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All sources NASA NTRS DOE OSTI

DOE OSTI2022

Uncertainty Quantification for Dissimilar Material Joints Under Corrosion Environment

Abstract Self-Piercing Riveting (SPR) is one of the most commonly used methods for joining dissimilar materials in the automotive industry. These joints are popular due to their adaptability, high performance and short cycle time. However, since these joints involve two dissimilar materials, they are susceptible to galvanic corrosion in the presence of an electrolyte which is driven by the difference in the equilibrium potential of the metals. This can affect the safety and resilience of these joints. In this paper, we focus on galvanic corrosion in Al-Fe SPR joints. A Machine learning (ML) based surrogate model, which is based off of FE simulations, for statistical corrosion analysis is developed. This model enables the resilience and reliability analysis of SPR joints under corrosion environment. In this study, first a physics-based finite element (FE) corrosion model has been developed to simulate the galvanic corrosion between a Fe cathode and an Al anode of a SPR joint. This model takes into account the effect of the crystal microstructure of the Al anode and the precipitation of the corrosion product. Several geometric and environmental factors including crevice gap, roughness of anode, conductivity, pH and the temperature of the electrolyte that effect corrosion are investigated. A thorough Uncertainty Quantification (UQ) analysis is conducted for the overall corrosion behavior of the Fe-Al SPR joints using a novelistic Probabilistic Confidence-Based Adaptive Sampling (PCAS) technique. PCAS is used to train the surrogate model by identifying the critical sampling points and thus reducing the overall computational costs. It is found that the electrolyte temperature has the largest effects on the material loss and needs to be managed closely for better corrosion control. By understanding the corrosion performance and resultant uncertainty impact on SPR joints, the reliability and resilience of these joints can be improved.

36 MATERIALS SCIENCE↗

DOE OSTI2021

An HPC-Based Hydrothermal Finite Element Simulator for Modeling Underground Response to Community-Scale Geothermal Energy Production

Geothermal heat, as renewable energy, shows great advantage with respect to its environmental impact due to its significantly lower CO2 emissions than conventional fossil fuel. Open and closed-loop geothermal heat pumps, which utilize shallow geothermal systems, are an efficient technology for cooling and heating buildings, especially in urban areas. Integrated use of geothermal energy technologies for district heating, cooling, and thermal energy storage can be applied to optimize the subsurface for communities to provide them with multiple sustainable energy and community resilience benefits. The utilization of the subsurface resources may lead to a variation in the underground environment, which might further impact local environmental conditions. However, very few simulators can handle such a highly complex set of coupled computations on a regional or city scale. We have developed high-performance computing (HPC) based hydrothermal finite element (FE) simulator that can simulate the subsurface and its hydrothermal conditions at a scale of tens of km. The HPC simulator enables us to investigate the subsurface thermal and hydrologic response to the built underground environment (such as basements and subways) at the community scale. In this study, a coupled hydrothermal simulator is developed based on the open-source finite element library deal.II. The HPC simulator was validated by comparing the results of a benchmark case study against COMSOL Multiphysics, in which Aquifer Thermal Energy Storage (ATES) is modeled and a process of heat injection into ATES is simulated. The use of an energy pile system at the Treasure Island redevelopment site (San Francisco, CA, USA) was selected as a case study to demonstrate the HPC capability of the developed simulator. The simulator is capable of modeling multiple city-scale geothermal scenarios in a reasonable amount of time.

Sun, Xiang↗

NASA NTRSDate not supplied

Development of a C-ELS Specimen-Based Numerical Benchmark for Mode II Delamination and Assessment of Two VCCT-Based Propagation Strategies

A finite element (FE) benchmark example inspired by the calibrated end-loaded split (C-ELS) specimen is developed and used to assess the performance of delamination propagation capabilities based on linear elastic fracture mechanics (LEFM). The C-ELS specimen has the advantage of a longer region of stable delamination propagation compared to the existing mode II benchmark case. The new benchmark example may therefore provide a better assessment tool by enabling more stable crack growth in regions further away from the boundary conditions or load application. First, a benchmark result is created manually using two-dimensional finite element models of the C-ELS specimen with different delamination lengths. Second, the performance of the virtual crack closure technique (VCCT) delamination propagation capabilities in the Abaqus/Standard®1 FE code and the recently developed Progressive Release eXplicit-VCCT (PRX-VCCT) method are assessed by comparing the results to the benchmark case. Two examples with different starter delamination lengths are studied. A shorter starter length is chosen to create a scenario with unstable delamination propagation. A longer delamination encourages stable delamination propagation. Detailed results from three-dimensional analyses with aligned and misaligned meshes and two levels of mesh refinement are provided. In general, good agreement can be achieved between the results obtained from the quasi-static propagation analysis and the benchmark analysis. Numerical artifacts including anomalous unreleased nodes in the crack wake and zig-zag crack fronts occur for propagation analyses using Abaqus/Standard VCCT. In comparison, continuous, smooth, delamination fronts are observed for PRX-VCCT. The use of the benchmark case to assess different VCCT-based propagation strategies illustrates the value of establishing benchmark cases.

