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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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

LLM-Based Adaptive Distribution Voltage Regulation Under Frequent Topology Changes: An In-Context MPC Framework

This paper proposes a large language model (LLM) based adaptive inverter control for distribution voltage regulation under frequent topology changes. We leverage the ability of the LLM to perform in-context learning and create a topology-adaptive surrogate model for power flow calculation. The surrogate model is then integrated with a long short-term memory-based load forecaster and a model predictive control (MPC) scheme to achieve the optimal inverter control that adapts to frequent topology changes. Unlike many existing works that assume fixed-topology grids or require the knowledge of all possible topologies when training a model, the proposed in-context MPC method tackles the distribution voltage control problem under various topologies and adapts to unknown topologies with limited data requirement for fine-tuning. The effectiveness of our method is demonstrated on a modified IEEE 123-bus test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Experimental investigation on phase change material–based finned tube heat exchanger for thermal energy storage and building envelope thermal management

Phase change materials (PCMs) are attractive solutions for thermal energy storage (TES) applications by absorbing and releasing large amounts of latent heat during solid–liquid phase transitions. However, their relatively low thermal conductivity requires novel heat exchanger–based solutions to improve the power density and overall energy storage efficiency of the TES system. This work presents the design and experimental results of a finned tube heat exchanger to store collected natural thermal energy from a building envelope in a latent-based TES and to release it later for building heating/cooling applications. We experimentally evaluate the finned tube heat exchanger and evaluate the performance of TES in reducing building heating and cooling loads over 3–4 h of desired time of operation (e.g., peak load). The optimized design allows for maximum energy density by minimizing the heat exchanger volume, and the system is evaluated experimentally using commercially available heat exchanger materials and an organic PCM. Here, the experimental results reveal that the TES system is able to charge and discharge stored latent energy within 3–4 h, matching peak building electricity demand duration under an average fluid flow rate of 0.136 kg/s and temperature difference of 5.55 °C. Importantly, such optimized designs illuminate a path toward TES designs that are low-cost, scalable, and optimized for thermal energy and power availability under the desired time of operation.

25 ENERGY STORAGE↗
DOE OSTI2023

Loose Belt Fault Detection and Virtual Flow Meter Development Using Identified Data-driven Energy Model for Fan Systems

An energy model that correlates fan airflow, head, speed, and system power input is essential to detect device faults and optimize control strategies in fan systems. Since the application of variable-frequency drives (VFDs) makes the motor-efficiency data published by manufacturers inapplicable for VFD–motor–fan systems, the fan efficiency and drive (belt–motor–VFD) efficiency must be identified for each individual system to obtain accurate energy models. The objectives of this paper are to identify an energy model of existing VFD–motor–fan systems using available experimental data and demonstrate its applications in loose belt fault detection and virtual airflow meter development for optimal control. First, an approach is developed to identify the fan head, fan efficiency, and drive-efficiency curves using available fan head, speed, and system power input as well as temporarily measured airflow rate without measuring shaft power. Then, the energy model is identified for an existing VFD–motor–fan system. Finally, the identified model is applied to detect the slipped belt faults and develop the virtual airflow meter. The experiment results reveal that the developed approach can effectively obtain the energy model of VFD–motor–fan systems and the model can be applied to effectively detect slipped belt faults and accurately calculate the fan airflow rate.

42 ENGINEERING↗
DOE OSTI2022

High Performance Flow Battery with Inexpensive Inorganic Reactants: DAYS Program (Final Technical Report)

RTRC’s DAYS projects focused on new flow battery (FB) chemistries for long duration energy storage: one that pairs aqueous polysulfide and manganese active materials in strongly alkaline electrolytes (S/Mn); another explores ligand-modified metal (LMM) chemistries in moderate pH electrolyte conditions. The S/Mn chemistry met durability targets by running for over 500 cycles and 1000 hours. Combined with this durability, power densities of up to 60 mW/cm2 at 80% round-trip efficiency, and exceptionally low-cost S and Mn active materials, the S/Mn FB offers a pathway to meeting the <5¢/kW-hr levelized cost of storage (LCOS) target first proposed by the DAYS Program and accepted by the DOE Energy Storage Grand Challenge. The LMM chemistry made impressive progress as well, including durability tests that retained performance over 600 hours of cycling. Cell optimization allowed this chemistry to operate as high as 500 mW/cm2 at 80% round-trip efficiency, nearly 10x the power density of S/Mn and comparable to the power density achieved in RTRC’s flow battery stacks using acidic vanadium battery solutions. This enabled the LMM chemistry to also offer a pathway to the <5¢/kW-hr LCOS DAYS and DOE targets. The promising results from the LMM chemistry have led to a recent DOE AMO award to advance the technology to a 5 kW, 20 kW-hr prototype.

