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At least 1,099 records · Page 61
All sourcesNASA NTRSDOE OSTI
NASA NTRS2022

A Cohesive Element Formulation for Simulation of General Mode I, II and III Delamination

Cohesive element formulations proposed thus far have assumed that Mode II and Mode III fracture processes, and hence traction-separation laws, are identical. However, experimental observations suggest that such an assumption may not hold in general. The approach described herein consists of a cohesive element formulation in which the assumption of identical Mode II and Mode III fracture processes is not required. This assumption is alleviated by estimating the normal to the delamination front based on the gradient of the displacement jumps determined within each element. The estimated normal is used to rotate the cohesive element coordinate system. Determining the displacement jumps in the rotated coordinate system enables the distinction between Mode II sliding, and Mode III tearing. This information is subsequently used to extend a recently proposed cohesive formulation, resulting in an approach that can simulate mixed-mode I/II/III fracture via prescribing piecewise-linear traction-separation laws combined with a 3D mixed-mode fracture criteria.

Delamination↗
DOE OSTI2014

Rolling Element Bearing Stiffness Matrix Determination (Presentation)

Current theoretical bearing models differ in their stiffness estimates because of different model assumptions. In this study, a finite element/contact mechanics model is developed for rolling element bearings with the focus of obtaining accurate bearing stiffness for a wide range of bearing types and parameters. A combined surface integral and finite element method is used to solve for the contact mechanics between the rolling elements and races. This model captures the time-dependent characteristics of the bearing contact due to the orbital motion of the rolling elements. A numerical method is developed to determine the full bearing stiffness matrix corresponding to two radial, one axial, and two angular coordinates; the rotation about the shaft axis is free by design. This proposed stiffness determination method is validated against experiments in the literature and compared to existing analytical models and widely used advanced computational methods. The fully-populated stiffness matrix demonstrates the coupling between bearing radial, axial, and tilting bearing deflections.

17 WIND ENERGY↗
DOE OSTI2026

Creep in multi-principal element materials –– A review

The ongoing push towards enhanced energy efficiency and reduced emissions has necessitated the creation of materials with superior performance, especially under extreme conditions. Modern industries, such as aerospace, energy production, and nuclear power, rely heavily on materials that can withstand elevated temperatures without compromising structural integrity. At these heightened temperatures, materials, even when subjected to mechanical stresses well below their yield strength, may experience slow deformation leading to eventual rupture — a phenomenon known as creep. With the expansive design space that comes with the high entropy concept and their reported excellent high temperature strength, multi-principal element materials (MPEMs) have attracted interest in the scientific community for high-temperature applications. Here, this review offers a comprehensive examination of existing studies on creep in MPEMs, which includes multi-principal element−alloys, −bulk metallic glasses, −ceramics, and −superalloys, comparing published findings on MPEMs with pure elements, traditional alloys, bulk metallic glasses, and superalloys. The sub-topics covered include a comparison among different creep-testing methods, creep mechanisms, creep exponents, creep strain rates, activation volume, and creep-activation energy. Modeling efforts for predicting creep behavior of MPEMs are also reviewed. Methods for improving creep resistance by performing heat treatments and/or modifying microstructures are discussed. Overall, the current state of MPEMs has not yet surpassed the creep performance of commercial alloys. Finally, directions for future efforts are suggested, such as experimenting in various controlled environments, expanding the number of compositions tested, exploring advanced manufacturing techniques, and using machine-learning to predict creep properties based on compositions and microstructures.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Swelling of Uranium Dioxide–Silumin Dispersion Fuel Composition in Experimental Fuel Elements of the SM Reactor

A variant of experimental dispersion fuel elements with a displacer and uranium dioxide-silumin fuel composition, which were proposed for modernizing the core of the SM reactor, was investigated. The fuel elements were irradiated in a wide spectrum of neutron- and thermophysical parameters of the reactor’s reflector channel. The fuel elements showed satisfactory radiation resistance at thermal flux density 5.8–8 MW/m{sup 2} and burnup to 45%. The swelling of the fuel composition was analyzed. It is shown that of three possible components of the swelling the one due to gaseous fission products makes the main contribution, approximately 3/4 of the total amount. The interaction of the fuel components results in compaction of the kernel and promotes some compensation of the swelling, increasing as the interaction increases. These investigations show that the depth of burnup at the achieved thermal flux density for fuel elements with a displacer is not the limit.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

A $C^1$-Conforming Arbitrary-Order Two-Dimensional Virtual Element Method for the Fourth-Order Phase-Field Equation