Composite Materials↗

NASA NTRS2005

Parallel Domain Decomposition Formulation and Software for Large-Scale Sparse Symmetrical/Unsymmetrical Aeroacoustic Applications

The overall objectives of this research work are to formulate and validate efficient parallel algorithms, and to efficiently design/implement computer software for solving large-scale acoustic problems, arised from the unified frameworks of the finite element procedures. The adopted parallel Finite Element (FE) Domain Decomposition (DD) procedures should fully take advantages of multiple processing capabilities offered by most modern high performance computing platforms for efficient parallel computation. To achieve this objective. the formulation needs to integrate efficient sparse (and dense) assembly techniques, hybrid (or mixed) direct and iterative equation solvers, proper pre-conditioned strategies, unrolling strategies, and effective processors' communicating schemes. Finally, the numerical performance of the developed parallel finite element procedures will be evaluated by solving series of structural, and acoustic (symmetrical and un-symmetrical) problems (in different computing platforms). Comparisons with existing "commercialized" and/or "public domain" software are also included, whenever possible.

Nguyen, D. T.↗

NASA NTRS1987

Power flow as a complement to statistical energy analysis and finite element analysis

Present methods of analysis of the structural response and the structure-borne transmission of vibrational energy use either finite element (FE) techniques or statistical energy analysis (SEA) methods. The FE methods are a very useful tool at low frequencies where the number of resonances involved in the analysis is rather small. On the other hand SEA methods can predict with acceptable accuracy the response and energy transmission between coupled structures at relatively high frequencies where the structural modal density is high and a statistical approach is the appropriate solution. In the mid-frequency range, a relatively large number of resonances exist which make finite element method too costly. On the other hand SEA methods can only predict an average level form. In this mid-frequency range a possible alternative is to use power flow techniques, where the input and flow of vibrational energy to excited and coupled structural components can be expressed in terms of input and transfer mobilities. This power flow technique can be extended from low to high frequencies and this can be integrated with established FE models at low frequencies and SEA models at high frequencies to form a verification of the method. This method of structural analysis using power flo and mobility methods, and its integration with SEA and FE analysis is applied to the case of two thin beams joined together at right angles.

Cuschieri, J. M.↗

DOE OSTI2022

Physics-informed machine learning assisted uncertainty quantification for the corrosion of dissimilar material joints

Jointing techniques like the Self-Piercing Riveting (SPR), Resistance Spot Welding (RSW) and Rivet-Weld (RW) joints are used for mass production of dissimilar material joints due to their high performance, short cycle time, and adaptability. However, the service life and safety usage of these joints can be largely impacted by the galvanic corrosion due to the difference in equilibrium potentials between the metals with the presence of electrolyte. Here, in this paper, we focus on Al-Fe galvanic corrosion and develop physics-informed machine learning based surrogate model for statistical corrosion analysis, which enables the reliability analysis of dissimilar material joints under corrosion environment. In this study, a physics-based finite element (FE) corrosion model has been developed to simulate the galvanic corrosion between a Fe cathode and an Al anode. Geometric and environmental factors including crevice gap, roughness of anode, conductivity, and the temperature of the electrolyte are investigated. Further, a thorough Uncertainty Quantification (UQ) analysis is conducted for the overall corrosion behavior of the Fe-Al joints. It is found that the electrolyte conductivity has the largest effects on the material loss and needs to be managed closely for better corrosion control. This will help in designing and manufacturing joints with improved corrosion performance.

