Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “tensor”

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

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

At least 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Quantitative study of the effect of grain boundary parameters on the slip system level Hall-Petch slope for basal slip system in Mg-4Al

Several theoretical studies have reported that the geometry and structure of grain boundaries in polycrystalline materials could impose a significant effect on the Hall-Petch slope. However, experimental observations are primarily limited by the ability of the techniques to accurately quantify the grain boundary strength and validate these theoretical models. Using high-resolution electron backscatter diffraction (HR-EBSD), the local stress tensor ahead of a slip band blocked by a grain boundary was quantified and coupled with a continuum dislocation pile-up model to assess the barrier strength of specific grain boundaries to specific slip systems, referred to as micro-Hall-Petch coefficient. For basal slip system in a deformed Mg-4Al alloy, the micro-Hall-Petch coefficient ($k^{basal}_{μ}$) varied significantly, from 0.054 to 0.184 MPa - m 1/2 for nine different grain boundaries. These results were correlated with geometric descriptors of the respective grain boundaries, with three-dimensional GB profile additionally measured via focused ion beam milling. It was found that the angle between the two slip plane traces on the grain boundary plane was the most sensitive parameter affecting $k^{basal}_{μ}$, followed by the angle between the slip directions. A functional form for calculation of $k^{basal}_{μ}$ depending on these two angles is proposed to augment crystal plasticity constitutive models with slip resistance dependent on some measure of the grain size. The method allows a new pathway to calibrate grain size strengthening parameters in crystal plasticity models, allowing further computational investigations of the interrelationship between texture, grain morphology, and the Hall Petch effect.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Estimation of micro-Hall-Petch coefficients for prismatic slip system in Mg-4Al as a function of grain boundary parameters

Grain size strengthening, referred to as the Hall-Petch effect, is a common strategy to improve the yield strength of magnesium (Mg) alloys. Several experimental studies have reported that the Hall-Petch slope strongly depends on the texture of the alloy. This effect arises from altering grain boundaries (GBs) resistance to different slip systems to transfer across adjacent grains. The grain boundary barrier strength of certain grain boundaries to basal slip, referred to as basal micro-Hall-Petch, was investigated in the previous work. Here in this study, the micro-Hall-Petch coefficient values for the prismatic slip $(k^{prismatic}_{μ})$ in Mg-4Al and their correlation with the grain boundary parameters were investigated. An experimental method was developed to initiate the prismatic slip band at low-stress levels. High-resolution electron backscatter diffraction (HR-EBSD) was used to measure the residual stress tensor, from which the resolved shear stress ahead of blocked prismatic slip bands was computed for seven different grain boundaries. $(k^{prismatic}_{μ})$ values for each individual GB were calculated by coupling the stress profile information with a continuum dislocation pile-up model. The $(k^{prismatic}_{μ})$ values vary from 0.138 MPa.m 1/2 to 0.685 MPa. m 1/2 which are almost three times larger than the calculated values for the basal micro-Hall-Petch. The $(k^{prismatic}_{μ})$ values were correlated with the GB parameters, and a functional relationship depending on the two most effective angles, the angle between the traces of the slip planes on the GB plane ($\phi$) and the angle between incoming and outgoing slip directions (κ), was proposed to estimate the Hall-Petch barrier for prismatic slip system. The work provides coefficients that can be supplied as input to crystal plasticity models to couple the effect of texture and grain size effectively.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Rules for the crystallite size and dislocation density evolution in phases during α-ω transformation in Zr under high-pressure and severe plastic flow

