enable Compression of Elementary Computations in Extreme-Scale Finite Element Simulators

Modern computing systems are capable of exascale calculations, which are revolutionizing the development and application of high-fidelity numerical models in computational science and engineering. While these systems continue to grow in processing power, the available system memory has not increased commensurately, and electrical power consumption continues to grow. A predominant approach to limit the memory usage in large-scale applications is to exploit the abundant processing power and continually recompute many low-level simulation quantities, rather than storing them. However, this approach can adversely impact the throughput of the simulation and diminish the benefits of modern computing architectures. We present three novel contributions to reduce the memory burden while maintaining, and sometimes improving, performance in simulations based on finite element discretizations. The first contribution develops dictionary-based data compression schemes that detect and exploit the structure of the discretization, due to redundancies across the finite element mesh. While these schemes are shown to reduce memory requirements by more than 99% on meshes with large numbers of identical mesh cells, there are applications where this structure does not exist. The second contribution leverages a recently developed augmented Lagrangian optimization algorithm to enable r-adaptivity for meshes with the goal of enhancing the redundancies in the mesh. The third contribution extends these methods to patch-based linear solvers and preconditioners by compressing local matrices. Numerical results demonstrate the effectiveness of the proposed methods to detect, enhance and exploit mesh structure on a suite of examples inspired by large-scale applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

In-situ, nanoscale fracture toughness measurements for improved mechanical interfaces

In this project, we demonstrated stable nanoscale fracture in single-crystal silicon using an in-situ wedge-loaded double cantilever beam (DCB) specimen. The fracture toughness KIC was calculated directly from instrumented measurement of force and displacement via finite element analysis with frictional corrections. Measurements on multiple test specimens were used to show K IC = 0.72 ± 0.07 MPa m 1/2 on {111} planes and observe the crack-growth resistance curve in <500 nm increments. The exquisite stability of crack growth, instrumented measurement of material response, and direct visual access to observe nanoscale fracture processes in an ideally brittle material differentiate this approach from prior DCB methods.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Mascon distribution techniques for asteroids and comets

The mass-concentration model is an approach that has been used to model the gravitational fields of irregularly shaped bodies such as asteroids and comets. By this approach, the body is treated as a collection of point masses. The method is conceptually simple, easy to program, valid down to the surface, and capable of modeling arbitrary density heterogeneities. How the mass concentrations are distributed as well as how mass is assigned to these concentrations is, however, nontrivial. These aspects significantly affect the accuracy and efficiency of the gravitational model. In this paper, we frame the distribution process in terms of numerical integration applied to finite volume meshes. We describe a new method using unstructured, curvilinear, finite volume meshes to significantly improve the accuracy of the mass-concentration model. We then compare the accuracy and efficiency of several variations of our distribution technique to those from literature using Asteroid Eros and Bennu as example bodies. Our results show that the mascon model can be as accurate as the analytic polyhedral model at the surface using an equivalent number of computational elements—i.e., mascon to surface facets. We report the improvement in the model’s performance can be mainly attributed to the volume mesh topology while mesh curving can provide modest case-dependent improvements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Empirical Model of Puncture Energy for Metals

The purpose of this work is to fit a previously developed empirical equation for puncture energy to simulation data. The conservative puncture energy equation could be used to expedite the process of performing calculations in the development of safety measures, avoiding the need to create complex finite element models for specific puncture scenarios. A total of 108 simulations are developed by varying coupon thickness, coupon material, probe shape, and probe diameter. The simulations are comprised of a low-velocity probe puncturing the coupons, from which the probe kinetic energy change is calculated. The empirical equation is fit to the dimensions, material properties, and energy results using a non-linear least-squares regression method within Python, which determines the two constant parameters for each fit. More statistically significant fit results are achieved by separating the data by probe shape and coupon material.

42 ENGINEERING↗
DOE OSTI2023

Application of the van der Pauw method for electrical conductivity measurements at high temperatures using an insulating compressing ring

High quality data on the high temperature electrical properties of ceramics, particularly oxides, is of great value for material selection, design, and modeling for a broad range of emerging applications. Utilizing the mismatch in the coefficient of thermal expansion between two materials, a purely mechanical method for establishing electrical contact in the van der Pauw geometry to measure the bulk resistivity of ceramic disks at high temperatures is presented. Measurements of a reference material, 20 mol. % Gd-doped cerium oxide, are presented up to 1000 °C. The viability of electrical measurements up to a maximum temperature of 1600 °C is also considered. Measurements are performed using multiple techniques and compared to literature values finding excellent agreement. Finally, the approach described in this work enables the van der Pauw method to be applied to many ceramic materials over a wide range of temperatures and environments.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Validation of Hole-Drilling Residual Stress Measurements in Workpieces of Various Thickness

A recent revision to the ASTM E837 standard for near-surface residual stress measurement by the hole-drilling method describes a new thickness-dependent stress calculation procedure applicable to “thin” and “intermediate” workpieces for which strain versus depth response depends on workpiece thickness. This new calculation procedure differs from that of the prior standard, which applies only to thick workpieces with strain versus depth response independent of thickness. Herein we assess the new calculation procedures by performing hole-drilling residual stress measurements in samples with a range of thickness. Near-surface residual stress is measured in a thick aluminum plate containing near-surface residual stress from a uniform shot peening treatment, and in samples of different thickness removed from the plate at the peened surface. A finite element (FE) model is used to assess consistency between measured residual stress across the range of sample thickness. Measured residual stress varies with sample thickness, with thinner samples exhibiting smaller near-surface compressive stress and a larger gradient of subsurface stress. These trends are consistent with both observed bending (curvature) of the removed samples and the trend in FE-calculated expected residual stress. The measured and expected residual stresses are in good agreement for samples of intermediate thickness, but the agreement decreases with sample thickness. Measured residual stress is invariant with gage circle diameter. The new thickness-dependent stress calculation procedure for hole-drilling provides meaningful improvement compared to thick-workpiece calculations.

