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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Virtual Self-Excited Induction Generator-Based Grid-Forming Inverter Control for Robust Voltage Regulation Under Nonideal Loading

This paper presents a generator-inspired control methodology for grid-forming (GFM) inverters that deliberately emulates a self-excited induction generator so that the inverter can hold its voltage and frequency under difficult loading and severe terminal disturbances across wide voltage and frequency ranges. The design integrates a Lyapunov energy function-based inner loop to provide high bandwidth and strong disturbance rejection, and it complements this with a passivity-based argument that furnishes a coherent large-signal stability guarantee beyond small-signal limits. Analytical insights are developed via the Krylov-Bogoliubov-Mitropolsky averaging method, which reveals an intrinsic resistive droop characteristic; these closed-form relations both explain the observed dynamics and yield simple, decentralized tuning rules. The methodology is validated on a controller-hardware-in-the-loop platform and exercised in real time across balanced, unbalanced, and nonlinear loads, as well as during parallel operation. Across these scenarios, the inverter maintains balanced three-phase voltages, limits harmonic content, settles quickly with well-damped transients, and remains resilient when multiple units operate in parallel. The contributions are a self-excited-machine-inspired GFM controller with enhanced dynamic performance and robustness, a single stability rationale grounded in passivity, closed-form expressions that guide tuning, and comprehensive hardware-in-the-loop validations demonstrating effectiveness and superiority under challenging operating conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Interaction of Soil pH and Mineralogy Controls Soil Organic Matter Persistence through Changes in the Composition and Amount of Microbial Necromass

Microbial necromass–mineral associations are key to long-term soil organic matter (SOM) persistence. However, how soil pH and mineralogy interact to regulate SOM stability remains poorly understood. Here, we used artificial soils to test how three clay minerals (bentonite, kaolinite, and goethite), adjusted to four pH levels (5–8), affect microbial activity (respiration), microbial physiology (carbon use efficiency, CUE), microbial-derived residue material (necromass), and the formation and stability of mineral-associated organic matter (MAOM). Artificial soils were inoculated with a rhizosphere-derived microbial community cultured under the same pH conditions and on two representative simulated exudate types (organic acids and carbohydrates) and incubated for 6 weeks. In two complementary experiments, we added necromass from known microbial taxa to the same minerals across pH levels to isolate the role of necromass chemistry and loading. We found that soil pH shaped MAOM chemistry by altering microbial activity and necromass composition. In interaction with mineral type, pH also controlled MAOM thermal stability. Higher necromass loading weakened mineral-organic bonding, reducing MAOM stability, consistent with zonal mineral–organic interaction models. Our results demonstrate that microbial activity, rather than carbon use efficiency, better predicts MAOM formation and that pH-dependent necromass composition and loading govern MAOM persistence. These findings advance mechanistic understanding of SOM stabilization and have implications for predicting soil carbon dynamics under shifting environmental conditions.

carbon use efficiency↗
DOE OSTI2024

Role of dislocations on martensitic transformation temperatures and microstructure: A molecular dynamics study

Microstructure and defects strongly affect martensitic transformations in metallic alloys. Significant progress has been made in understanding the atomic-level processes that control the role of grain boundaries and precipitates in these solid-to-solid phase transformations. Yet, the role of dislocations and their structures on martensitic transformation temperature and the resulting microstructure remains unclear. Therefore, we used large-scale molecular dynamics simulations to study the forward and reverse transformation of a martensitic material modeled after Ni63Al37 under cyclic thermal loading. The simulations reveal that dislocations in the austenite phase act as one-dimensional seeds for the martensite phase, which is present at temperatures significantly above the martensite start value. We find a reduction in the dislocation density during cyclic thermal loading, which results in the increase in martensite and austenite transition temperatures, in agreement with experiments. Importantly, we extracted a critical martensitic nuclei size for developing stable domains and found that relatively low dislocation densities are needed to grow independent martensitic variants resulting in a multi-domain structure.

