Search NASA⌕ Search

SEARCH · Search NASA

Results for “energy function”

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 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Recent progress in the phase-field dislocation dynamics method

The phase-field dislocation dynamics (PFDD) method, originated in 2002, is a continuum dislocation model that uses order parameters to describe dislocation slips in crystalline materials. In the past two decades, and especially since it was last reviewed in 2016, PFDD was advanced significantly in terms of the mathematical formulation, numerical implementation, and applicability. The main purpose of this short review is to summarize recent progress made to improve the energy functional formulation and numerical techniques of PFDD as well as its recent applications. Additionally, some recommendations for future work to further extend the PFDD method are presented.

36 MATERIALS SCIENCE↗
DOE OSTI2015

A new variation of the Buckingham exponential-6 potential with a tunable, singularity-free short-range repulsion and an adjustable long-range attraction

We introduce new generalized (reverting to the original) and extended (not reverting to the original) 4-parameter forms of the (B-2) Potential Energy Function (PEF) of Wang etal. (L.-P. Wang, J. Chen and T. van Voorhis, J. Chem. Theor. Comp. 9, 452 (2013)), which is itself a modification of the Buckingham exponential-6 PEF. The new forms have a tunable, singularity-free short-range repulsion and an adjustable long-range attraction. They produce fits to high quality ab initio data for the X–(H2O), X=F, Cl, Br, I and M+(H2O), M=Li, Na, K, Rb, Cs dimers that are between 1 and 2 orders of magnitude better than the original 3-parameter (B-2) and modified Buckingham exponential-6 PEFs. They are also slightly better than the 4-parameter generalized Buckingham exponential-6(gBe-6) and of comparable quality with the 4-parameter extended Morse (eM) PEFs introduced recently by us.

Werhahn, Jasper C.↗
DOE OSTI2025

Physics augmented machine learning discovery of composition-dependent constitutive laws for 3D printed digital materials

Multi-material 3D printing, particularly through polymer jetting, enables the fabrication of digital materials by mixing distinct photopolymers at the micron scale within a single build to create a composite with tunable mechanical properties. Here, this work presents an integrated experimental and computational investigation into the composition-dependent mechanical behavior of 3D printed digital materials. We experimentally characterize five formulations, combining soft and rigid UV-cured polymers under uniaxial tension and torsion across three strain and twist rates. The results reveal nonlinear and rate-dependent responses that strongly depend on composition. To model this behavior, we develop a physics-augmented neural network (PANN) that combines a partially input convex neural network (pICNN) for learning the composition-dependent hyperelastic strain energy function with a quasi-linear viscoelastic (QLV) formulation for time-dependent response. The pICNN ensures convexity with respect to strain invariants while allowing non-convex dependence on composition. To enhance interpretability, we apply $L_0$ sparsification. For the time-dependent response, we introduce a multilayer perceptron (MLP) to predict viscoelastic relaxation parameters from composition. The proposed model accurately captures the nonlinear, rate-dependent behavior of 3D printed digital materials in both uniaxial tension and torsion, achieving high predictive accuracy for interpolated material compositions. This approach provides a scalable framework for automated, composition-aware constitutive model discovery for multi-material 3D printing.

Constitutive modeling↗
DOE OSTI2021

Learning constitutive relations using symmetric positive definite neural networks

In this work, we present a new neural-network architecture, called the Cholesky-factored symmetric positive definite neural network (SPD-NN), for modeling constitutive relations in computational mechanics. Instead of directly predicting the stress of the material, the SPD-NN trains a neural network to predict the Cholesky factor of the tangent stiffness matrix, based on which the stress is calculated in incremental form. As a result of this special structure, SPD-NN weakly imposes convexity on the strain energy function, satisfies the second order work criterion (Hill's criterion) and time consistency for path-dependent materials, and therefore improves numerical stability, especially when the SPD-NN is used in finite element simulations. Depending on the types of available data, we propose two training methods, namely direct training for strain and stress pairs and indirect training for loads and displacement pairs. We demonstrate the effectiveness of SPD-NN on hyperelastic, elasto-plastic, and multiscale fiber-reinforced plate problems from solid mechanics. The generality and robustness of SPD-NN make it a promising tool for a wide range of constitutive modeling applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Development of novel Cu-Cr-Nb-Zr alloys with the aid of computational thermodynamics

