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

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At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A Mixed Discontinuous Galerkin Method for Linear Elasticity with Strongly Imposed Symmetry

In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in d -dimension ( \(d=2,3\) ). This method uses polynomials of degree \(k+1\) for the stress and of degree k for the displacement ( \(k\ge 0\) ). The mixed DG scheme is proved to be well-posed under proper norms. Specifically, we prove that, for any \(k \ge 0\) , the \(H(\mathrm{div})\) -like error estimate for the stress and \(L^2\) error estimate for the displacement are optimal. We further establish the optimal \(L^2\) error estimate for the stress provided that the \({\mathcal {P}}_{k+2}-{\mathcal {P}}_{k+1}^{-1}\) Stokes pair is stable and \(k \ge d\) . Finally, we also provide numerical results of MDG showing that the orders of convergence are actually sharp.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Direct sensitivity analysis on the parameterization of crystal plasticity models

Various methods for calibrating crystal plasticity finite element (CPFE) models lead to non-unique input parameter values, which subsequently introduce uncertainty in the predicted mechanical response. Sensitivity analysis (SA) conducted on crystal plasticity models is used to identify how variability in these parameters contribute to output uncertainty. Traditional SA on CPFE parameters uses simplified surrogate models to save computational time. However, the accuracy of the surrogate models depends on the quantity of training data used, and any modeling error can propagate into the SA results, potentially affecting their reliability. In this work, the elementary effects test (EET) method, a global SA technique using direct CPFE simulations was employed, and the results obtained were compared with the First Order Second Moment (FOSM) method. ExaConstit, an open-source GPU-enabled CPFE code, was used to perform the simulations and direct SA. The EET method was accurately able to capture the non-linear effects of all the input parameters on the output and is a valuable approach for reliably attributing parameter sensitivities in CPFE models. Based on the results, efficient strategies to perform future parameter calibration and SA are discussed. Additionally, the SA trends observed in different single crystal orientations closely mirrored the activity of the slip systems.

Elementary Effects Test↗
DOE OSTI2022

Reciprocal swimming at intermediate Reynolds number

In Stokes flow, Purcell's scallop theorem forbids objects with time-reversible (reciprocal) swimming strokes from moving. In the presence of inertia, this restriction is eased and reciprocally deforming bodies can swim. A number of recent works have investigated dimer models that swim reciprocally at intermediate Reynolds numbers Re≈1–1000. These show interesting results (e.g. switches of the swim direction as a function of inertia) but the results vary and seem to be case specific. Here, in this work, we introduce a general model and investigate the behaviour of an asymmetric spherical dimer of oscillating length for small-amplitude motion at intermediate Re. In our analysis we make the important distinction between particle and fluid inertia, both of which need to be considered separately. We asymptotically expand the Navier–Stokes equations in the small-amplitude limit to obtain a system of linear partial differential equations. Using a combination of numerical (finite element) and analytical (reciprocal theorem, method of reflections) methods we solve the system to obtain the dimer's swim speed and show that there are two mechanisms that give rise to motion: boundary conditions (an effective slip velocity) and Reynolds stresses. Each mechanism is driven by two classes of sphere–sphere interactions, between one sphere's motion and (1) the oscillating background flow induced by the other's motion, and (2) a geometric asymmetry induced by the other's presence. We can thus unify and explain behaviours observed in other works. Our results show how sensitive, counterintuitive and rich motility is in the parameter space of finite inertia of particles and fluid.

42 ENGINEERING↗
DOE OSTI2021

A crystal plasticity finite element model embedding strain-rate sensitivities inherent to deformation mechanisms: Application to alloy AZ31

We report the fundamental power-law relationship representing the flow rule in crystal visco-plasticity ensures uniqueness in the selection of slip systems accommodating imposed plastic strain-rates. The power-law relationship also introduces an artificially high strain-rate sensitivity in crystal plasticity simulations, unless a high value of the power-law exponent is used. However, the use of high values for the exponent is limited by numerical tractability. This paper presents a numerical method implemented in a crystal plasticity finite element (CPFE) model for embedding any value of the power-law exponent reflecting the true material strain-rate sensitivity. Importantly, the method does not increase computation time involved in the simulations. The enhanced CPFE model is used to interpret and predict a complex strain-rate sensitive response and microstructural evolution of AZ31 Mg alloy. Measured values of strain-rate sensitivity for slip and twinning modes are used in the simulations. Calculations show that the model successfully captures the phenomena pertaining to the effect of changing applied strain-rate on the mechanical response including flow stress and evolution of texture and twinning for a broad range of strain-rates ranging from 10 -3 s -1 to 10 3 s -1 and loading orientations in tension and compression. It is shown that such predictions are a consequence of not only relative amounts of slip and twinning activities driven by a set of accurately characterized hardening law parameters but also values of the strain-rate sensitivities inherent to individual deformation mechanisms. Besides, the model validates the measured strain-rate dependency of deformation mechanisms while accurately reproducing the mechanical data. Hence, the model can be used to verify and further refine or infer measured strain-rate sensitivity per deformation mechanism by reproducing experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Heat transfer optimization of uo 2 -mo fuel using genetic algorithms