42 ENGINEERING↗

NASA NTRS2019

Automatic Incorporation of Flaws into Cad and FEA Models Based On Measured NDE Data

Automatic incorporation of non-destructive evaluation (NDE) data into CAD and finite element (FE) models for structural analysis is essential for accurate residual-life and strength analyses of composite structures. Currently, two significant but independent challenges exist for incorporating NDE data in such analyses: interpretation of the NDE signals to locate and characterize the structural defects and the incorporation of that information into structural analysis tools. The first challenge will be addressed through linear inversion of calculated synthetic responses generated by a simulation engine to evaluate flaw size, location, and other characteristics. The second challenge will be addressed by building on prior and parallel defect modeling efforts to integrate suitable flaw models into the CAD/finite-element representation of a specimen. Ultrasonic NDE information is usually represented using C-Scans of time-of-flight or intensity information. Other modalities such as thermography and computed tomography (CT) could also be used to characterize the structure. This information will first be projected into material coordinates and then aligned with the specimen’s finite element mesh. The NDE data can then be incorporated by inserting flaw geometry into the CAD and FE analysis model and automatic modification of local material properties and boundary conditions. This process will enable the use of structural analysis tools even for practical modalities such as ultrasound and thermography which may not directly give accurate-enough geometric information to fully define the flaw. The full flaw characteristics will be inferred using prior expert and modeling knowledge to categorize flaw signatures. Outputs for this project will include demonstrated methods for creating structural analysis geometric models that incorporate flaw characterization information; these models can then be used directly in popular commercial FEA software. In addition, the primary deliverable for the project will include a software that will be able to automatically incorporate different kinds of flaws into an existing FE models. The models will be generated in standard file formats to enable direct import into the analysis software.

Adarsh Krishnamurthy↗

NASA NTRS1996

A General Interface Method for Aeroelastic Analysis of Aircraft

The aeroelastic analysis of an aircraft requires an accurate and efficient procedure to couple aerodynamics and structures. The procedure needs an interface method to bridge the gap between the aerodynamic and structural models in order to transform loads and displacements. Such an interface method is described in this report. This interface method transforms loads computed by any aerodynamic code to a structural finite element (FE) model and converts the displacements from the FE model to the aerodynamic model. The approach is based on FE technology in which virtual work is employed to transform the aerodynamic pressures into FE nodal forces. The displacements at the FE nodes are then converted back to aerodynamic grid points on the aircraft surface through the reciprocal theorem in structural engineering. The method allows both high and crude fidelities of both models and does not require an intermediate modeling. In addition, the method performs the conversion of loads and displacements directly between individual aerodynamic grid point and its corresponding structural finite element and, hence, is very efficient for large aircraft models. This report also describes the application of this aero-structure interface method to a simple wing and an MD-90 wing. The results show that the aeroelastic effect is very important. For the simple wing, both linear and nonlinear approaches are used. In the linear approach, the deformation of the structural model is considered small, and the loads from the deformed aerodynamic model are applied to the original geometry of the structure. In the nonlinear approach, the geometry of the structure and its stiffness matrix are updated in every iteration and the increments of loads from the previous iteration are applied to the new structural geometry in order to compute the displacement increments. Additional studies to apply the aero-structure interaction procedure to more complicated geometry will be conducted in the second phase of the present contract.

Tzong, T.↗

DOE OSTI2022

Damage of prismatic lithium‐ion cells subject to bending: Test, model, and detection

Abstract The mechanically induced internal short circuit (ISC) is one of the major safety concerns of lithium‐ion batteries. Mechanical abuse tests are often performed to evaluate the integrity and safety of lithium‐ion batteries under mechanical loadings. Except for the widely explored compression‐dominated indentation tests, bending is another typical real‐world loading condition that is tension‐dominated. To investigate the mechanical damage and ISC behavior of batteries under bending, we carried out controlled three‐point bending tests in four progressive steps on prismatic battery cells with maximum deflections ranging from 38% to 76% of the cell thickness. None of the tested cells experienced an ISC. We then conducted 3D X‐ray computed tomography (CT) scanning on the bent cells after unloading. X‐ray CT images showed three out of the four tested cells have extensive cracking in the electrode layers at the bottom side (opposite to the loading head). This indicates that cracking does not necessarily lead to an ISC under bending. Electrochemical impedance spectroscopy was also measured on the bent cells and substantial changes were observed. Both the bulk resistance and charge‐transfer resistance increased significantly after bending, which could influence the battery performance and lifespan. We then developed a detailed finite (FE) element model to further investigate the mechanical deformation and failure mechanisms. The FE model successfully predicts the load–displacement response and reproduces the deformation patterns. The findings and the FE model developed in the present study provide useful insights and tools for the battery structure and crash safety design. image