Multi-modal precipitate distribution in the microstructure, with coarse precipitates pinning the grain boundaries and finer precipitates strengthening the matrix, is beneficial to suppress grain boundary sliding and dislocation creep, respectively, of structural materials. However, achievement of a multi-modal precipitate distribution remains a challenge in developing creep-resistant advanced Cu alloys while retaining high strength and high conductivity at elevated temperature. This work overcame this challenge with the aid of computational thermodynamics. Thermodynamic models for Gibbs energy functions of phases in the Cu-Cr-Nb-Zr system have been developed in this study. These models were then used to calculate solidification paths and phase equilibria at different temperatures, guiding the design of chemical composition and heat treatment parameters of novel copper alloys with a target multi-modal distribution of precipitates. The new alloy, fabricated through traditional ingot metallurgy method, has achieved the desired microstructure as validated by optical and transmission electron microscopy. Electrical conductivity and mechanical properties were screened and compared with the existing commercial Cu alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Thermodynamic properties of ZrCl 4 with LiCl, NaCl, KCl, CsCl, MgCl 2 , and UCl 3 for molten salt reactor applications

Here, a set of self-consistent Gibbs energy functions has been developed to describe the thermochemical behavior of the major reactive fission product ZrCl 4 with key components in chloride molten salt reactors (MSRs): LiCl–ZrCl 4 , NaCl–ZrCl 4 , KCl–ZrCl 4 , CsCl–ZrCl 4 , MgCl 2 –ZrCl 4 and UCl 3 –ZrCl 4 . Low ZrCl 4 concentration phase equilibria most relevant to MSR applications have been confirmed via differential scanning calorimetry for NaCl–ZrCl 4 , and X-ray diffraction analysis performed on equilibrated samples of NaCl–ZrCl 4 , KCl–ZrCl 4 , MgCl 2 –ZrCl 4 , and UCl 3 –ZrCl 4 . Within the framework of the modified quasi-chemical model in the quadruplet approximation, extrapolations of pseudo-binary models were generated to represent KCl–MgCl 2 –ZrCl 4 , KCl–NaCl–ZrCl 4 , and MgCl 2 –NaCl–ZrCl 4 , which show agreement with phase equilibria data where available without the use of ternary interaction parameters. The optimized thermodynamic descriptions for these systems and others are available in the open-source compendium Molten Salt Thermal Properties Database – Thermochemical (MSTDB–TC).

CALPHAD↗
DOE OSTI2013

Phase-field simulations of intragranular fission gas bubble evolution in UO2 under post-irradiation thermal annealing

Fission gas bubble is one of evolving microstructures, which affect thermal mechanical properties such as thermo-conductivity, gas release, volume swelling, and cracking, in operating nuclear fuels. Therefore, fundamental understanding of gas bubble evolution kinetics is essential to predict the thermodynamic property and performance changes of fuels. In this work, a generic phasefield model was developed to describe the evolution kinetics of intra-granular fission gas bubbles in UO2 fuels under post-irradiation thermal annealing conditions. Free energy functional and model parameters are evaluated from atomistic simulations and experiments. Critical nuclei size of the gas bubble and gas bubble evolution were simulated. A linear relationship between logarithmic bubble number density and logarithmic mean bubble diameter is predicted which is in a good agreement with experimental data.