The first in-situ X-ray diffraction (XRD) study of the evolution of the crystallite size and dislocation density in phases during plastic strain-induced phase transformation (PT) is performed utilizing α-ω PT in strongly pre-deformed commercially pure Zr as an important example. Rough diamond anvils (rough-DA) are introduced to intensify all occurring processes during heterogeneous compression of Zr in a diamond anvil cell (DAC). The main rule is found that during α-ω PT the crystallite size and dislocation density in ω-Zr depend solely on the volume fraction of ω-Zr and are independent of pressure, plastic strain tensor, its path, and initial nanostructure. Crystallite size in ω-Zr increases from 10 to 60 nm during the PT, while dislocation density reduces from 1.83×10 15 /m 2 to 0.6×10 15 /m 2 . Rough-DA produce a steady nanostructure in α-Zr before PT with smaller crystallite size and larger dislocation density than smooth-DA, leading to a reduction of the minimum pressure for α-ω PT to a record value 0.67 GPa, 9 times smaller than under hydrostatic loading and 5.1 times lower than the phase equilibrium pressure. In addition to strain, the kinetics of strain-induced PT unexpectedly depends on time. Also, strain-controlled part of kinetics is zero order, in contrast to the first-order kinetics with smooth-DA. The obtained results open a new window for understanding the mutual effects of nanostructure evolution and PT during severe plastic flow in various technological and natural processes. In conclusion, they may bring up economic strategies of producing nanocomposites and single-phase nanostructured materials with optimal properties.

Crystalline size↗
DOE OSTI2025

The structure and migration of twin boundaries in tetragonal β -Sn: An application of machine learning based interatomic potentials

Although atomistic simulations have contributed significantly to our understanding of twin boundary structure and migration in metals and alloys with hexagonal close packed (HCP) crystal structures, few direct atomistic studies of twinning have been conducted for other types of low symmetry materials, in large part due to a lack of reliable interatomic potentials. In this work, we examine twin boundary structure and migration in a tetragonal material, β-Sn, comparing high resolution Transmission Electron Microscopy (TEM) images of deformation twins in β-Sn to the results of direct atomistic simulations using multiple interatomic potentials. ML-based potentials developed in this work are found to give results consistent with our experimental data, revealing faceted twin boundary structures formed by the nucleation and motion of twinning disconnections. We use bicrystallographic methods in combination with atomistic simulations to analyze the structure, energy and shear coupled migration of observed twin facets in β-Sn. In analogy to Prismatic-Basal (PB/BP) interfaces in HCP metals, we discover low energy asymmetric Prismatic-A-plane (PA/AP) interfaces important to twin growth in β-Sn. Finally, a Moment Tensor Potential (MTP) and Rapid Artificial Neural Network (RANN) interatomic potential suitable for studying twinning and phase transformations in Sn are made publicly available as part of this work.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Informed unsupervised machine learning analysis of dislocation microstructure from high-resolution differential aperture X-ray structural microscopy data

This study leverages high-resolution differential-aperture X-ray structural microscopy (DAXM) to probe the local dislocation structure in deformed 304L-stainless steel at small strain, by measuring the lattice rotation and deviatoric elastic strain with a sub-micron resolution. For a single grain in a polycrystalline specimen, the measured lattice rotation field over the measured volume exhibited a multimodal distribution while the deviatoric elastic strain showed a single-mode distribution. An unsupervised Cauchy mixture machine learning model was developed to resolve the multimodal distribution of the lattice rotation. By mapping the lattice rotation data associated with each Cauchy peak in the model back onto the measured volume, we identify contiguous regions of the crystal rotated near the average values corresponding to the peaks of the overall rotation distribution. These regions represent the grain subdivision in the microstructure. Finally, the dislocation density tensor was also computed and its norm was laid over the rotation field to detect the subgrain boundaries. This step provided a validation of the Cauchy mixture model for the analysis of the lattice rotation distribution. The current study highlights the integration of advanced X-ray microscopy techniques with data-driven analysis methods to uncover detailed microstructure scales in deformed crystals.

Machine learning; Lattice rotation; High-energy X-↗
DOE OSTI2026

Fragile-to-strong transition in liquid As 2 S 3 under pressure: The effect of melt metallization

The well-known classification of glass-forming melts into fragile and strong liquids has several notable exceptions, including water, silica, and certain phase-change materials (PCMs). These exceptional fluid systems exhibit a fragile-to-strong transition (FST) upon cooling: a transformation from a high-temperature liquid with fast atomic dynamics, low viscosity, and low flow activation energy, to a viscous supercooled melt with high energy barriers near the glass transition temperature T g . This behavior is critically important for non-volatile memories, photonic tensor cores, reconfigurable metamaterials, and other devices, that use PCMs, enabling nanosecond-scale crystallization in the fragile regime and long data retention in the strong regime near or below T g . A significant structural transformation is expected between these two viscosity regimes, along with a semiconductor-metal (SC-M) transition upon heating, driven by high internal pressure and associated density increase. By applying high external pressure to the canonical low-conducting chalcogenide melt As 2 S 3 , we observed both the FST and the SC-M transition, occurring simultaneously within the same domain of the P, T−phase space. These findings suggest that the FST is not limited to a few exceptional liquids but is a common phenomenon, at least in systems that exhibit melt metallization within specific regions of their P, T−phase diagrams.