25 ENERGY STORAGE↗

NASA NTRS2001

Fatigue and Damage Tolerance Analysis of a Hybrid Composite Tapered Flexbeam

The behavior of nonlinear tapered composite flexbeams under combined axial tension and cyclic bending loading was studied using coupon test specimens and finite element (FE) analyses. The flexbeams used a hybrid material system of graphite/epoxy and glass/epoxy and had internal dropped plies, dropped in an overlapping stepwise pattern. Two material configurations, differing only in the use of glass or graphite plies in the continuous plies near the midplane, were studied. Test specimens were cut from a full-size helicopter tail-rotor flexbeam and were tested in a hydraulic load frame under combined constant axialtension load and transverse cyclic bending loads. The first determination damage observed in the specimens occurred at the area around the tip of the outermost ply-drop group in the tapered region of the flexbeam, near the thick end. Delaminations grew slowly and stably, toward the thick end of the flexbeam, at the interfaces above and below the dropped-ply region. A 2D finite element model of the flexbeam was developed. The model was analyzed using a geometrically non-linear analysis with both the ANSYS and ABAQUS FE codes. The global responses of each analysis agreed well with the test results. The ANSYS model was used to calculate strain energy release rates (G) for delaminations initiating at two different ply-ending locations. The results showed that delaminations were more inclined to grow at the locations where they were observed in the test specimens. Both ANSYS and ABAQUS were used to calculate G values associated with delamination initiating at the observed location but growing in different interfaces, either above or below the ply-ending group toward the thick end, or toward the thin end from the tip of the resin pocket. The different analysis codes generated the same trends and comparable peak values, within 5-11 % for each delamination path. Both codes showed that delamination toward the thick region was largely mode II, and toward the thin region was predominantly mode I. The calculated peak G-values from either analysis predict delamination is most likely to occur along the same interface where it was observed in the test specimens. Calculated peak G values were used with material characterization data to calculate a curve relating the fatigue life of the specimens, N, to the applied transverse load, V, for a given constant axial load.

Murri, Gretchen B.↗

DOE OSTI2026

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⁢(1⁢0 2 −1⁢0 3 )⁢s −1 ) and larger overpressure magnitudes (𝒪⁡(1⁢0 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⁡(1⁢0 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⁢(1⁢0 2 −1⁢0 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.

42 ENGINEERING↗

NASA NTRS2017

Constitutive Modeling of the Facesheet to Core Interface in Honeycomb Sandwich Panels Subject to Mode I Delamination

A new cohesive zone traction-separation law, which includes the effects of fiber bridging, has been developed, implemented with a finite element (FE) model, and applied to simulate the delamination between the facesheet and core of a composite honeycomb sandwich panel. The proposed traction-separation law includes a standard initial cohesive component, which accounts for the initial interfacial stiffness and energy release rate, along with a new component to account for the fiber bridging contribution to the delamination process. Single cantilever beam tests on aluminum honeycomb sandwich panels with carbon fiber reinforced polymer facesheets were used to characterize and evaluate the new formulation and its finite element implementation. These tests, designed to evaluate the mode I toughness of the facesheet to core interface, exhibited significant fiber bridging and large crack process zones, giving rise to a concave downward concave upward pre-peak shape in the load-displacement curve. Unlike standard cohesive formulations, the proposed formulation captures this observed shape, and its results have been shown to be in excellent quantitative agreement with experimental load-displacement and apparent critical energy release rate results, representative of a payload fairing structure, as well as local strain fields measured with digital image correlation.

composites↗

NASA NTRS1997

Fatigue Life Methodology for Tapered Composite Flexbeam Laminates

The viability of a method for determining the fatigue life of composite rotor hub flexbeam laminates using delamination fatigue characterization data and a geometric non-linear finite element (FE) analysis was studied. Combined tension and bending loading was applied to non-linear tapered flexbeam laminates with internal ply drops. These laminates, consisting of coupon specimens cut from a full-size S2/E7T1 glass-epoxy flexbeam were tested in a hydraulic load frame under combined axial-tension and transverse cyclic bending. The magnitude of the axial load remained constant and the direction of the load rotated with the specimen as the cyclic bending load was applied. The first delamination damage observed in the specimens occurred at the area around the tip of the outermost ply-drop group. Subsequently, unstable delamination occurred by complete delamination along the length of the specimen. Continued cycling resulted in multiple delaminations. A 2D finite element model of the flexbeam was developed and a geometrically non-linear analysis was performed. The global responses of the model and test specimens agreed very well in terms of the transverse displacement. The FE model was used to calculate strain energy release rates (G) for delaminations initiating at the tip of the outer ply-drop area and growing toward the thick or thin regions of the flexbeam, as was observed in the specimens. The delamination growth toward the thick region was primarily mode 2, whereas delamination growth toward the thin region was almost completely mode 1. Material characterization data from cyclic double-cantilevered beam tests was used with the peak calculated G values to generate a curve predicting fatigue failure by unstable delamination as a function of the number of loading cycles. The calculated fatigue lives compared well with the test data.