Intra-granular gas bubbles evolution↗
DOE OSTI2020

Insights into grain boundary energy structure-property relationships by examining computed [100] disorientation axis grain boundaries in Nickel

A study of 346 computed [100] disorientation axis grain boundaries provides insight into grain boundary energy structure-property relationships. The grain boundaries come from 6 coincidence site lattice misorientations at regularly spaced disorientation angles, and cover the full range of boundary plane orientations. The computed energy has clear trends in disorientation angle and boundary plane orientation. Here, the data are used to reexamine the 'special' attribute frequently applied to low Σ coincidence site lattice misorientations and low-angle boundaries and to assess the accuracy of a face-centered cubic grain boundary energy function.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Metal Sulfide Ion Exchangers: High Acid Stability of Na 2 x Mg 2 y – x Sn 4– y S 8 (NMS) and Topotactic Conversion to 2D Solid Acids with Semiconducting Character

Metal sulfide ion exchange materials (MSIEs) are of interest for nuclear waste remediation applications. Here, we report the high stability of two structurally related metal sulfide ion exchange materials, Na 2x Mg 2y–x Sn 4–y S 8 (Mg-NMS) and Na 2 SnS 3 (Na-NMS), in strongly acid media, in addition to the preparation of Na 2x Ni 2y–x Sn 4–y S 8 (Ni-NMS). Their formation progress during synthesis is studied with in-situ methods, with the target phases appearing in <15 min, reaction completion in <12 h, and high yields (75–80%). Upon contact with nitric or hydrochloric acid, these materials topotactically exchange Na + for H + , proceeding in a stepwise protonation pathway for Na 5.33 Sn 2.67 S 8 . Na-NMS is stable in 2 M HNO 3 and Mg-NMS is stable in 4 M HNO 3 for up to 4 h, while both NMS materials are stable in 6 M HCl for up to 4 days. However, the treatment of Mg-NMS and Na-NMS with 2–6 M H 2 SO 4 reveals a much slower protonation process since after 4 h of contact both NMS and HMS are present in the solution. The resultant protonated materials, H 2x Mg 2y–x Sn 4–y S 8 and H 4x [(H y Na y–1 ) 1.33x Sn 4––1.33x ]S 8 , are themselves solid acids and readily react with and intercalate a variety of organic amines, where the band gap of the resultant adduct is influenced by amine choice and can be tuned within the range of 1.88(5)–2.27(5) eV. The work function energy values for all materials were extracted from photoemission yield spectroscopy in air (PYSA) measurements and range from 5.47 (2) to 5.76 (2) eV, and the relative band alignments of the materials are discussed. DFT calculations suggest that the electronic structure of Na 2 MgSn 3 S 8 and H 2 MgSn 3 S 8 makes them indirect gap semiconductors with multi-valley band edges, with carriers confined to the [MgSn 3 S 8 ] 2– layers. Light electron effective masses indicate high electron mobilities.

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

Control of monodomain polymer-stabilized cuboidal nanocrystals of chiral nematics by confinement.

Liquid crystals are important components of optical technologies. Cuboidal crystals consisting of chiral liquid crystals-the so-called blue phases (BPs), are of particular interest due to their crystalline structures and fast response times, but it is critical that control be gained over their phase behavior as well as the underlying dislocations and grain boundaries that arise in such systems. Blue phases exhibit cubic crystalline symmetries with lattice parameters in the 100 nm range and a network of disclination lines that can be polymerized to widen the range of temperatures over which they occur. Here, we introduce the concept of strain-controlled polymerization of BPs under confinement, which enables formation of strain-correlated stabilized morphologies that, under some circumstances, can adopt perfect single-crystal monodomain structures and undergo reversible crystal-to-crystal transformations, even if their disclination lines are polymerized. We have used super-resolution laser confocal microscopy to reveal the periodic structure and the lattice planes of the strain and polymerization stabilized BPs in 3D real space. Our experimental observations are supported and interpreted by relying on theory and computational simulations in terms of a free energy functional for a tensorial order parameter. Simulations are used to determine the orientation of the lattice planes unambiguously. The findings presented here offer opportunities for engineering optical devices based on single-crystal, polymer-stabilized BPs whose inherent liquid nature, fast dynamics, and long-range crystalline order can be fully exploited.