first-principles molecular dynamics↗
DOE OSTI2024

Enforcing global constraints for the dispersion closure problem: τ 2 -SIMPLE algorithm

Permeability and effective dispersion tensors are critical parameters to characterize flow and transport in porous media at the continuum scale. Homogenization theory defines a framework in which such effective properties are first computed from solving a closure problem in a repeating unit cell of the periodic microstructure and then used in a macroscopic formulation for efficient computation. The closure problem is formulated as a local boundary value problem subjected to global constraints, which guarantee the uniqueness of the solution and can be difficult to satisfy for complex geometries and at high flow conditions. These constraints also ensure that pore-scale pressure, velocity, and concentration fields can be accurately reconstructed from the closure variable. Building on a previous work, here we present a framework that allows to satisfy global constraints associated to both the permeability and the dispersion closure problems by introducing two artificial time scales. The algorithm, called τ 2 -SIMPLE, computes both permeability and effective dispersion given an arbitrarily complex geometry and flow condition. Furthermore, this algorithm is demonstrated to be accurate for both 2D and 3D geometries across varying flow conditions, and thus it can be used to quickly characterize effective properties from porous media images in many applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A multiphysics model of the versatile test reactor based on the MOOSE framework

The traditional modeling approach for sodium fast reactor cores relies on separate physics models, where the fuel performance, thermal–hydraulics, and neutronics calculations required to predict the core physics characteristics for nominal conditions are decoupled by relying on user-imposed boundary conditions. Here, this paper aims at evaluating the impact of multiphysics simulations for predicting the core characteristics of the Versatile Test Reactor, which is being designed as a 300-MWt sodium-cooled fast reactor. The purpose of the Versatile Test Reactor is to accelerate the testing of advanced nuclear materials in the United States. The proposed multiphysics model relies on the Griffin reactor physics code, the SAM thermal–hydraulic system code, the BISON fuel performance code, as well as generic Multiphysics Object-Oriented Simulation Environment capabilities implemented in the open-source tensor mechanics module. For k eff calculations, the introduction of a tight coupling between the neutronics, thermo-mechanical and thermal–hydraulics models induces a change of around 543 pcm in the eigenvalue, compared to the traditional standalone neutronics calculation where approximate temperature profiles are used. The multiphysics model is then employed for quantifying the impact of the thermal conductivity uncertainties on some of the key figures of merit, such as the fuel centerline temperature, assembly powers, and keff for nominal core conditions. As anticipated, uncertainties on fuel thermal conductivity mostly impact the fuel centerline temperature, and to a lesser extend the k eff .

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Fracton phases via exotic higher-form symmetry-breaking

We study p-string condensation mechanisms for fracton phases from the viewpoint of higher-form symmetry, focusing on the examples of the X-cube model and the rank-two symmetric-tensor scalar charge theory. This work is motivated by questions of the relationship between fracton phases and continuum quantum field theories, and also provides general principles to describe p-string condensation independent of specific lattice model constructions. We give a perspective on higher-form symmetry in lattice models in terms of cellular homology. Applying this perspective to the coupled-layer construction of the X-cube model, we identify a foliated 1-form symmetry that is broken in the X-cube phase, but preserved in the phase of decoupled toric code layers. Similar considerations for the scalar charge theory lead to a framed 1-form symmetry. These symmetries are distinct from standard 1-form symmetries that arise, for instance, in relativistic quantum field theory. Here, we also give a general discussion on interpreting p-string condensation, and related constructions involving gauging of symmetry, in terms of higher-form symmetry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Evaluation of PbTe and SnTe as Ohmic Contact Layers in CdTe Solar Cell Devices