Murri, Gretchen B.↗

DOE OSTI2022

Mesh objective stochastic simulations of quasibrittle fracture

Continuum finite element (FE) modeling of damage and failure of quasibrittle structures suffers from the spurious mesh sensitivity due to strain localization. Here this issue has been addressed for deterministic analysis through the development of localization limiters. Here this study proposes a mechanism-based model to mitigate the mesh sensitivity in stochastic FE simulations of quasibrittle fracture. The interest is placed on the analysis of large-size structures, where the mesh size is conveniently chosen to be larger than the width of the fracture process zone as well as the correlation length of the random fields of constitutive properties. The present model is formulated within the framework of continuum damage mechanics. Two localization parameters are introduced to describe the evolution of the damage pattern of each finite element. These parameters are used to guide the energy regularization of the constitutive law, as well as to formulate the mesh-dependent probability distributions of constitutive properties. Depending on the prevailing damage pattern, different energy regularization schemes and mesh dependence of the probability distribution functions are used in the constitutive law. The model is applied to simulate the stochastic failure behavior of quasibrittle structures of different geometries featuring different failure processes including damage initiation, localization, and propagation. It is shown that using fixed probability distribution functions of constitutive properties could lead to strong mesh dependence of the prediction of the mean and variance of the structural load capacity. The probability distribution functions of constitutive properties must be linked to the damage pattern, which may evolve during the failure process. Such a mechanism-based modeling of the probability distributions of constitutive properties is essential for mitigating the spurious mesh sensitivity in stochastic FE analysis of quasibrittle fracture.

42 ENGINEERING↗

NASA NTRS1997

Fatigue Life Methodology for Tapered Composite Flexbeam Laminates

The viability of a method for determining the fatigue life of composite rotor hub flexbeam laminates using delamination fatigue characterization data and a geometric non-linear finite element (FE) analysis was studied. Combined tension and bending loading was applied to nonlinear tapered flexbeam laminates with internal ply drops. These laminates, consisting of coupon specimens cut from a full-size S2/E7T1 glass-epoxy flexbeam were tested in a hydraulic load frame under combined axial-tension and transverse cyclic bending loads. The magnitude of the axial load remained constant and the direction of the load rotated with the specimen as the cyclic bending load was applied. The first delamination damage observed in the specimens occurred at the area around the tip of the outermost ply-drop group. Subsequently, unstable delamination occurred by complete delamination along the length of the specimen. Continued cycling resulted in multiple delaminations. A 2D finite element model of the flexbeam was developed and a geometrically non-linear analysis was performed. The global responses of the model and test specimens agreed very well in terms of the transverse flexbeam tip-displacement and flapping angle. The FE model was used to calculate strain energy release rates (G) for delaminations initiating at the tip of the outer ply-drop area and growing toward the thick or thin regions of the flexbeam, as was observed in the specimens. The delamination growth toward the thick region was primarily mode 2, whereas delamination growth toward the thin region was almost completely mode 1. Material characterization data from cyclic double-cantilevered beam tests was used with the peak calculated G values to generate a curve predicting fatigue failure by unstable delamination as a function of the number of loading cycles. The calculated fatigue lives compared well with the test data.