Physics↗
DOE OSTI2024

Dynamic performance of a passively self-adjusting floating wind farm layout to increase the annual energy production

One of the main differences between floating offshore wind turbines (FOWTs) and fixed-bottom turbines is the angular and translational motions of FOWTs. When it comes to planning a floating wind farm (FWF), the translational motions introduce an additional layer of complexity to the FWF layout. The ability of a FOWT to relocate its position represents an opportunity to mitigate wake losses within an FWF. By passively relocating downwind turbines out of the wake generated by upwind turbines, we can reduce wake-induced energy losses and enhance overall energy production. The translational movements of FOWTs are governed by the mooring system attached to it. The way a FOWT relocates its position changes if the design of the mooring system attached to it changes. Additionally, the translational motion of a FOWT attached to a given mooring system is different for different wind directions. Hence, we can tailor a mooring system design for a FOWT to passively control its motions according to the wind direction. In this work, we present a new self-adjusting FWF layout design and assess its performance using both static and dynamic methods. The results show that relocating the FOWTs in an FWF can increase the energy production by 3 % using a steady-state wake model and 1.4 % using a dynamic wake model at a wind speed of 10 m s -1 . Moreover, we compare the fatigue and ultimate loads of the mooring systems of the self-adjusting FWF layout design to the mooring systems in a current state-of-the-art FWF baseline design. The comparison shows that with smaller mooring system diameters, the self-adjusting FWF design has similar fatigue damage compared to the baseline design with bigger mooring system diameters at rated wind speed. Finally, the ultimate loads on the mooring systems of the self-adjusting FWF design are lower than those on the mooring systems of the baseline design.

17 WIND ENERGY↗
DOE OSTI2026

LAF-Net: A Deep Residual and Cross-Attention Framework for Day-Ahead Load Forecasting: Preprint

Accurate day-ahead load forecasting is essential for reliable power system operations and market efficiency. System operators such as the Midcontinent Independent System Operator (MISO) rely on forecasts from multiple vendors, yet combining them effectively remains a persistent challenge due to vendor-specific biases. This paper presents a novel LSTM-Attention Fusion Network with Error Representation (LAF-Net) that enhances day-ahead hourly load forecasting through deep residual learning and multi-modal cross-attention. The proposed model builds a historical error memory from past vendor performance and dynamically queries it with future hour context to generate adaptive, hour-specific trust weights for each vendor. A bounded residual correction further refines forecasts by mitigating systematic and temporally localized errors. Tested on real MISO LBA data with multi-vendor forecasts, LAF-Net consistently outperforms the best vendor baseline across all 38 LBAs, achieving more than a 40% reduction in system-level mean absolute error (MAE) during peak load hours relative to the best vendor baseline.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Holistic Small-Signal Stability Analysis for Large-Scale Inverter-Intensive Power Systems with Coupled and Full-Order Dynamics from Control Systems and Power Networks

The increasing penetration of inverter-based resources (IBRs) into the existing power systems introduces tremendous benefits for enhanced sustainability but also poses inevitable challenges in terms of insufficient inertia, potential instability, and complex network dynamics, among others. However, the additional coupling introduced by the interactions among gridfollowing (GFL) and grid-forming (GFM) IBRs and the other components (i.e., synchronous generators [SGs], loads, and network, etc.) has not been clearly explored. A holistic, scalable, and quantitative stability analysis framework with the control systems and power networks is still missing. Here, in this paper, to fill in the technical gaps, a holistic small-signal model of the entire system with both rotating generation units and IBRs is established. An extended power flow model with operation dynamics from both generator control schemes and power networks is proposed to provide the varying steady-state operating points for small-signal modeling. The proposed method is compared with MATLAB solvers, and the results show that the proposed approach has a minimum calculation time, which can be less than 12 seconds for a large-scale power system with up to 2,000 buses. Furthermore, a quantitative method is developed to identify the impacts of IBRs on system performance with emphases on the potential stability issues with GFL IBRs, additional benefits of employing GFM IBRs, the feasibility of replacing SGs with GFM IBRs, and the impact of penetration level of different kinds of generation units. Finally, a field island power system is used to verify the proposed approach, and hardware-in-the-loop (HIL) tests are provided to further demonstrate the effectiveness of the proposed analysis.