Two genetic algorithm (GA) methods were applied to thermal finite element models to optimize the heat transfer efficacy of a UO 2 -Mo composite fuel pellet with typical pressurized water reactor fuel geometry. Mo additions to UO 2 have been shown to increase the thermal conductivity, thus reducing centerline temperatures and temperature gradients. Previous studies evaluated uniformly dispersed Mo or continuous Mo internal geometries (e.g., fins, plates, discs) that were selected using engineering intuition. The current study uses two different implementations of the same GA to optimize Mo placement and minimize the fuel temperature with the only constraint being a maximum 10% Mo volume fraction. One approach superimposed Mo line elements onto the monolithic UO 2 pellet model, and the other converted entire UO 2 volume elements to Mo. The former method generated 1D heat transfer connections between nodes, whereas the latter method allowed for the formation of 3D structures. Features of the optimal fuel design produced by the GAs included dispersed Mo near the centerline that shifted the peak fuel temperature outward by 0.6 mm, Mo chains in the high-heat-flux region in the mid-to-outer radial zone, and a large continuous structure that spanned the full radius and height of the pellet and accounted for 87.7 % of the total Mo in the pellet. Analysis of this design indicates that the optimal Mo configuration is a balance between creating continuous heat transfer pathways and optimally dispersing Mo to minimize the heat transfer distance through UO 2 . This architecture ultimately produced an effective thermal conductivity of 11.3 W/m·K under the assumed boundary conditions. This result is higher than any previous values from the literature. In conclusion, potential fabrication methods and challenges are discussed in addition to the implications on fuel performance.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements

Within finite element models of fluids, vector-valued fields such as velocity or momentum variables are commonly discretised using the Raviart-Thomas elements. However, when using the lowest-order quadrilateral Raviart-Thomas elements, standard finite element discretisations of the vector transport equation typically have a low order of spatial accuracy. This paper describes two schemes that improve the accuracy of transporting such vector-valued fields on two-dimensional curved manifolds. The first scheme that is presented reconstructs the transported field in a higher-order function space, where the transport equation is then solved. The second scheme applies a mixed finite element formulation to the vector transport equation, simultaneously solving for the transported field and its vorticity. In this work, an approach to stabilising this mixed vector-vorticity formulation is presented that uses a Streamline Upwind Petrov-Galerkin (SUPG) method. These schemes are then demonstrated, along with their accuracy properties, through some numerical tests. Two new test cases are used to assess the transport of vector-valued fields on curved manifolds, solving the vector transport equation in isolation. The improvement of the schemes is also shown through two standard test cases for rotating shallow-water models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

