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NASA NTRSDate not supplied

Improved Benchmarking of Cohesive Elements in Abaqus Standard for Predicting Disbond and Delamination in Composite Structures

Traditional approaches for aircraft certification require the assumption of an initial flaw condition, either represented as barely visible impact damage (BVID) or through inclusion of a Teflon insert to serve as surrogate damage. Based on the initial composite damage state, the structure must be shown to demonstrate structural durability and damage tolerance (DaDT) according to the following criteria: a. Damage displays no detrimental growth under cyclic loading b. The structure is able to sustain design limit load (DLL) Currently, the only available manner for validating structural performance is through test. Since damage can occur over a wide variety of areas within a structure, this approach has proven to be increasingly expensive and time consuming for composite airframes and acreage structure within the design-test-certification building block. A further complicating factor is the requirement to accurately capture the most critical damage morphologies as a starting condition. To understand the severity of the damage, it is either required to experimentally determine the most critical areas at tremendous expense or rely on legacy data of similar structural testing, which limits design space expansion. A preferred solution is to use advanced analysis to provide improved understanding of load margins for critical locations based on a wide variety of potential starting damage conditions. The standard industry approach for DaDT certification adheres to the use of the traditional virtual crack closure technique (VCCT) method. VCCT is generally a preferred method because it conforms to the current certification principles of damage from a known flaw, and when used correctly, can be effective at predicting delamination propagation under static and cyclic loading. The VCCT method requires the inclusion of an initial flaw in the finite element (FE) model requiring a-priori knowledge of the flaw location. This in turn requires a plethora of analysis cases to be examined to cover a reasonable span of potential damage states. Additionally, the VCCT approach requires node-to-node connectivity rendering it incompatible with the best practices and approaches for using continuum damage mechanics (CDM) based progressive damage and failure analysis (PDFA) tools within a typical FE solver. Alternatives to VCCT have emerged in the form of cohesive elements which utilize the cohesive zone model (CZM). Unlike VCCT which models linear elastic fracture mechanics, cohesive elements couples continuum and fracture based responses through the use of bilinear traction separation laws. These laws are defined based on a penalty stiffness, a cohesive strength, and a strain energy release rate. The approach can be mesh regularized with native cohesive elements within many FE solvers such as Abaqus and LS-DYNA. In Phase I of the NASA Advanced Composites Consortium (ACC) post-buckled stiffened panel with BVID, Strength and Life [1], the performance of cohesive elements were benchmarked in comparison to VCCT and LEFM solutions and showed good agreement using Abaqus explicit [2]. To realize savings on current and future programs, it is still necessary to close technical gaps related to the use of cohesive elements with Abaqus Standard. Within a program environment, standard finite element analysis is the preferred analytical capability for quasi-static loading as it eliminates uncertainty due to oscillatory behavior commonly seen with explicit analysis. This oscillatory behavior creates difficulties in writing margins of safety based on the analysis. The use of negative tangent stiffness material models complicates convergence which typically requires the use of numerical controls such as viscous damping to overcome. To date, there has not been a comprehensive study on how to establish best practices for cohesive element convergence for predictive capability within the Abaqus implicit solver. In pursuit of these goals, under the NASA ACC program, several numerical benchmark problems were proposed including pure mode I (double cantilevered beam – DCB), pure mode II (end notch flexure – ENF), and symmetric/unsymmetric evolving mixed mode (single leg bend – SLB). This paper focuses on the use of cohesive elements to model the delamination through the use of CZM. Specifically, finite element models for the DCB, ENF, symmetric SLB, and unsymmetric SLB, are developed and various solution controls for convergence are studied to develop a best practice. Once the best practice has been developed, the predictive capability of the objective CZM model is used to analyze the hat pull-off strength of a standard hat stiffened configuration under various loading conditions.