42 ENGINEERING↗
DOE OSTI2024

Predicting non-linear stress–strain response of mesostructured cellular materials using supervised autoencoder

Recent breakthroughs in advanced manufacturing capabilities have made it possible to design and print sophisticated topologies of cellular structures using diverse engineering materials such as metals, polymers, and ceramics. In these architectured materials, it is often desirable to tailor the mechanical properties by altering the unit cell topology. This necessitates an in-depth understanding of how the topology of the unit cell structure affects the macroscopic behavior of the material in both the linear and the non-linear regimes encountered under large compression. Here, we have developed a machine learning (ML) approach capable of accelerating the prediction of the stress–strain response of a polymer-based cellular structure under uniaxial confined compression. As part of generating the training data for ML, 60,000 mesostructures were generated using a relatively novel approach based on cellular automata, and their corresponding stress–strain responses were obtained from the finite element simulations. Principal component analysis (PCA) was used to reduce the dimensionality of the stress–strain curves. With only 20 principal components, PCA captured 99.89% of the variance in the stress–strain curves while reducing the dimensionality by 5X. ML using supervised autoencoder was able to successfully speed up the prediction of the non-linear stress–strain response of a unit cell by up to 4600X. The proposed method can serve as an efficient data generation tool and a rapid means for predicting the structure–property relationship through accelerated forward modeling of cellular materials under compaction, in cases where the macroscopic stress–strain response is governed by the unit-cell topology.

36 MATERIALS SCIENCE↗
DOE OSTI2023

An in-silico NMR laboratory for nuclear magnetic shieldings computed via finite fields: Exploring nucleus-specific renormalizations of MP2 and MP3

Here we developed and implemented a method-independent, fully numerical, finite difference approach to calculating nuclear magnetic resonance shieldings, using gauge-including atomic orbitals. The resulting capability can be used to explore non-standard methods, given only the energy as a function of finite-applied magnetic fields and nuclear spins. For example, standard second-order Møller-Plesset theory (MP2) has well-known efficacy for 1H and 13C shieldings and known limitations for other nuclei such as 15N and 17O. It is, therefore, interesting to seek methods that offer good accuracy for 15N and 17O shieldings without greatly increased compute costs, as well as exploring whether such methods can further improve 1H and 13C shieldings. Using a small molecule test set of 28 species, we assessed two alternatives: κ regularized MP2 (κ-MP2), which provides energy-dependent damping of large amplitudes, and MP2.X, which includes a variable fraction, X, of third-order correlation (MP3). The aug-cc-pVTZ basis was used, and coupled cluster with singles and doubles and perturbative triples [CCSD(T)] results were taken as reference values. Our κ-MP2 results reveal significant improvements over MP2 for 13C and 15N, with the optimal κ value being element-specific. κ-MP2 with κ = 2 offers a 30% rms error reduction over MP2. For 15N, κ-MP2 with κ = 1.1 provides a 90% error reduction vs MP2 and a 60% error reduction vs CCSD. On the other hand, MP2.X with a scaling factor of 0.6 outperformed CCSD for all heavy nuclei. These results can be understood as providing renormalization of doubles amplitudes to partially account for neglected triple and higher substitutions and offer promising opportunities for future applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Fluid structural interaction simulation of the MP-1 plate performance irradiated in the advanced test reactor

Due to the high neutron fluxes they generate and increased heat transfer performance, plate type fuels are used in the U.S. high-performance research reactors. During irradiation, a significant amount of fission energy (i.e., ~200 MeV per atom) is released by the U-235 chain reaction that is carried away by the coolant. Through thermal hydraulic analysis, the coolant’s heat transfer capability is investigated to ensure that the desired fuel temperature can be maintained. At high temperatures, the plate undergoes elastic/plastic deformation, creep, and swelling as a result of both the temperature gradients and the fission gas production within the fuel. These effects are studied via fuel performance analysis. When the plate deformation is small enough that the coolant flow remains relatively unchanged, conducting these two types of analyses independently will suffice. But at high fuel burnups, the swollen plates may encroach into the coolant channels that separate the fuel plates from each other and cause these channels to narrow. Large reductions in channel gap size imperil cooling performance, causing fuel temperatures to rise. Further, if the plate deformation is asymmetric, the fuel centerline will shift toward one side of the channel, causing an uneven reduction in coolability. In addition, a boehmite (oxide) layer will, over time, grow on the plate surface, further obstructing the heat transfer process. To precisely predict fuel temperatures/deformation, a complete coupled analysis that considers coolant flow, heat transfer, oxide growth, elastic/plastic deformation, creep, and swelling is needed; however, this type of analysis method is not available in the literature. To fill the gap, this research developed a fluid structure interaction (FSI) approach to the fuel plate analysis, then successfully applied it to the Mini-Plate (MP)-1 experiment, which was irradiated in the Advanced Test Reactor (ATR) for both one and two cycles. The complete analysis coupled STAR-CCM+, a computational fluid dynamic (CFD) software for calculating flow, with Abaqus, a finite element analysis code for calculating plate deformation. Improvements in the results were found when comparing the fully coupled analysis to the independently conducted analyses but they were not significant due to the miniature size of the plates and the relatively short irradiation time. In the future, the fully coupled approach presented herein will be applied to full-size fuel plates with longer irradiation cycles once additional experiments become available.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