For solar cells based on CdTe, the choice of a suitable back contact material is limited by CdTe's deep work function. Here, we explored p-type PbTe and SnTe as ohmic contacts to CdTe. These contact layers were grown on single crystal CdTe substrates by molecular beam epitaxy, and the valence band offset between film and substrate was measured using X-ray photoemission spectroscopy. Polycrystalline device structures were also grown by sublimation to assess performance improvements. Doping was achieved in PbTe by thallium incorporation. Only the highest Tl doped PbTe resulted in a desirable band alignment with the CdTe, forming an electron reflector and no hole barrier. Time-resolved photoluminescence measurements also revealed significant photocarrier lifetime improvements for only the highest doped PbTe. Consequentially, devices incorporating the highest doped PbTe layers showed increased power conversion efficiency, primarily from increased fill factor. Doping of the PbTe was measured via Hall effect with variable magnetic field, which was required due to the formation of an n-type parasitic interface layer. To properly interpret the variable field Hall measurements, we derived an expression for the magnetic field-dependent conductivity tensor of an L-valley semiconductor.

anisotropic band valley↗
DOE OSTI2024

Resonant Raman in armchair graphene nanoribbons from first-principles

Resonant Raman spectra of armchair graphene nanoribbons (AGNRs) are computed using Density Functional Theory (DFT) and third-order perturbation theory. Results are benchmarked against available experimental data and compared to previously used theoretical approaches based on the Placzek approximation. Comparable agreement with experiments is found for both previously and presently used methods. In addition, a numerical analysis is carried out to provide a justification for the resonant modeling method based on the use of the frequency-dependent dielectric tensor in the Placzek approximation. Finally, this work also provides additional predictions and references for wide AGNRs that might be investigated with Raman scattering experiments in the future.

42 ENGINEERING↗
DOE OSTI2020

Data-driven variational multiscale reduced order models

We propose a new data-driven reduced order model (ROM) framework that centers around the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data to increase the ROM accuracy at a modest computational cost. The VMS methodology is a natural fit for the hierarchical structure of the ROM basis: In the first step, we use the ROM projection to separate the scales into three categories: (i) resolved large scales, (ii) resolved small scales, and (iii) unresolved scales. In the second step, we explicitly identify the VMS–ROM closure terms, i.e., the terms representing the interactions among the three types of scales. In the third step, we use available data to model the VMS–ROM closure terms. Thus, instead of phenomenological models used in VMS for standard numerical discretizations (e.g., eddy viscosity models), we utilize available data to construct new structural VMS–ROM closure models. Specifically, we build ROM operators (vectors, matrices, and tensors) that are closest to the true ROM closure terms evaluated with the available data. We test the new data-driven VMS–ROM in the numerical simulation of four test cases: (i) the 1D Burgers equation with viscosity coefficient v = 10 -3 ; (ii) a 2D flow past a circular cylinder at Reynolds numbers, Re = 100, Re = 500, and Re= 1000; (iii) the quasi-geostrophic equations at Reynolds number Re = 450 and Rossby number Ro = 0.0036; and (iv) a 2D flow over a backward facing step at Reynolds number Re = 1000. The numerical results show that the data-driven VMS–ROM is significantly more accurate than standard ROMs.

42 ENGINEERING↗
DOE OSTI2021

Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries

This paper introduces the scaled boundary cubature (SBC) scheme for accurate and efficient integration of functions over polygons and two-dimensional regions bounded by parametric curves. Over two-dimensional domains, the SBC method reduces integration over a region bounded by m curves to integration over m regions (referred to as curved triangular regions), where each region is bounded by two line segments and a curve. With proper (counterclockwise) orientation of the boundary curves, the scheme is applicable to convex and nonconvex domains. Additionally, for star-convex domains, a tensor-product cubature rule with positive weights and integration points in the interior of the domain is obtained. If the integrand is homogeneous, we show that this new method reduces to the homogeneous numerical integration scheme; however, the SBC scheme is more versatile since it is equally applicable to both homogeneous and non-homogeneous functions. This paper also introduces several methods for smoothing integrands with point singularities and near-singularities. When these methods are used, highly efficient integration of weakly singular functions is realized. Finally, the SBC method is applied to a number of benchmark problems, which reveal its broad applicability and superior performance (in terms of time to generate a rule and accuracy per cubature point) when compared to existing methods for integration.