Abaqus↗
DOE OSTI2023

Mechanisms and Impacts of Earth System Tipping Elements

Tipping elements are components of the Earth system which may respond nonlinearly to anthropogenic climate change by transitioning toward substantially different long-term states upon passing key thresholds or “tipping points.” In some cases, such changes could produce additional greenhouse gas emissions or radiative forcing that could compound global warming. Improved understanding of tipping elements is important for predicting future climate risks and their impacts. Here we review mechanisms, predictions, impacts, and knowledge gaps associated with 10 notable Earth system components proposed to be tipping elements. We evaluate which tipping elements are approaching critical thresholds and whether shifts may manifest rapidly or over longer timescales. Some tipping elements have a higher risk of crossing tipping points under middle-of-the-road emissions pathways and will possibly affect major ecosystems, climate patterns, and/or carbon cycling within the 21st century. However, literature assessing different emissions scenarios indicates a strong potential to reduce impacts associated with many tipping elements through climate change mitigation. The studies synthesized in our review suggest most tipping elements do not possess the potential for abrupt future change within years, and some proposed tipping elements may not exhibit tipping behavior, rather responding more predictably and directly to the magnitude of forcing. Nevertheless, uncertainties remain associated with many tipping elements, highlighting an acute need for further research and modeling to better constrain risks.

58 GEOSCIENCES↗
DOE OSTI2023

Gas-mediated trace element incorporation into rhyolite-hosted topaz: A synchrotron microbeam XAS study

Magmatic gas exsolving during late-stage cooling of shallow magmas has been considered an important facilitator of low-pressure alteration and metal transport. However, the chemical properties of such gas, particularly its metal transport mechanisms and capacity, remain elusive. Trace elements in minerals produced by gas-mediated surface reaction or precipitation from gas capture details of gas composition and reaction pathways. However, interpretation of mineral trace element contents is dependent on understanding crystallographic controls on gas/mineral partitioning. Here, this work investigates the structural accommodation of As, Mn, Ga, Ge, Fe, and Ti in vapor-deposited topaz of vesicular topaz rhyolite from the Thomas Range, Utah, through single-crystal synchrotron microbeam X-ray techniques on picogram quantities of those trace elements. X-ray absorption near edge structure (XANES) data indicates that these elements are incorporated into topaz as As 5+ , Fe 3+ , Mn 3+ , Ti 4+ , Ga 3+ , and Ge 4+ . Extended X-ray absorption fine structure (EXAFS) analysis for these trace elements, compared to EXAFS of structural Al and Si, reveals that As 5+ and Ge 4+ are incorporated directly into the tetrahedral site of the topaz structure, with the octahedral site accommodating Mn 3+ , Fe 3+ , Ga 3+ , and Ti 4+ . For As 5+ and Fe 3+ , the structural impact of substitution extends to at least second neighbors (other elements were only resolvable to first neighbors). Further interpretation of the EXAFS results suggests that the substitution of Ti 4+ results in increased distortion of the octahedral site, while the other trace elements induce more uniform expansion correlating in magnitude to their ionic radius. Comparison of quantified X-ray fluorescence (XRF) data for two topaz crystals from this rhyolite reveals variable trace element concentrations for As 5+ , Fe 3+ , Ga 3+ , and Ti 4+ , reflective of a source gas undersaturated in these trace elements changing in concentration over the period of topaz deposition. The identical Ge 4+ content of the two topaz crystals suggests that Ge 4+ in the gas was buffered by the growth of another Ge 4+ -bearing phase, such as quartz. The very low Mn 3+ content in the topaz crystals does not reflect the abundance of Mn 3+ in the gas (saturation of Mn is evidenced by coexisting bixbyite). Instead, it suggests a strong Jahn-Teller inhibitory effect to the substitution of Mn 3+ for Al 3+ in the distorted octahedral site of topaz. It is proposed that exsolution of an HF-enriched gas from cooling rhyolitic magma led to local scouring of Al, Si, and trace metals from the magma. Once topaz crystals nucleated, self-catalyzed reactions that recycle HF led to continued growth of topaz.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Preserving Superconvergence of Spectral Elements for Curved Domains via $h$ and $p$-Geometric Refinement