In the last 50 years there has been a tremendous progress in solving numerically the Navier-Stokes equations using finite differences, finite elements, spectral, and even meshless methods. Yet, in many real cases, we still cannot incorporate seamlessly (multi-fidelity) data into existing algorithms, and for industrial-complexity applications the mesh generation is time consuming and still an art. Moreover, solving ill-posed problems (e.g., lacking boundary conditions) or inverse problems is often prohibitively expensive and requires different formulations and new computer codes. Here, we employ physics-informed neural networks (PINNs), encoding the governing equations directly into the deep neural network via automatic differentiation, to overcome some of the aforementioned limitations for simulating incompressible laminar and turbulent flows. We develop the Navier-Stokes flow nets (NSFnets) by considering two different mathematical formulations of the Navier-Stokes equations: the velocity-pressure (VP) formulation and the vorticity-velocity (VV) formulation. Since this is a new approach, we first select some standard benchmark problems to assess the accuracy, convergence rate, computational cost and flexibility of NSFnets; analytical solutions and direct numerical simulation (DNS) databases provide proper initial and boundary conditions for the NSFnet simulations. The spatial and temporal coordinates are the inputs of the NSFnets, while the instantaneous velocity and pressure fields are the outputs for the VP-NSFnet, and the instantaneous velocity and vorticity fields are the outputs for the VV-NSFnet. This is unsupervised learning and, hence, no labeled data are required beyond boundary and initial conditions and the fluid properties. The residuals of the VP or VV governing equations, together with the initial and boundary conditions, are embedded into the loss function of the NSFnets. No data is provided for the pressure to the VP-NSFnet, which is a hidden state and is obtained via the incompressibility constraint without extra computational cost. Unlike the traditional numerical methods, NSFnets inherit the properties of neural networks (NNs), hence the total error is composed of the approximation, the optimization, and the generalization errors. Here, we empirically attempt to quantify these errors by varying the sampling (“residual”) points, the iterative solvers, and the size of the NN architecture. For the laminar flow solutions, we show that both the VP and the VV formulations are comparable in accuracy but their best performance corresponds to different NN architectures. The initial convergence rate is fast but the error eventually saturates to a plateau due to the dominance of the optimization error. For the turbulent channel flow, we show that NSFnets can sustain turbulence at , but due to expensive training we only consider part of the channel domain and enforce velocity boundary conditions on the subdomain boundaries provided by the DNS data base. We also perform a systematic study on the weights used in the loss function for balancing the data and physics components, and investigate a new way of computing the weights dynamically to accelerate training and enhance accuracy. In the last part, we demonstrate how NSFnets should be used in practice, namely for ill-posed problems with incomplete or noisy boundary conditions as well as for inverse problems. We obtain reasonably accurate solutions for such cases as well without the need to change the NSFnets and at the same computational cost as in the forward well-posed problems. As a result, we also present a simple example of transfer learning that will aid in accelerating the training of NSFnets for different parameter settings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Bridging Scales in Bioenergy and Catalysis: A Review of Mesoscale Modeling Applications, Methods, and Future Directions

Between the molecular and reactor scales, which are familiar to the chemical engineering community, lies an intermediate regime, here termed the “mesoscale,” where transport phenomena and reaction kinetics compete on similar time scales. Bioenergy and catalytic processes offer particularly important examples of mesoscale phenomena owing to their multiphase nature and the complex, highly variable porosity characteristic of biomass and many structured catalysts. In this review, we overview applications and methods central to mesoscale modeling as they apply to reaction engineering of biomass conversion and catalytic processing. A brief historical perspective is offered to put recent advances in context. Applications of mesoscale modeling are described, and several specific examples from biomass pyrolysis and catalytic upgrading of bioderived intermediates are highlighted. Methods including reduced order modeling, finite element and finite volume approaches, geometry construction and import, and visualization of simulation results are described; in each category, recent advances, current limitations, and areas for future development are presented. Owing to improved access to high-performance computational resources, advances in algorithm development, and sustained interest in reaction engineering to sustainably meet societal needs, we conclude that a significant upsurge in mesoscale modeling capabilities is on the horizon that will accelerate design, deployment, and optimization of new bioenergy and catalytic technologies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

An Analytical Solution for the Initiation and Early Progression of Fretting Wear in Spherical Contacts

Abstract This article derives analytical solutions to calculate the wear volume at the initiation of fretting motion and its early progression over the first few oscillation cycles. The Archard-based model considers a deformable hemisphere that is contact with a deformable flat block. The material pairs investigated are special alloys, the Inconel 617/Incoloy 800H, and Inconel 617/Inconel 617. The analytical study begins with a unidirectional frictional sliding contact, where the local interfacial sliding distance and the nominal sliding distance at the initiation of gross slip are derived. The obtained analytical expressions for unidirectional sliding are then used to derive the corresponding wear volume for the initiation and early progression of gross slip and the wear volume for a general fretting cycle under elastic conditions. These analytical derivations are all verified by the finite element analysis (FEA). The FEA method and the analytical solutions render virtually identical results for both similar and dissimilar material pairs. The effects of plasticity on the wear volume under elastic–plastic conditions are also investigated. It is found that the fretting wear volumes obtained from the FEA simulations, which include plasticity, are close to those obtained from the analytical expressions for purely elastic regimes. All the results are presented in normalized forms, which can be easily generalized and applied to three-dimensional fretting wear of other material pairs.