14 SOLAR ENERGY↗
DOE OSTI2024

Near wake evolution of a tidal stream turbine due to asymmetric sheared turbulent inflow with different integral length scales

Tidal stream turbines deployed at highly energetic open water sites are subjected to sheared inflow in the rotor plane. The inflow shear is expected to cause asymmetric loading on the rotor blades and affect the downstream wake. In the current study, two different turbulent inflow conditions, static-high shear and dynamic shear, were generated via an active-grid turbulence generator. A 1:20 scaled three-bladed horizontal axis tidal turbine model was tested in those conditions. The results were compared to a quasi-laminar case with no imposed turbulence or shear. The results show that the high shear reduces the average performance, with a drop of up to 16% in the optimal power coefficient. Besides, the shear profiles increase torque fluctuations and induce significant differences in wake hydrodynamics between the high-speed (upper) and low-speed (lower) regions. The large integral length scales further enhance the load fluctuations perceived by the rotor but have a negligible effect on the mean wake field quantities and the wake recovery. The lower half region featured a faster breakdown of tip vortex structure and a rapid drop of swirl number, a phenomenon conjectured to be a consequence of the strong turbulence intensities and Reynolds stresses in the lower half region. Furthermore, the sheared turbulent inflow also results in a very intensive energy redistribution process towards large-scale, low-frequency motions, which is important to the downstream turbines.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Operando FTIR investigation of salt dynamics in Li-ion batteries during fast charging

Li-ion batteries, when charged at fast-charging rates ($>$2C), suffer from reduced lifetimes and can undergo catastrophic failure. During high-rate charging, Li-ions are unable to rapidly transport through high-loading electrodes ($>$4 mAh cm −2 ). This results in unequal charge distributions, potentials, and utilization of the active material, which can lead to Li plating. Li-ion concentration polarization, in which Li-ions deplete in the anode and accumulate in the cathode during charging, precedes Li plating. An operando FTIR-ATR graphite/NMC cell developed in this research captured Li-ion concentration polarization in real-time. During fast charging, decreases in Li-ion concentration ($>$95%) were measured at the back of the anode. This is the first verification of complete Li-ion depletion within the anode at high C-rates. The measurements also showed graphite stage transition. A P2D model was developed for comparison to the operando measurements. The measurements agreed with the model in some cases, but disparities existed at high C-rates and loadings. In the experiment, the Li-ion concentration often failed to recover to 1.2 M until several hours after charging, whereas the model Li-ion concentration rapidly recovered. The contrast between the model and experiment results indicates that further investigation is required to improve understanding of Li-ion concentration dynamics during fast charging.

25 - ENERGY STORAGE↗
DOE OSTI2024

Shock-induced twinning/detwinning and spall failure in Cu–Ta nanolaminates at atomic scales

Here, this study provides new insights into the role of interfaces on the deformation and failure mechanisms in shock-loaded Cu–Ta–Cu trilayer system. The thickness of the Ta layer, piston velocities, and shock pulse durations were varied to explore the impact of impedance mismatch and loading conditions on spallation behavior and twin formation. It was found that the interfaces play a crucial role in the dynamic response of these multilayered systems since secondary reflection waves generated at the interfaces significantly affected the peak stress and pressure profiles, influencing void nucleation and failure modes. In the trilayer systems, failure predominantly occurred at interfaces and within the Ta layer, with void nucleation sites and twinning behavior being markedly different compared to single-crystal Cu and Ta. Increasing the Ta layer thickness modified the wave interactions, leading to different failure locations. Higher piston velocities were associated with increased spall strength by enhancing wave interactions and void formation, particularly at the interfaces and within the Ta layer, under specific configurations. Additionally, shorter shock pulse durations facilitated earlier initiation of the release fan, reducing twin formation and altering the failure dynamics by accelerating twin annihilation and pressure release.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Synchronous Machine Governor Upgrade