Spectral element methods (SEM), extensions of finite element methods (FEM), have emerged as significant techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver superior accuracy due to the potential superconvergence in nodal solutions for well-shaped tensor-product elements. However, the accuracy of SEM often degrades in complex geometries due to geometric inaccuracies near curved boundaries and the loss of superconvergence with simplicial or non-tensor-product elements. To overcome the first issue, we propose using h- and p-geometric refinement, which refines the mesh near high-curvature regions and increases the degree of geometric basis functions, respectively. We show that when using mixed-element meshes with tensor-product elements in the interior of the domain, curvature-based geometric refinement near boundaries can improve the accuracy of the interior elements by reducing pollution errors and preserving the superconvergence in nodal solutions. To address the second issue, we introduce a post-processing technique using the adaptive extended stencil finite element method (AES-FEM) to recover the accuracy near the curved boundaries. The combination of curvature-based geometric refinement and accurate post-processing offers an effective and easier-to-implement alternative to methods reliant on exact geometries. We demonstrate our techniques by solving the convection-diffusion equation in 2D and show up to two orders of magnitude of improvement in the solution accuracy, even when the elements are poorly shaped near boundaries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Trace elements and heavy metals in black vultures ( Coragyps atratus ) and turkey vultures ( Cathartes aura ) in the southeastern United States

Many vulture species worldwide are declining at alarming rates due to a variety of anthropogenic causes, including exposure to pollutants and pharmaceuticals through consumption of contaminated carrion. However, little is known about the extent to which vultures are exposed to various contaminants as well as toxicity thresholds for trace elements and heavy metals. Our objective was to quantify levels of trace elements and heavy metals within black vulture (Coragyps atratus) and turkey vulture (Cathartes aura) tissues to determine the extent to which populations in the southeastern United States are exposed to carrion that contains high levels of contaminants. We collected black vulture liver samples and examined differences in trace element and heavy metal concentrations between sexes and age classes (adult and juvenile). Further, we collected 81 blood and 42 feather samples from additional black and turkey vultures and compared differences between species and age classes. We found similar element concentrations between juvenile and adult black vultures with the exception of Cu, where levels 40 were higher in juveniles compared to adults. However, we did observe substantial differences in element concentrations between species for both blood and feather samples, with black vultures generally having higher concentrations of most elements. Our data revealed higher element levels in both species compared to toxicity thresholds found in other bird of prey species, such as blood and liver toxicity threshold suggestions for Pb poisoning in Falconiformes. Further, while average contaminant levels were generally low, extreme outliers were observed for some elements, including Pb, suggesting some individuals were exposed to high levels of potentially toxic elements. In conclusion, more research is needed to better understand contaminant exposure in black and turkey vultures across a broader geographic region, as well as elucidate toxicity thresholds and non-lethal impacts of contaminant exposure in these species.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗
DOE OSTI2024

Evaluation of flow-induced plate deflection for University of Missouri research reactor low-enriched uranium fuel element

The University of Missouri Research Reactor (MURR), located on the campus of the University of Missouri in Columbia, Missouri, is one of the six United States (U.S.) High Performance Research Reactors (USHPRR), including one critical facility, that are actively collaborating with the U.S. Department of Energy (DOE) National Nuclear Security Administration (NNSA) Office of Material Management and Minimization (M3) Reactor Conversion Program to convert from highly enriched uranium (HEU, ≥20 wt% U-235) fuel to low-enriched uranium (LEU, <20 wt% U-235) fuel. A new type of very high-density LEU fuel based on a monolithic alloy of uranium and 10 wt% molybdenum (U-10Mo) is expected to allow conversion of some USHPRR, including MURR. In the design of its fuel elements, MURR is using thin parallel curved fuel plates separated by coolant channels. In this work, fluid-structure interaction (FSI) analysis of the MURR LEU fuel element is performed at the element level (as compared to the plate level analysis), which models all components of the LEU fuel element, including fuel plates and the supporting structures. Therefore, the effect of supporting structures on the flow distribution within the element and the fuel plate deflection are evaluated. In addition to the element nominal flow rate and dimensions, the tolerances in the geometry of the coolant channel and plate thickness, the effect of a comb on plate deflection, and the uncertainty of the flow rate per element are evaluated. For the LEU fuel plates, which are thinner than the current HEU plates, the predicted plate deflection is found to be small compared to the fabrication and assembly tolerances. Thus, the FSI-induced deflections are not expected to noticeably reduce the coolant flow rate or predicted safety margins in the limiting channels for the MURR LEU fuel element. In addition to the simulation work, a hydraulic performance test of the MURR LEU fuel element is currently being planned to support conversion to the use of LEU fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