Murri, Gretchen B.↗

NASA NTRS2017

Integrated Model of the Eye/Optic Nerve Head Biomechanical Environment

Visual Impairment and Intracranial Pressure (VIIP) syndrome is a concern for long-duration space flight. Previously, it has been suggested that ocular changes observed in VIIP syndrome are related to the cephalad fluid shift that results in altered fluid pressures [1]. We are investigating the impact of changes in intracranial pressure (ICP) using a combination of numerical models, which simulate the effects of various environment conditions, including finite element (FE) models of the posterior eye. The specific interest is to understand how altered pressures due to gravitational changes affect the biomechanical environment of tissues of the posterior eye and optic nerve sheath. METHODS: Additional description of the numerical modeling is provided in the IWS abstract by Nelson et al. In brief, to simulate the effects of a cephalad fluid shift on the cardiovascular and ocular systems, we utilized a lumped-parameter compartment model of these systems. The outputs of this lumped-parameter model then inform boundary conditions (pressures) for a finite element model of the optic nerve head (Figure 1). As an example, we show here a simulation of postural change from supine to 15 degree head-down tilt (HDT), with primary outcomes being the predicted change in strains at the optic nerve head (ONH) region, specifically in the lamina cribrosa (LC), retrolaminar optic nerve, and prelaminar neural tissue (PLNT). The strain field can be decomposed into three orthogonal components, denoted as the first, second and third principal strains. We compare the peak tensile (first principal) and compressive (third principal) strains, since elevated strain alters cell phenotype and induces tissue remodeling. RESULTS AND CONCLUSIONS: Our lumped-parameter model predicted an IOP increase of c. 7 mmHg after 21 minutes of 15 degree HDT, which agreed with previous reports of IOP in HDT [1]. The corresponding FEM simulations predicted a relative increase in the magnitudes of the peak tensile and compressive strains in the lamina cribrosa of 42 and 43, respectively (Fig. 2). The corresponding changes in the optic nerve strains were 17 and 39, while in the PLNT they were 47 and 43. These magnitudes of relative elevations in peak strains may induce a phenotypic response in resident mechano-responsive resident cells [2]. This approach may be expanded to investigate other environmental changes (e.g. parabolic flight). Through our VIIP SCHOLAR project, we will validate and improve these integrated models by measuring patient-specific changes in optic nerve sheath geometry in patients with idiopathic intracranial hypertension before and after lumbar puncture and CSF removal.

biomechanics↗

NASA NTRS1994

Superconducting axisymmetric finite elements based on a gauged potential variational principle. Part 1: Formulation

The present work is part of a research program for the numerical simulation of electromagnetic (EM) fields within conventional Ginzburg-Landau (GL) superconductors. The final goal of this research is to formulate, develop and validate finite element (FE) models that can accurately capture electromagnetic thermal and material phase changes in a superconductor. The formulations presented here are for a time-independent Ginzburg-Landau superconductor and are derived from a potential-based variational principle. We develop an appropriate variational formulation of time-independent supercontivity for the general three-dimensional case and specialize it to the one-dimensional case. Also developed are expressions for the material-dependent parameters alpha and beta of GL theory and their dependence upon the temperature T. The one-dimensional formulation is then discretized for finite element purposes and the first variation of these equations is obtained. The resultant Euler equations contain nonlinear terms in the primary variables. To solve these equations, an incremental-iterative solution method is used. Expressions for the internal force vector, external force vector, loading vector and tangent stiffness matrix are therefore developed for use with the solution procedure.

Schuler, James J.↗

DOE OSTI2020

Influence of crystal structure on constitutive anisotropy of silica sand at particle-scale

In spite of recent advanced geotechnical research regarding the influence of particle-scale morphology and fabric on the constitutive behavior of silica sands, there is still no published literature that investigated the influence of crystal structure of sand particles on their constitutive behavior. The main constituent of silica sand particles is quartz mineral, which has a trigonal crystal system and hexagonal lattice. This paper investigates the influence of quartz crystal structure on the constitutive response of silica sand particles using 3D X-ray diffraction (3DXRD), synchrotron micro-computed tomography (SMT), and 3D finite element (FE) analysis. Here, unconfined uniaxial compression experiments on single particles of synthetic silica cubes exposed the notion of constitutive anisotropy caused by the crystal structure of quartz. Since the silica cubes have simple regular geometry (1 mm) 3 , they were loaded in different directions with respect to their crystal local planes. The crystal structure was also identified for a natural silica sand specimen composed of 2705 particles and loaded in confined uniaxial compression. Physical limitations of the experimental measurements made a strong case for the use of 3D FE analysis to study how the change in crystal local orientation of individual sand particles can fundamentally produce anisotropy in the constitutive response of natural sand specimens. The 3D FE analysis was validated to accurately model the crystal-based constitutive anisotropy in silica particles using the results of the silica cube experiments. The analysis was then executed on 3D FE meshes that closely matched the physical shape and fabric of the 2705 particles in the natural sand specimen. Both the experiments and 3D FE analysis showed that the crystal structure of quartz essentially causes a directional anisotropy in the constitutive behavior of silica particles.

58 GEOSCIENCES↗