Conventional generation sources play a critical role in the stability and reliability of the electrical grid, particularly as we transition towards more renewable energy sources. To understand and accurately emulate their behavior for optimizing grid operations and ensuring seamless integration with renewable technologies, it is essential to better emulate the grid- and plant-level impacts of conventional generation sources, such as natural gas (NG) driven heat recovery steam generators (HRSGs) and combustion turbines (CTs). Therefore, a governor model is developed in a programmable logic controller (PLC) to investigate the performance of the conventional generator under various dynamic operating conditions and to identify the impact on grid stability in a controlled environment. The governor model aims to enable the hardware-in-the-loop (HIL) based emulation of these conventional generation sources using the existing 2 MVA synchronous machine/generator that is driven by a flexible 2.5 MW variable speed drive. This setup will allow us to replicate the dynamic characteristics and response behaviors of NG-driven HRSGs and CTs. The controls for the emulated conventional plants follow the industry standard and are adjustable, ensuring they accurately reflect the operational capabilities and limitations of real-world systems. These controls include load-following capabilities, ramp rates, startup and shutdown sequences, and emissions characteristics. By incorporating these adjustable controls, we aim to capture the nuanced impacts of conventional generation, such as their ability to provide ancillary services like frequency regulation, voltage support, and spinning reserve. In this report, we simulate two types of dynamic operations: grid-connected and islanding. For each dynamic operation, representative starting sequences are tested, including turbine purge, ignition, speed ramping up, generator excitation and synchronizing, and breaker close. The HIL based tests provides insights for field deployment, specifically the high-fidelity governor model provides results to predict the potential stability and reliability risk and suggest possible integration measures (e.g., generation and load balancing, tuning of governor control parameters). Ultimately, this enhanced emulation capability will be integrated into our Advanced Research on Integrated Energy Systems (ARIES), enabling us to conduct comprehensive studies on the interactions between conventional and renewable energy sources. By better understanding these interactions, we can develop strategies to optimize the overall performance and reliability of the grid. This will support the deployment of advanced grid management techniques, such as demand response, grid-forming inverters, and energy storage systems. The main contributions are summarized as follows: (1) This report introduces a PLC-based governor model for gas turbines. This model accurately simulates the dynamic behavior of conventional generation sources under various operational scenarios; (2) The model is integrated with an HIL testbed that includes a 2.5 MW variable speed drive and a 2 MVA synchronous machine. This setup enables realistic, real-time emulation of conventional power plants, particularly NG driven HRSGs and CTs; (3) The developed model is adaptable to various gas turbine configurations and allows for precise control over parameters such as MW ramp rates. This flexibility makes it a valuable tool for future research and industry collaboration; and (4) By incorporating the model into the National Renewable Energy Laboratory's Advanced Research on Integrated Energy Systems, the report lays the groundwork for future studies on interactions between conventional and renewable energy sources, enhancing the ability to develop advanced grid management strategies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

H ∞ Control for Energy Dispatch in Autonomous Nanogrid With Communication Delays

This paper proposes an optimal controller and estimator for energy dispatch to balance the power supply and demand considering communication delays. The proposed algorithm involves modeling an autonomous nanogrid (ANG) consisting of distributed energy resources, energy storage systems, loads, an $H$ ∞ controller with a reference power modulation technique, and a state estimator. The ANG was developed to express the dynamic supply-demand energy balance of a nanogird system. Reference power modulation was designed to generate the desired ESS power based on the imbalanced energy. Random communication delays were modeled using a stochastic variable satisfying the Bernoulli random binary distribution. The optimal $H$ ∞ controller and estimator were developed using a linear matrix inequality approach to exponentially stabilize the closed-loop system. Simulations were performed using real daily demand forecasts obtained from the Korea Meteorological Administration to demonstrate the effectiveness of the proposed real-time optimization algorithm.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Simultaneous Thermal Analysis of Anion and Cation Exchange Resins

The decomposition reactions of one anion exchange resin (Bio-Rad AG MP-1) and one cerium-loaded cation exchange resin (DOWEX 50W-X8), both in nitrate form, were analyzed using simultaneous thermal analysis methods. Thermogravimetric analysis, dynamic scanning calorimetry, and evolved gas analysis were deployed in combination to probe the temperature profiles, reaction enthalpies, and off-gases from these resins under process-relevant temperature ranges. Analysis indicates that both resins undergo three clear phases during heating. The first is a dehydration step with prominent off-gassing of water, the second is a decomposition step with evolution of several gaseous species, and lastly is a combustion step with a large release of CO 2 . The temperature at which combustion ends varies slightly between AG MP-1 and DOWEX 50W: combustion completed at ~690°C and ~810°C, respectively. For the DOWEX cation resin, the combustion reaction showed greater sensitivity to the availability of oxygen under the test conditions. Both resins displayed broad exotherms during the combustion step of the decomposition, but the DOWEX cation resin demonstrated a 4.5 times higher specific enthalpy than that of the AG MP-1.