From ash to oxides: Recovery of rare-earth elements as a step towards valorization of coal fly ash waste

Coal fly ash (CFA) is both a valuable waste material and a potential source of environmental contamination. The inclusion of metals such as rare-earth elements offer a possible incentive towards waste valorization if the metals can be extracted and recovered in an economical manner. Rare-earth elements (REEs) have many technological applications and are critically important in the manufacture of electric vehicles, communication devices, and industrial magnets. However, the global supply of rare-earth elements has faced shortages and price shocks. Current methods for separating and isolating individual rare-earth elements use large amounts of energy and organic solvents, raising concerns over environmental impacts. These factors have led to the investigation of nontraditional sources and separation techniques for these elements. Here, we describe a column-based system that uses a newly developed ligand-associated organosilica sorbent to concentrate and separate rare-earth elements from fly ash leachate. The fly ash used in this study originally contained 0.024 wt% rare-earth elements and the final oxide powder after enrichment contained > 10 wt% rare-earth elements, which is a enrichment of > 400 times. This process requires no additional organic solvents after the sorbent media has been synthesized, offering an alternative to the current standard using solvent extraction for rare-earth element recovery.

42 ENGINEERING↗
DOE OSTI2024

Preserving Superconvergence of Spectral Elements for Curved Domains

Spectral element methods (SEM), extensions of finite element methods (FEM), have emerged as significant techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver superior accuracy due to the potential superconvergence in nodal solutions for well-shaped tensor-product elements. However, the accuracy of SEM often degrades in complex geometries due to geometric inaccuracies near curved boundaries and the loss of superconvergence with simplicial or non-tensor-product elements. To overcome the first issue, we propose using geometric refinement, which both refines the mesh near high-curvature regions and increases the degree of geometric basis functions. We show that when using mixed-element meshes with tensor-product elements in the interior of the domain, curvature-based geometric refinement near boundaries can improve the accuracy of the interior elements by reducing pollution errors and preserving the superconvergence in nodal solutions. To address the second issue, we introduce ApSEM, a post-processing technique using the adaptive extended stencil finite element method (AES-FEM) to recover the accuracy near the curved boundaries. The combination of curvature-based geometric refinement and accurate post-processing offers an effective and easier-to-implement alternative to methods reliant on exact geometries. We demonstrate our techniques by solving the convection-diffusion equation in 2D and 3D and show up to two orders of magnitude of improvement in the solution accuracy, even when the elements are poorly shaped near boundaries. We also show the efficiency of ApSEM as it can recover superconvergence in nodal solutions without drastically increasing the computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Rare earth element enrichment in coal and coal-adjacent strata of the Uinta Region, Utah and Colorado

This study aims to quantify rare earth element enrichment within coal and coal-adjacent strata in the Uinta Region of central Utah and western Colorado. Rare earth elements are a subset of critical minerals as defined by the U.S. Geological Survey. These elements are used for a wide variety of applications, including renewable energy technology in the transition toward carbon-neutral energy. While rare earth element enrichment has been associated with Appalachian coals, there has been a more limited evaluation of western U.S. coals. Here, samples from six active mines, four idle/historical mines, four mine waste piles, and seven stratigraphically complete cores within the Uinta Region were geochemically evaluated using portable X-ray fluorescence ( n = 3,113) and inductively coupled plasma-mass spectrometry ( n = 145) elemental analytical methods. Results suggest that 24%–45% of stratigraphically coal-adjacent carbonaceous shale and siltstone units show rare earth element enrichment (>200 ppm), as do 100% of sampled igneous material. A small subset (5%–8%) of coal samples display rare earth element enrichment, specifically in cases containing volcanic ash. This study proposes two multi-step depositional and diagenetic models to explain the enrichment process, requiring the emplacement and mobilization of rare earth element source material due to hydrothermal and other external influences. Historical geochemical evaluations of Uinta Region coal and coal-adjacent data are sparse, emphasizing the statistical significance of this research. These results support the utilization of active mines and coal processing waste piles for the future of domestic rare earth element extraction, offering economic and environmental solutions to pressing global demands.