Engineering↗
DOE OSTI2025

Modeling Electrodeposition in 3D Porous Architectures for Solid-State Li-Metal Batteries

Li-metal storage in three-dimensional (3D) electrodes is considered a potential dendrite-mitigation strategy. The large surface area and high porosity of these electrodes result in reduced local Li-plating current densities. The porous topology provides a scaffold for Li-deposition and stripping, maintaining both mechanical integrity and Li accessibility. The goal of this study is to understand how characteristics, such as geometry and material properties, affect the current distribution and deposition pattern. To this end, we developed a computational method to track material growth driven by electrodeposition within a complex geometry. This method ensures that the finite-element discretization remains conforming to the moving boundary while preserving an adequate mesh quality, and thus maintains solution accuracy. Using this new computational tool, we analyze the conditions under which porous anode architectures effectively expand the surface area of the charge-transfer interface, and self-regulate current density and dendrite growth.

3D electrode architectures↗
DOE OSTI2021

On the computational solution of vector-density based continuum dislocation dynamics models: A comparison of two plastic distortion and stress update algorithms

Continuum dislocation dynamics models of mesoscale plasticity consist of dislocation transport-reaction equations coupled with crystal mechanics equations. The coupling between these two sets of equations is such that dislocation transport gives rise to the evolution of plastic distortion (strain), while the evolution of the latter fixes the stress from which the dislocation velocity field is found via a mobility law. Earlier solutions of these equations employed a staggered solution scheme for the two sets of equations in which the plastic distortion was updated via time integration of its rate, as found from Orowan's law. In this work, we show that such a direct time integration scheme can suffer from accumulation of numerical errors. We introduce an alternative scheme based on field dislocation mechanics that ensures consistency between the plastic distortion and the dislocation content in the crystal. The new scheme is based on calculating the compatible and incompatible parts of the plastic distortion separately, and the incompatible part is calculated from the current dislocation density field. Stress field and dislocation transport calculations were implemented within a finite element based discretization of the governing equations, with the crystal mechanics part solved by a conventional Galerkin method and the dislocation transport equations by the least squares method. A simple test was first performed to show the accuracy of the two schemes for updating the plastic distortion, which shows that the solution method based on field dislocation mechanics is more accurate. This method then was used to simulate an austenitic steel crystal under uniaxial loading and multiple slip conditions. By considering dislocation interactions caused by junctions, a hardening rate similar to discrete dislocation dynamics simulation results was obtained. Finally, the simulations show that dislocations exhibit some self-organized structures as the strain is increased.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Analytical integration of the tractions induced by non-singular dislocations on an arbitrary shaped triangular quadratic element

Here, an analytical model is proposed to evaluate the nodal force induced by a segment of dislocation upon an arbitrary shaped triangular element. This calculation is required in hybrid methods that associate dislocation dynamics to boundary or finite element to solve simultaneously the evolution of large ensembles of dislocations with complex boundary conditions. Nodal forces are defined as the triple integration of the unbalanced traction field induced by a straight dislocation upon the surface of the element. Following our previous approach (Queyreau et al 2014 Modelling Simul. Mater. Sci. Eng. 22 035004) on a simpler geometry and in the case of linear isotropic elasticity, triple integrals are solved by sequences of integration by parts that exhibit recurrence relations. The traction field is defined and finite everywhere even at the core of dislocations, thanks to the use of the non-singular stress expression formulated by Cai et al (2006 J. Mech. Phys. Solids 54 561–587). The nodal force expressions can be used when considering both a single convolution or double convolution of the Green's function with the core distribution. A solution is also proposed for the case of a semi-infinite segment through the study of the asymptotic behavior of the analytical expressions. The proposed approach is exact and very computationally efficient. The choice of an arbitrary shaped triangular element and quadratic shape functions allow the consideration of complex geometries and comply with automatic meshing procedures. These analytical expressions could also be employed to estimate dislocation interactions with interfaces.

42 ENGINEERING↗
DOE OSTI2022

Comparison of three state-of-the-art crystal plasticity based deformation twinning models for magnesium alloys