36 MATERIALS SCIENCE↗
DOE OSTI2026

The Hydropower Game: An Interactive Learning Tool for the Future Hydropower Workforce

This report documents a Seedling project supported by the U.S. Department of Energy (DOE) Water Power Technologies Office (WPTO), conducted by Argonne National Laboratory (ANL) and the National Laboratory of the Rockies (NLR). The Seedling and Sapling Program provides small grants over short duration to enable early-stage research at national laboratories. This funding mechanism is intended to cultivate innovative ideas and expand research road maps in hydropower and marine energy technologies. Under this Seedling award, the project team developed an educational outreach tool, or “serious game”, built in Python and powered by the Pygame library, aimed at teaching fundamental hydropower concepts through an engaging, interactive learning experience. The game features multiple lessons covering several hydropower topics while allowing for expansion and customization in the instance of future funding availability: • Hydropower Plant Types: Players explore and compare the mechanics and applications of run-of-river, dam hydropower, and pumped-storage hydropower. • Flow Dynamics and Power Generation: Interactive tasks demonstrate how release rate and hydraulic head combine to determine power output. • Grid Operations and Load Following: Simulations illustrate how hydropower facilities respond to fluctuating electricity demand to balance the grid. • Market Integration: Levels scaffold understanding of how hydropower interfaces with the broader energy market, including operational and economic considerations. The tool was showcased at several science, technology, engineering, and mathematics (STEM) outreach events, where it was demoed to students, educators, and the general public. These events provided valuable opportunities to collect feedback on the gameplay, storyline, and educational objectives from a wide audience. The game was presented at STEMapalooza, Introduce a Girl to Engineering Day, STEMCON, and Clean Currents 2025. Insights gathered during these demonstrations informed refinements to the game’s user experience and strengthened its effectiveness as an educational tool for teaching hydropower concepts. This report outlines the game’s design philosophy, educational objectives, technical implementation, user experience insights, and potential for broader deployment within educational and workforce development contexts. It emphasizes how gamified learning can demystify complex hydropower science and inspire interest in water-power technologies. The project’s success demonstrates the value of Seedling funding in fostering creative, lowcost educational tools that support DOE’s mission to advance energy literacy and innovation. The report concludes with recommendations for expanding the tool by adding new levels, integrating assessment metrics, and exploring commercialization or deployment pathways through future Sapling funding. The official webpage of the Hydropower Game, which includes a link to the educational tool, can be accessed at www.anl.gov/hydropower/hydropower-game.

13 HYDRO ENERGY↗
DOE OSTI2024

Alfalfa

Alfalfa-based testbeds enable building equipment, control products, and workforce development tools to interact with dynamic building simulations representing the desired building, system, weather, and grid configuration. Alfalfa is used to de-risk implementation of load flexibility prior to field deployment, reducing the costs and timelines associated with adoption of decarbonization technology at the grid edge.

building energy modeling↗
DOE OSTI2025

Dynamic compression effects of H 2 ⁡O in a dynamic diamond anvil cell: Origin of metastable ice VII and its crystal growth kinetics

We report on the structural verification of metastable ice VII solidifying in the phase space of ice VI at 1.80 GPa at room temperature. Using time-resolved (TR) x-ray diffraction and TR ruby luminescence paired with high-speed microphotography utilizing a dynamic diamond anvil cell, an initial compression rate range from 0.12 to 95.84 GPa/s was explored. The solidification pressure of metastable ice VII has a potential sigmoidal dependence upon compression rate with a turnover compression rate of ∼80 GPa/s. The preferred crystallization of ice VII in the stability field of ice VI is due to the increased nucleation rate of ice VII over ice VI at 1.77 GPa that is driven by the surface energy difference between the liquid and solid phases along with the change in Gibbs free energy of solidification. The dynamic pressure-volume–compression behaviors of ice phases (VI and VII) show a lattice stiffening in both phases, especially during the compression loading. It is also found that the compression rate greatly affects the solid-solid phase transition between ice VI and VII but does not affect the liquid-solid transition between water and ice VI as much. Lastly, a third phase transition was found to occur after metastable ice VII transforms into high-density amorphous (HDA) ice, which could be a disordered hydrogen-bonded network configuration of ice VII forming out of HDA ice facilitated by the decoupling of the oxygen movement and reorientation of the H 2⁡ O molecule. These results demonstrate the complexity of a seemingly simple molecule H 2⁡ O, how it can readily change its static properties with the modification of (de)compression rate, and highlight the need to use multiple TR structural and spectroscopic probes at higher time resolutions to realize the most comprehensive understanding.