Coe, Haley H.↗
NASA NTRS1976

The development of the Poincare-similar elements with eccentric anomaly as the independent variable

A new set of element differential equations for the perturbed two-body motion is derived. The elements are canonical and are similar to the classical canonical Poincare elements, which have time as the independent variable. The phase space is extended by introducing the total energy and time as canonically conjugated variables. The new independent variable is, to within an additive constant, the eccentric anomaly. These elements are compared to the Kustaanheimo-Stiefel (KS) element differential equations, which also have the eccentric anomaly as the independent variable. For several numerical examples, the accuracy and stability of the new set are equal to those of the KS solution. This comparable accuracy result can probably be attributed to the fact that both sets have the same time element and very similar energy elements. The new set has only 8 elements, compared to 10 elements for the KS set. Both sets are free from singularities due to vanishing eccentricity and inclination.

Bond, V. R.↗
NASA NTRS1988

Evidence for a single impact at the Cretaceous-Tertiary boundary from trace elements

Not only meteoritic elements (Ir, Ni, Au, Pt metals), but also some patently non-meteoritic elements (As, Sb) are enriched at the K-T boundary. Eight enriched elements at 7 K-T sites were compared and it was found that: All have fairly constant proportions to Ir and Kilauea (invoked as an example of a volcanic source of Ir by opponents of the impact theory) has too little of 7 of these 8 elements to account for the boundary enrichments. The distribution of trace elements at the K-T boundary was reexamined using data from 11 sites for which comprehensive are available. The meteoritic component can be assessed by first normalizing the data to Ir, the most obviously extraterrestrial element, and then to Cl chondrites. The double normalization reduces the concentration range from 11 decades to 5 and also facilitates the identification of meteoritic elements. At sites where trace elements were analyzed in sub-divided samples of boundary clay, namely, Caravaca (SP), Stevns Klint (DK), Flaxbourne River (NZ) and Woodside Creek (NZ), Sb, As and Zn are well correlated with Ir across the boundary implying a common deposition mechanism. Elemental carbon is also enriched by up to 10,000 x in boundary clay from 5 K-T sides and is correlated with Ir across the boundary at Woodside Creek. While biomass would appear to be the primary fuel source for this carbon a contribution from a fossil fuel source may be necessary in order to account for the observed C abundance.

Gilmour, Iain↗
NASA NTRS1990

Direct formulation of a 4-node hybrid shell element with rotational degrees of freedom

A simple 4-node assumed-stress hybrid quadrilateral shell element with rotational or 'drilling' degrees of freedom is formulated. The element formulation is based directly on a 4-node element rather than being derived from an 'internal' 8-node isoparametric element. The formulation is based on the principle of minimum complementary energy. The membrane part of the element has 12 degrees of freedom. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner-Mindlin plate theory which takes into account the transverse shear effects. Quadratic variations for both in-plane and out-of-plane displacement fields and linear variations for both in-plane and out-of-plane rotation fields are assumed along the edges of the element. The element passes the patch test, is nearly insensitive to mesh distortion, has no spurious modes, and is invariant with respect to node numbering.

Aminpour, Mohammad A.↗
NASA NTRS1990

Behaviour of plate elements based on the first-order shear deformation theory

A new analytical technique to assess the performance of shear deformable elements is presented, which makes it possible to determine a priori whether a given element will lock when used to model thin structures. The role that shear constraints play in determining the behavior of thin elements was established by comparing the results of key numerical tests with the predictions of element behavior made by studying the form of the shear constraints. Conclusions regarding locking behavior and the effects of reduced integration in thin shear deformable elements are presented, including the findings (1) that singularity of the shear stiffness matrix is not sufficient to avoid locking; (2) that the effect of mesh refinement on an element that contains spurious constraints is two-fold; and (3) that reduced integration does not remove spurious constraints but rather relaxes them. The results of the study are in agreement with previous studies of Mindlin plate elements in regarding Lagrangian elements as superior to serendipity elements when either full or reduced integration is employed.