confinement↗
DOE OSTI2016

Surface-Plasmon-Mediated Gradient Force Enhancement and Mechanical State Transitions of Graphene Sheets

Graphene, a two-dimensional material possessing extraordinary properties in electronics as well as mechanics, provides a great platform for various optoelectronic and opto-mechanical devices. Here in this article, we theoretically study the optical gradient force arising from the coupling of surface plasmon modes on parallel graphene sheets, which can be several orders stronger than that between regular dielectric waveguides. Furthermore, with an energy functional optimization model, possible force-induced deformation of graphene sheets is calculated. We show that the significantly enhanced optical gradient force may lead to mechanical state transitions of graphene sheets, which are accompanied by abrupt changes in reflection and transmission spectra of the system. Our demonstrations illustrate the potential for a broader graphene-related applications such as force sensors and actuators.

36 MATERIALS SCIENCE↗
DOE OSTI2012

Curvature and Frontier Orbital Energies in Density Functional Theory

Perdew et al. [Phys. Rev. Lett 49, 1691 (1982)] discovered and proved two different properties that exact Kohn-Sham density functional theory (DFT) must obey: (i) The exact total energy versus particle number must be a series of linear segments between integer electron points; (ii) Across an integer number of electrons, the exchange-correlation potential may ``jump’’ by a constant, known as the derivative discontinuity (DD). Here, we show analytically that in both the original and the generalized Kohn-Sham formulation of DFT, the two are in fact two sides of the same coin. Absence of a derivative discontinuity necessitates deviation from piecewise linearity, and the latter can be used to correct for the former, thereby restoring the physical meaning of the orbital energies. Using selected small molecules, we show that this results in a simple correction scheme for any underlying functional, including semi-local and hybrid functionals as well as Hartree-Fock theory, suggesting a practical correction for the infamous gap problem of density functional theory. Moreover, we show that optimally-tuned range-separated hybrid functionals can inherently minimize both DD and curvature, thus requiring no correction, and show that this can be used as a sound theoretical basis for novel tuning strategies.

density functional theory↗
DOE OSTI2019

Degenerate conic anchoring and colloidal elastic dipole-hexadecapole transformations

The defect structure associated with a colloid in a nematic liquid crystal is dictated by molecular orientation at the colloid surface. Perpendicular or parallel orientations to the surface lead to dipole-like or quadrupole-like defect structures. However, the so-called elastic hexadecapole discovered recently, has been assumed to result from a conic anchoring condition. In order to understand it at a fundamental level, a model for this anchoring is introduced here in the context of a Landau-de Gennes free energy functional. We investigate the evolution of defect configurations, as well as colloidal interactions, by tuning the preferred tilt angle (θ e ). The model predicts an elastic dipole whose stability decreases as θ e increases, along with a dipole-hexadecapole transformation, which are confirmed by our experimental observations. Taken together, our results suggest that previously unanticipated avenues may exist for design of self-assembled structures via control of tilt angle.

42 ENGINEERING↗
DOE OSTI2022

Protein sequence design with a learned potential

The task of protein sequence design is central to nearly all rational protein engineering problems, and enormous effort has gone into the development of energy functions to guide design. Here, we investigate the capability of a deep neural network model to automate design of sequences onto protein backbones, having learned directly from crystal structure data and without any human-specified priors. The model generalizes to native topologies not seen during training, producing experimentally stable designs. We evaluate the generalizability of our method to a de novo TIM-barrel scaffold. The model produces novel sequences, and high-resolution crystal structures of two designs show excellent agreement with in silico models. Our findings demonstrate the tractability of an entirely learned method for protein sequence design.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Anomalous softening of 3D printed elastomeric foam irradiated under compressive strain