We present a two-dimensional conforming virtual element method for the fourth-order phase-field equation. Our proposed numerical approach to the solution of this high-order phase-field (HOPF) equation relies on the design of an arbitrary-order accurate, virtual element space with $C^1$ global regularity. Such regularity is guaranteed by taking the values of the virtual element functions and their full gradient at the mesh vertices as degrees of freedom. Attaining high-order accuracy requires also edge polynomial moments of the trace of the virtual element functions and their normal derivatives. In this work, we detail the scheme construction, and prove its convergence by deriving error estimates in different norms. A set of representative test cases allows us to assess the behavior of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Estimation of Errors in Stress Distributions Computed in Finite Element Simulations of Polycrystals

The accuracy of the stresses predicted from crystal plasticity-based finite element formulation depends on estimation and control of the errors associated with the discretization. In the current work, the errors in the stress distribution are estimated in virtual polycrystalline samples of α-phase titanium (hexagonal close-packed phase of Ti–6Al– 4 V). To estimate the error, the stress field, which does not possess inter-element continuity, is smoothed over a grain using an L 2 projection, thereby providing continuous stress distributions with inter-element continuity. The differences between the continuous (smooth) and discontinuous (raw) stress fields are calculated at individual Gauss quadrature points and used to estimate errors for corresponding elements and grains. Error estimations are performed for a Voronoi-tessellated microstructure, an equiaxed microstructure, and two microstructures with varying grain sizes for tensile loading extending into the fully plastic regime (≈ 5% extension). Magnitudes of the errors are found to depend on microstructural characteristics, particularly the shape and size of grains. Samples having variations in grain size or having less spherical grains exhibited higher errors than samples with uniformly sized, equiaxed grains, with the size variations having a more pronounced effect. In conclusion, errors correlate with proximity to grain boundaries at small (elastic) strains and with deformation-induced features (deformation bands) at large strains.

42 ENGINEERING↗
DOE OSTI2020

Synthesis of precipitation-strengthened Al-Sc, Al-Zr and Al-Sc-Zr alloys via selective laser melting of elemental powder blends

Selective laser melting is used to create Al-1.5Sc, Al-1.5Zr and Al-0.75Sc-0.75Zr (at.%) alloys from blends of elemental Al, Sc, and Zr powders. This study investigates elemental alloying elements (Sc and Zr) which are high-melting and highly reactive, unlike previous work which focused on more concentrated elemental additions of lower-melting, lower-reactivity Cu and Si to aluminum. High-speed in situ synchrotron x-ray imaging and diffraction show that the 20–30 μm Al, Sc, and Zr powders fully melt and sufficiently mix in the molten state to create, on solidification, a homogeneous distribution of primary, micron-size L12 precipitates (Al 3 Sc, Al 3 Zr, and Al 3 (Sc,Zr), respectively) and nucleate micron-size Al matrix grains, as confirmed by SEM imaging of cross-sections. Here, a second laser pass, simulating a realistic additive-manufacturing build condition, fully remelts the initial volume which shows, after solidification, the same Al 3 (Sc,Zr) L1 2 primary micro-precipitates and very fine Al grains. After aging at 300–400°C, the alloys show large increases in hardness, consistent with an exceptionally high number density (1.4 × 10 24 m –3 ) and volume fraction (2.5%) of secondary Al 3 (Sc,Zr) nano-precipitates with a Sc-rich core and Zr-rich shell, as measured via atom-probe tomography.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A coupled multipoint stress–multipoint flux mixed finite element method for the Biot system of poroelasticity

In this work, we present a mixed finite element method for a five-field formulation of the Biot system of poroelasticity that reduces to a cell-centered pressure–displacement system on simplicial and quadrilateral grids. A mixed stress–displacement–rotation formulation for elasticity with weak stress symmetry is coupled with a mixed velocity–pressure Darcy formulation. The spatial discretization is based on combining the multipoint stress mixed finite element (MSMFE) method for elasticity and the multipoint flux mixed finite element (MFMFE) method for Darcy flow. It uses the lowest order Brezzi–Douglas–Marini mixed finite element spaces for the poroelastic stress and Darcy velocity, piecewise constant displacement and pressure, and continuous piecewise linear or bilinear rotation. A vertex quadrature rule is applied to the velocity, stress, and stress–rotation bilinear forms, which block-diagonalizes the corresponding matrices and allows for local velocity, stress, and rotation elimination. This leads to a cell-centered positive-definite system for pressure and displacement at each time step. We perform error analysis for the semidiscrete and fully discrete formulations, establishing first order convergence for all variables in their natural norms. The numerical tests confirm the theoretical convergence rates and illustrate the locking-free property of the method.