In magnesium alloys, deformation twinning and its interactions with dislocation slip are responsible for a sigmoidal shape stress–strain behavior and an asymmetrical tension–compression yield strength in magnesium alloys. The sensitivity of twinning to the underlying microstructure renders the crystal plasticity method the most commonly adopted modeling approach for magnesium-twinning. This paper compares three state-of-the-art crystal plasticity-based twinning models from the literature, namely the elastic-viscoplastic self-consistent twinning-detwinning (EVPSC-TDT) model, crystal plasticity finite element model based on enhanced predominate twin reorientation approach (CPFE-ePTR), and the crystal plasticity finite element model based on “discrete twinning” approach (CPFE-DT). A polycrystalline microstructure is simulated with all three methods to compare the resulting stress–strain curves and lattice strains to those from the experimentally measured data. All three methods showed the capability of capturing the experimental results with different levels of accuracy. Additionally, the EVPSC-TDT method avoids solving the finite element matrices and showed the highest computational efficiency. The CPFE-ePTR model shows a higher accuracy in capturing the lattice strain. The CPFE-DT relies on high-resolution finite element mesh and is much slower than the other two methods, but it captured the local deformation concentration and stress reversal phenomena near the twin band, which was not possible with the other two methods. Based on the comparison, guidance for the selection of the appropriate model based on the specific modeling target is provided in this paper.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Stabilized bases for high-order, interpolation semi-Lagrangian, element-based tracer transport

In a computational fluid model of the atmosphere, the advective transport of trace species, or tracers, can be computationally expensive. For efficiency, models often use semi-Lagrangian advection methods. High-order interpolation semi-Lagrangian (ISL) methods, in particular, can be extremely efficient, if the problem of property preservation specific to them can be addressed. Atmosphere models often use geometrically and logically nonuniform grids for efficiency and, as a result, element-based discretizations. Such grids and discretizations make stability a particular problem for ISL methods. Generally, high-order, element-based ISL methods that use the natural polynomial interpolant associated with a nodal finite-element discretization are unstable. Here, we derive new bases having order of accuracy up to nine, with positive nodal weights, that stabilize the element-based ISL method. We use these bases to construct the linear advection operator in the property-preserving Interpolation Semi-Lagrangian Element-based Transport (Islet) method. Then we discuss key software implementation details. Finally, we show performance results for the Energy Exascale Earth System Model's atmosphere dynamical core, comparing the original and new transport methods. These simulations used up to 27,600 Graphical Processing Units (GPU) on the Oak Ridge Leadership Computing Facility's Summit supercomputer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Hybrid Particle Method for Computational Shock Physics

A long-standing area of research for Eulerian shock wave physics codes has been the treatment of strength and damage for materials. Here we present a method that will aid in the analysis of strength and failure in shock physics applications where excessive diffusion of critical variables can occur and control the solution outcome. Eulerian methods excel for large deformation simulations in general but are inaccurate in capturing structural behavior. Lagrangian methods provide better structural response, but finite element meshes can become tangled. Therefore, a technique for merging Lagrangian and Eulerian treatments of material response, within a single numerical framework, was implemented in the Multiple Component computational shock physics hydrocode. The capability is a Lagrangian/Eulerian Particle Method (LEPM) that uses particles to interface a Lagrangian treatment of material strength with a more traditional Eulerian treatment of the Equation of State (EOS). Lagrangian numerical methods avoid the advection diffusion found in Eulerian methods, which typically strongly affects strength constitutive law internal variables, such as equivalent plastic strain, porosity and/or damage. The Lagrangian capability enhances existing capabilities and permits accurate predictions of high rate, large deformation and/or shock of mechanical structures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Island scanning pattern optimization for residual deformation mitigation in laser powder bed fusion via sequential inherent strain method and sensitivity analysis

Laser powder bed fusion (L-PBF) has emerged as one of the mainstream additive manufacturing approaches for fabricating metal parts with complex geometries and intricate internal structures. However, large deformation associated with rapid heating and cooling can lead to build failure and requires post-processing which may increase manufacturing cost and prolong the production period. Here in this work, an island scanning pattern design method is proposed to optimize the scanning direction of each island in order to reduce part deformation after cutting off the build platform. The objective of this optimization is to minimize the upward bending of the part after sectioning, which allows the part deformation to satisfy the tolerance requirement or reduce the post heat treatment time. Inherent strain method is employed in the sequential finite element analysis consisting of layer-by-layer activations and sectioning for fast residual distortion prediction. Full sequential sensitivity analysis for the formulated optimization is provided to update the island scanning directions. To show the feasibility and effectiveness of the proposed method, the scanning patterns of a block structure and a connecting rod were designed and parts were fabricated using an open architecture L-PBF machine. The fabrication experiments demonstrated that the residual deformation of both parts fabricated by optimized scanning pattern can be reduced by over 50% compared to the initial scanning patterns, which demonstrate the effectiveness of the proposed method.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM

Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. Here, the two primary approaches in the experimental mechanics community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, we conduct a series of test cases to assess both methods under practical challenges using a finite strain elastoplasticity model.

Automatic differentiation↗