Elastomeric foam is an essential component in many industrial and technological settings, primarily as thermal insulators and as positional/mechanical support cushions. In particular, silicone foam is utilized in harsh environments due to exceptional thermal and chemical stability. Under service conditions within certain applications such material gets exposed to a high dosage of gamma radiation, which can permanently alter the material’s structural and mechanical response properties. Most studies on gamma-exposure under inert or oxidative atmosphere indicate hardening of silicone foam, which is attributed to radiation-induced enhancement in chemical cross-linking. Here we report two contrasting effects depending on whether (non-oxidative) radiation exposure is carried out with the foam under zero or finite compressive strain. While in the former case we observe radiation-hardening consistent with previous studies, in the latter case (50% porous foam under 30% uniaxial compression) we see a monotonic decrease in Young’s modulus with increasing dosage, although solvent swelling experiments on the constituent rubber indicate a net increase in cross-link density independent of the state of strain. We quantitatively model all dose-dependent data using the Ogden Hyperfoam strain-energy function within the framework of Tobolsky two-network scheme and attribute the above anomaly to a combined effect of radiation-induced thickness change (compression set) and inherent nonlinearity in the foam’s stress-strain response.

Coarse-grained models↗
DOE OSTI2024

Mapping the nonequilibrium order parameter of a quasi-two dimensional charge density wave system

The driving force of a charge density wave (CDW) transition in quasi-two dimensional systems is still debated, while being crucial in understanding electronic correlation in such materials. Here we use femtosecond time- and angle-resolved photoemission spectroscopy combined with computational methods to investigate the coherent lattice dynamics of a prototypical CDW system. The photo-induced temporal evolution of the periodic lattice distortion associated with the amplitude mode reveals the dynamics of the free energy functional governing the order parameter. Our approach establishes that optically-induced screening rather than CDW melting at the electronic level leads to a transiently modified potential which explains the anharmonic behaviour of the amplitude mode and discloses the structural origin of the symmetry-breaking phase transition.

electronic properties and materials↗
DOE OSTI2012

Morphological transitions in liquid crystal nanodroplets

A continuum theory is utilized to study ordering in liquid crystal nanodroplets. The free energy functional that describes the system is minimized using an Euler–Lagrange approach and an unsymmetric radial basis function method. The equilibrium morphology in nanodroplets is shown to represent a delicate balance between bulk and surface contributions; when the radius of the droplet reaches a critical value, that balance is altered and the droplet undergoes a transition. By controlling the anchoring conditions at the droplet's surface, one can control the radius where the transition occurs and even prepare metastable droplets where small perturbations can trigger a morphological transition. The findings of the theory are shown to be consistent with recent experimental observations on monodisperse nematic liquid crystal nanodroplets.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Cuboidal Liquid Crystal Phases Under Multiaxial Geometrical Frustration.

Cuboidal liquid crystal phases - the so-called blue phases - consist of a network of topological defects arranged into a cubic symmetry. They exhibit striking optical properties, including Bragg reflection in the visible range and fast response times. Confining surfaces can interfere with the packing of such a network, leading to structures that have not been explored before. In this work, a Landau-de Gennes free energy formalism for the tensor alignment field Q is used to investigate the behavior of chiral liquid crystals under non-isotropic confinement. The underlying free energy functional is solved by relying on a Monte Carlo method that facilitates efficient exploration of configuration space. The results of simulations are expressed in terms of phase diagrams as a function of chirality and temperature for three families of spheroids: oblate, spherical, and prolate. Upon deformation, blue phases adapt and transform to accommodate the geometrical constraints, thereby resulting in a wider range of thermal stability. For oblate spheroids, confinement interferes with the development of a full blue phase structure, resulting on a combination of half skyrmions. For prolate spheroids, the blue phases are hybridized and exhibit features of blue phases I and II. More generally, it is shown that mechanical deformation provides an effective means to control, manipulate and stabilize blue phases and cholesterics confined in tactoids.

Palacio-Betancur, Viviana↗