Chemical bonding↗
DOE OSTI2026

Computational simulation of asymmetric phase transformation in cracked Li₇La₃Zr₂O₁₂: Variant selection and chemo-mechanical implications

Coupling between microcracks and phase transformation in ion-conducting ceramics can jointly affect mechanical responses and ion transport. In this work we investigate the cubic-to-tetragonal phase transformation in Li₇La₃Zr₂O₁₂ in the presence of a microcrack under hydrostatic loading and quantify its implications for crack-tip stress concentration and Li-ion transport using phase-field and molecular dynamics simulations. The phase transformation exhibits a strong asymmetry between hydrostatic tension and compression. Under tension, the crack edge nucleates one tetragonal variant that amplifies the crack-tip stress intensity and promotes crack opening. Under compression, the crack tip nucleates a different tetragonal variant that enhances the stress-induced crack-closure tendency. Effective Li diffusivity analysis shows faster transport degradation under compression due to accelerated transformation kinetics, exposing a trade-off between mechanical stability and ionic conductivity. These results highlight the intertwined nature of cracking, phase transformation, and ionic transport in ion-conducting oxides and provide mechanistic insights into chemo-mechanical degradation of solid electrolytes.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Structural response reconstruction using a system-equivalent singular vector basis

Here, this paper develops a novel method for reconstructing the full-field response of structural dynamic systems using sparse measurements. The singular value decomposition is applied to a frequency response matrix relating the structural response to physical loads, base motion, or modal loads. The left singular vectors form a non-physical reduced basis that can be used for response reconstruction with far fewer sensors than existing methods. The contributions of the singular vectors to measured response are termed singular-vector loads (SVLs) and are used in a regularized Bayesian framework to generate full-field response estimates and confidence intervals. The reconstruction framework is applicable to the estimation of single data records and power spectral densities from multiple records. Reconstruction is successfully performed in configurations where the number of SVLs to identify is less than, equal to, and greater than the number of sensors used for reconstruction. In a simulation featuring a seismically excited shear structure, SVL reconstruction significantly outperforms modal FRF-based reconstruction and successfully estimates full-field responses with as few as two uniaxial accelerometers. SVL reconstruction is further verified in a simulation featuring an acoustically excited cylinder. Finally, response reconstruction and uncertainty quantification are performed on an experimental structure with three shaker inputs and 27 triaxial accelerometer outputs.

42 ENGINEERING↗
DOE OSTI2026

Modeling the contributions to acoustic nonlinearity from complex dislocation networks using 3D dislocation dynamics

Nonlinear ultrasonic parameters are highly sensitive to microstructural features that affect macroscale material behavior, providing a nondestructive means to characterize their evolution. Although dislocations are known to be a strong source of acoustic nonlinearity, establishing quantitative links between the acoustic nonlinearity parameter (β), measured via Second Harmonic Generation, and dislocation morphology—such as dislocation length and density—remains an open challenge. This work advances the numerical modeling of dislocation–β relationships using 3D dislocation dynamics (DD) simulations in two approaches: a “static” method computing strain and stress fields from dislocation configurations in the absence of external loading, and a “quasi-static” method to estimate β from the curvature of dislocation lines under applied load. First, the static method is combined with finite element analysis to investigate a recent assertion that heterogeneous initial strain fields can induce higher harmonic generation in a linear elastic medium; the present results do not corroborate this outcome. Then, the quasi-static method is applied to multiple-dislocation scenarios through parametric studies, revealing behaviors not predicted by analytical models, such as the competing interactions of edge and screw dislocations and the significant influence of applied stress on β. Finally, the simulations are used to model SHG experimental results and validate the hypothesis that β can decrease during plastic deformation, despite increasing dislocation density. As the DD code used here is open-source, it provides a practical platform for future investigation into microstructure–β relationships important to the interpretation of SHG results.

Materials science↗