Averill, R. C.↗
NASA NTRS1987

A new methodology for free wake analysis using curved vortex elements

A method using curved vortex elements was developed for helicopter rotor free wake calculations. The Basic Curve Vortex Element (BCVE) is derived from the approximate Biot-Savart integration for a parabolic arc filament. When used in conjunction with a scheme to fit the elements along a vortex filament contour, this method has a significant advantage in overall accuracy and efficiency when compared to the traditional straight-line element approach. A theoretical and numerical analysis shows that free wake flows involving close interactions between filaments should utilize curved vortex elements in order to guarantee a consistent level of accuracy. The curved element method was implemented into a forward flight free wake analysis, featuring an adaptive far wake model that utilizes free wake information to extend the vortex filaments beyond the free wake regions. The curved vortex element free wake, coupled with this far wake model, exhibited rapid convergence, even in regions where the free wake and far wake turns are interlaced. Sample calculations are presented for tip vortex motion at various advance ratios for single and multiple blade rotors. Cross-flow plots reveal that the overall downstream wake flow resembles a trailing vortex pair. A preliminary assessment shows that the rotor downwash field is insensitive to element size, even for relatively large curved elements.

Bliss, Donald B.↗
NASA NTRS1991

An algorithm for domain decomposition in finite element analysis

A simple and efficient algorithm is described for automatic decomposition of an arbitrary finite element domain into a specified number of subdomains for finite element and substructuring analysis in a multiprocessor computer environment. The algorithm is designed to balance the work loads, to minimize the communication among processors and to minimize the bandwidths of the resulting system of equations. Small- to large-scale finite element models, which have two-node elements (truss, beam element), three-node elements (triangular element) and four-node elements (quadrilateral element), are solved on the Convex computer to illustrate the effectiveness of the proposed algorithm. A FORTRAN computer program is also included.

Al-Nasra, M.↗
NASA NTRS1992

Hierarchical flux-based thermal-structural finite element analysis method

A hierarchical flux-based finite element method is developed for both a one and two dimensional thermal structural analyses. Derivation of the finite element equations is presented. The resulting finite element matrices associated with the flux based formulation are evaluated in a closed form. The hierarchical finite elements include additional degrees of freedom in the approximation of the element variable distributions by the use of nodeless variables. The nodeless variables offer increased solution accuracy without the need for defining actual nodes and rediscretizing the finite element model. Thermal and structural responses are obtained from a conventional linear finite element method and exact solutions. Results show that the hierarchical flux-based method can provide improved thermal and structural solution accuracy with fewer elements when compared to results for the conventional linear element method.

Polesky, Sandra P.↗
NASA NTRS1995

ANSYS duplicate finite-element checker routine

An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.

Ortega, R.↗
NASA NTRS1995

A unified multigrid solver for the Navier-Stokes equations on mixed element meshes

A unified multigrid solution technique is presented for solving the Euler and Reynolds-averaged Navier-Stokes equations on unstructured meshes using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms, and tetrahedra in three dimensions. While the use of mixed elements is by no means a novel idea, the contribution of the paper lies in the formulation of a complete solution technique which can handle structured grids, block structured grids, and unstructured grids of tetrahedra or mixed elements without any modification. This is achieved by discretizing the full Navier-Stokes equations on tetrahedral elements, and the thin layer version of these equations on other types of elements, while using a single edge-based data-structure to construct the discretization over all element types. An agglomeration multigrid algorithm, which naturally handles meshes of any types of elements, is employed to accelerate convergence. An automatic algorithm which reduces the complexity of a given triangular or tetrahedral mesh by merging candidate triangular or tetrahedral elements into quadrilateral or prismatic elements is also described. The gains in computational efficiency afforded by the use of non-simplicial meshes over fully tetrahedral meshes are demonstrated through several examples.

Mavriplis, D. J.↗