42 ENGINEERING↗
DOE OSTI2018

Distribution and speciation of rare earth elements in coal combustion by-products via synchrotron microscopy and spectroscopy

Rare earth element (REE) binding environments and associated mineral phases in coal and coal combustion byproducts (CCBs) are not well understood. Advanced characterization of REEs' binding environments before, during, and after production can be vital in establishing an economically viable recovery method for REEs from these materials. Here, this study characterized different REE distributions, cerium (Ce) oxidation states, and Ce binding environments in 11 CCBs collected from various locales via X-ray fluorescence (XRF) elemental mapping and X-ray absorption near edge structure (XANES) at Stanford Synchrotron Radiation Lightsource (SSRL). Bulk Ce LIII edge XANES identified Ce(III) (>85%) as the predominant Ce oxidation state in all studied samples. Ce speciation and XRF elemental map analyses further reveal the REEs in studied samples can be (1) dispersed throughout the aluminosilicate glass phase, (2) as micro-particles in large glass grain, or (3) as independent trace phases in studied samples. Both fly ash and bottom ash contain mainly Ce(III) micro-hotspots (<40 μm), co-localization with a range of elements, including, but not limited to: P, S, Ca, Ti, and Mn. At microscale, Ce can change from Ce(III) to mixture of Ce(III) and Ce(IV) and to 100% Ce(IV) oxide, revealing potential REE-phase decomposition and oxidation in coal and coal combustion process. Our study also observed intraparticle and interparticle distribution difference between light REEs and heavy REEs. Finally, the synchrotron-based characterization confirmed the presence of these trace, previously only theorized, phases during the combustion process and ultimately may inform the simplification of separation and extraction processes for REE from different CCBs.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Matrix-free subcell residual distribution for Bernstein finite elements: Monolithic limiting

This paper is focused on the aspects of limiting in residual distribution (RD) schemes for high-order finite element approximations to advection problems. Both continuous and discontinuous Galerkin methods are considered in this work. Discrete maximum principles are enforced using algebraic manipulations of element contributions to the global nonlinear system. The required modifications can be carried out without calculating the element matrices and assembling their global counterparts. The components of element vectors associated with the standard Galerkin discretization are manipulated directly using localized subcell weights to achieve optimal accuracy. Low-order nonlinear RD schemes of this kind were originally developed to calculate local extremum diminishing predictors for flux-corrected transport (FCT) algorithms. In the present paper, we incorporate limiters directly into the residual distribution procedure, which makes it applicable to stationary problems and leads to well-posed nonlinear discrete problems. To circumvent the second-order accuracy barrier, the correction factors of monolithic limiting approaches and FCT schemes are adjusted using smoothness sensors based on second derivatives. Finally, the convergence behavior of presented methods is illustrated by numerical studies for two-dimensional test problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Poromechanical cohesive interface element with combined Mode I-II cohesive zone elastoplasticity for simulating fracture in fluid-saturated porous media

A combined Mode I-II cohesive zone (CZ) elasto-plastic constitutive model, and a two-dimensional (2D) cohesive interface element (CIE) are formulated and implemented at small strain within an ABAQUS User Element (UEL) for simulating 2D crack nucleation and propagation in fluid-saturated porous media. Here, the CZ model mitigates problems of convergence for the global Newton-Raphson solver within ABAQUS, which when combined with a viscous stabilization procedure allows for simulation of post-peak response under load control for coupled poromechanical finite element analysis, such as concrete gravity dam stability analysis. Verification examples are presented, along with a more complex ambient limestone-concrete wedge fracture experiment, water-pressurized concrete wedge experiment, and concrete gravity dam stability analyses. A calibration procedure for estimating the CZ parameters is demonstrated with the limestone-concrete wedge fracture process. For the water-pressurized concrete wedge fracture experiment it is shown that the inherent time-dependence of the poromechanical CIE analysis provides a good match with experimental force versus displacement results at various crack mouth opening rates, yet misses the pore water pressure evolution ahead of the crack tip propagation. This is likely a result of the concrete being partially-saturated in the experiment, whereas the finite element analysis assumes fully water saturated concrete. For the concrete gravity dam analysis, it is shown that base crack opening and associated water uplift pressure leads to a reduced Factor of Safety, which is confirmed by separate analytical calculations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Coordinated U–Pb geochronology, trace element, Ti-in-zircon thermometry and microstructural analysis of Apollo zircons