42 ENGINEERING↗
DOE OSTI2021

COVID-19 dynamics across the US: A deep learning study of human mobility and social behavior

This paper presents a deep learning framework for epidemiology system identification from noisy and sparse observations with quantified uncertainty. The proposed approach employs an ensemble of deep neural networks to infer the time-dependent reproduction number of an infectious disease by formulating a tensor-based multi-step loss function that allows us to efficiently calibrate the model on multiple observed trajectories. The method is applied to a mobility and social behavior-based SEIR model of COVID-19 spread. The model is trained on Google and Unacast mobility data spanning a period of 66 days, and is able to yield accurate future forecasts of COVID-19 spread in 203 US counties within a time-window of 15 days. Interestingly, a sensitivity analysis that assesses the importance of different mobility and social behavior parameters reveals that attendance of close places, including workplaces, residential, and retail and recreational locations, has the largest impact on the effective reproduction number. Furthermore, the model enables us to rapidly probe and quantify the effects of government interventions, such as lock-down and re-opening strategies. Taken together, the proposed framework provides a robust workflow for data-driven epidemiology model discovery under uncertainty and produces probabilistic forecasts for the evolution of a pandemic that can judiciously provide information for policy and decision making. All codes and data accompanying this manuscript are available at https://github.com/PredictiveIntelligenceLab/DeepCOVID19.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

A compute-bound formulation of Galerkin model reduction for linear time-invariant dynamical systems

This work aims to advance computational methods for projection-based reduced-order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern architectures. This weakness can be particularly limiting when tackling many-query studies, where one needs to run a large number of simulations. This work introduces a reformulation, called rank-2 Galerkin, of the Galerkin ROM for LTI dynamical systems which converts the nature of the ROM problem from memory bandwidth to compute bound. We present the details of the formulation and its implementation, and demonstrate its utility through numerical experiments using, as a test case, the simulation of elastic seismic shear waves in an axisymmetric domain. We quantify and analyze performance and scaling results for varying numbers of threads and problem sizes. In conclusion, we present an end-to-end demonstration of using the rank-2 Galerkin ROM for a Monte Carlo sampling study. We show that the rank-2 Galerkin ROM is one order of magnitude more efficient than the rank-1 Galerkin ROM (the current practice) and about 970 times more efficient than the full-order model, while maintaining accuracy in both the mean and statistics of the field.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity

In this paper, we present a first-order Stress-Hybrid Virtual Element Method (SH-VEM) on six-noded triangular meshes for linear plane elasticity. Here, we adopt the Hellinger–Reissner variational principle to construct a weak equilibrium condition and a stress based projection operator. In each element, the stress projection operator is expressed in terms of the nodal displacements, which leads to a displacement based formulation. This stress-hybrid approach assumes a globally continuous displacement field while the stress field is discontinuous across each element. The stress field is initially represented by divergence-free tensor polynomials based on Airy stress functions, but we also present a formulation that uses a penalty term to enforce the element equilibrium conditions, referred to as the Penalty Stress-Hybrid Virtual Element Method (PSH-VEM). Numerical results are presented for PSH-VEM and SH-VEM, and we compare their convergence to the composite triangle FEM and B-bar VEM on benchmark problems in linear elasticity. The SH-VEM converges optimally in the L 2 norm of the displacement, energy seminorm, and the L 2 norm of hydrostatic stress. Furthermore, the results reveal that PSH-VEM converges in most cases at a faster rate than the expected optimal rate, but it requires the selection of a suitably chosen penalty parameter.

42 ENGINEERING↗
DOE OSTI2024

Equivariant graph convolutional neural networks for the representation of homogenized anisotropic microstructural mechanical response

Composite materials with different microstructural material symmetries are common in engineering applications where grain structure, alloying and particle/fiber packing are optimized via controlled manufacturing. In fact these microstructural tunings can be done throughout a part to achieve functional gradation and optimization at a structural level. To predict the performance of particular microstructural configuration and thereby overall performance, constitutive models of materials with microstructure are needed. In this work we provide neural network architectures that provide effective homogenization models of materials with anisotropic components. These models satisfy equivariance and material symmetry principles inherently through a combination of equivariant and tensor basis operations. We demonstrate them on datasets of stochastic volume elements with different textures and phases where the material undergoes elastic and plastic deformation, and show that the these network architectures provide significant performance improvements.

anisotropy↗
DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