Here, we present the results of a coordinated SIMS U–Pb, trace element, Ti-in-zircon thermometry, and microstructural study of 155 lunar zircons separated from Apollo 14, 15, and 17 breccia and soil samples that help resolve discrepancies between the zircon data, the lunar whole rock history and lunar magma ocean crystallization models. The majority of lunar grains are detrital fragments, some nearly 1 mm in length, of large parent crystals suggesting that they crystallized in highly enriched KREEP magmas. The zircon age distributions for all three landing sites exhibit an abundance of ages at ~4.33 Ga, however they differ in that only Apollo 14 samples have a population of zircons with ages between 4.1 and 3.9 Ga. These younger grains comprise only 10% of all dated lunar zircons and are usually small and highly shocked making them more susceptible to Pb-loss. These observations suggest that the majority of zircons crystallized before 4.1 Ga and that KREEP magmatism had predominantly ceased by this time. We also observed that trace element analyses are easily affected by contributions from inclusions (typically injected impact melt) within SIMS analyses spots. After filtering for these effects, rare-earth element (REE) abundances of pristine zircon are consistent with one pattern characterized by a negative Eu anomaly and no positive Ce anomaly, implying that the zircons formed in a reducing environment. This inference is consistent with crystallization temperatures based on measured Ti concentrations and new estimates of oxide activities which imply temperatures ranging between 958 ± 57 and 1321 ± 100 °C, suggesting that zircon parent magmas were anhydrous. Together, the lunar zircon ages and trace elements are consistent with a ≤300 My duration of KREEP magmatism under anhydrous, reducing conditions. We also report two granular texture zircons that contain baddeleyite cores, which both yield 207 Pb– 206 Pb ages of 4.33 Ga. These grains are our best constraints on impact ages within our sample population, and suggest at least one large impact is contemporaneous with the most common time of magmatic zircon formation on the Moon’s crust visited by the Apollo missions.

58 GEOSCIENCES↗
DOE OSTI2013

Optical tomography reconstruction algorithm with the finite element method: An optimal approach with regularization tools

Highlights: •New strategies to improve the accuracy of the reconstruction through mesh and finite element parameterization. •Use of gradient filtering through an alternative inner product within the adjoint method. •An integral form of the cost function is used to make the reconstruction compatible with all finite element formulations, continuous and discontinuous. •Gradient-based algorithm with the adjoint method is used for the reconstruction. -- Abstract: Optical tomography is mathematically treated as a non-linear inverse problem where the optical properties of the probed medium are recovered through the minimization of the errors between the experimental measurements and their predictions with a numerical model at the locations of the detectors. According to the ill-posed behavior of the inverse problem, some regularization tools must be performed and the Tikhonov penalization type is the most commonly used in optical tomography applications. This paper introduces an optimized approach for optical tomography reconstruction with the finite element method. An integral form of the cost function is used to take into account the surfaces of the detectors and make the reconstruction compatible with all finite element formulations, continuous and discontinuous. Through a gradient-based algorithm where the adjoint method is used to compute the gradient of the cost function, an alternative inner product is employed for preconditioning the reconstruction algorithm. Moreover, appropriate re-parameterization of the optical properties is performed. These regularization strategies are compared with the classical Tikhonov penalization one. It is shown that both the re-parameterization and the use of the Sobolev cost function gradient are efficient for solving such an ill-posed inverse problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach can be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

An enriched finite element model with q-refinement for radiative boundary layers in glass cooling

Radiative cooling in glass manufacturing is simulated using the partition of unity finite element method. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary simplified P{sub 1} approximation for the radiation in non-grey semitransparent media. To integrate the coupled equations in time we consider a linearly implicit scheme in the finite element framework. A class of hyperbolic enrichment functions is proposed to resolve boundary layers near the enclosure walls. Using an industrial electromagnetic spectrum, the proposed method shows an immense reduction in the number of degrees of freedom required to achieve a certain accuracy compared to the conventional h-version finite element method. Furthermore the method shows a stable behaviour in treating the boundary layers which is shown by studying the solution close to the domain boundaries. The time integration choice is essential to implement a q-refinement procedure introduced in the current study. The enrichment is refined with respect to the steepness of the solution gradient near the domain boundary in the first few time steps and is shown to lead to a further significant reduction on top of what is already achieved with the enrichment. The performance of the proposed method is analysed for glass annealing in two enclosures where the simplified P{sub 1} approximation solution with the partition of unity method, the conventional finite element method and the finite difference method are compared to each other and to the full radiative heat transfer as well as the canonical Rosseland model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A new weak Galerkin finite element method for elliptic interface problems

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments in order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Spectral element method for elastic and acoustic waves in frequency domain

Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Accelerating high-order mesh optimization using finite element partial assembly on GPUs

In this paper we present a new GPU-oriented mesh optimization method based on high order finite elements. Our approach relies on node movement with fixed topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a global nonlinear solve over the whole computational mesh, i.e., all mesh nodes are moved together. A key property of the method is that the mesh optimization process is recast in terms of finite element operations, which allows us to utilize recent advances in the field of GPU-accelerated high order finite element algorithms. For example, we reduce data motion by using tensor factorization and matrix-free methods, which have superior performance characteristics compared to traditional full finite element matrix assembly and offer advantages for GPU based HPC hardware. Furthermore, we describe the major mathematical components of the method along with their efficient GPU-oriented implementation. In addition, we propose an easily reproducible mesh optimization test that can serve as a performance benchmark for the mesh optimization community.

97 MATHEMATICS AND COMPUTING↗