25 ENERGY STORAGE↗
DOE OSTI2021

A System of Agents for Supporting Optimization and Control of a Connected Community

The residential sector consumes a significant portion of the electricity sold in the United States. Above 60% of the energy used in the sector is used to operate heating, ventilation, and air conditioning (HVAC) systems and water heating (WH) systems. With the increase of intelligence in the grid and the new decision and control options enabled by the Internet of Things; control of these devices can be used to support the grid. Therefore, this article presents a scalable multiagent system for optimizing HVAC and WH systems while maintaining comfort. It allows a utility to orchestrate the shifting of energy from critical periods without direct control, but instead by using a price signal. The architecture, optimization formulation, implementation strategy and results from an implementation project are discussed.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Artificial Intelligence-Aided Wind Plant Optimization for Nationwide Evaluation of Land Use and Economic Benefits of Wake Steering

If clean energy pathways are to harness massive increases in wind power, innovations with broad geographic viability will be needed to support buildout in diverse locations. However, geodiversity in impact potential is seldom captured in technology assessment. Here we propose a scalable approach to plant-level optimization using artificial intelligence to evaluate land sparing and economic benefits of wake steering at more than 6,800 plausible onshore wind locations in the USA. This emerging controls strategy optimizes plant energy production by directing turbine wakes. On the basis of estimates from our artificial intelligence model trained on engineering wind flow simulations, co-optimizing plant layouts with wake steering can reduce land requirements by an average of 18% per plant (site-specific benefits range from 2% to 34%), subject to errors and uncertainties in the flow model, wind resource estimates, buildout scenario and geographic factors. According to model estimates, wake steering is predicted to increase power production during high-value (relatively low wind) periods, boosting the annual revenue of individual plants by up to US$3.7 million (equivalent to US$13,000 MW-1 yr-1) but producing negligible gains in some settings. Consideration of wake steering’s geographic potential reveals divergent nationwide prospects for improved economics and siting flexibility.

deployment↗
DOE OSTI2023

Water Recovery From Cooling Tower Plumes

According to studies by the UN and the US State Department, we are on the path to an extreme freshwater shortage by 2030. The US’s largest water withdrawal source is power plants, which account for 39% of total US freshwater withdrawals, mostly for cooling. Cooling towers are the most common cooling system. To solve these problems and enable efficient water- based cooling – Infinite Cooling’s novel technology uses electric fields to ionize the air, charge the escaping water leaving cooling towers and direct the water toward mesh collectors where it collects and gets recycled for use in the cooling system. This technology was developed at MIT and was reduced to practice on a lab-scale prototype, and a prototype at the MIT Cogeneration Power Plant. This DOE award funded taking this technology from a lab-scale prototype to TRL 5 on an operating cooling tower in the field at the MIT Nuclear Research Laboratory. The funding helped to design and optimize an electrostatic plume collection system and test it in high-fidelity lab setting and in actual field conditions on a cooling tower. Throughout the award, Infinite Cooling investigated the formation of plumes on cooling towers, used that information to optimize the design, material and electrical properties of the collection device and quantified the collection yield via flow rate and water quality.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2025

Comparison of wind farm control strategies under realistic offshore wind conditions: turbine quantities of interest

Abstract. Wind farm flow control is a strategy to increase the efficiency and therefore lower the levelized cost of energy of a wind farm. This is done using turbine settings such as the yaw angle, blade pitch angles, or generator torque to manipulate the flow behind the turbine, affecting downstream turbines in the farm. Two inherently different wind farm flow control methods have been identified in the literature: wake steering and wake mixing. This paper focuses on comparing the turbine quantities of interest between these methods for a simple two-turbine wind farm setup, while a companion article (Brown et al., 2025) focuses on the wake quantities of interest for a single wind turbine setup. Both papers use the same set of wind farm simulations based on high-fidelity large-eddy simulations (LESs) coupled with OpenFAST turbine models. First, precursor simulations are executed in order to match wind conditions measured with lidars in an offshore wind farm off the east coast of the USA. These measurements show general wind conditions that exhibit substantially higher vertical wind shear and veer than any of the LES studies performed with wind farm flow control strategies currently available in the literature. The precursors are used to evaluate the effectiveness of the control methods. In the LES, the wind veer leads to highly skewed wakes, which have considerable influence on the power uplift of wind farm flow control strategies. In addition to a baseline controller, four different control strategies, each of which uses either pitch or yaw control, are performed on the upstream turbine of a simple two-turbine wind farm. Assuming that the wind direction is known and constant over time, the simulations show that wake steering is generally the superior wind farm flow control strategy, considering both wind farm power production and turbine damage equivalent loads when substantial wind veer is present. This result is consistent over different wind speeds and wind directions. On the other hand, for similar wind conditions with lower veer, wake mixing was found to yield the highest power production, although at the expense of generally higher loads. This leads us to conclude that the effect of wind veer, which has so far not usually been considered, can not be neglected when determining the optimal wind farm flow control strategy.

17 WIND ENERGY↗
DOE OSTI2023

Optimization of Dimensions of Smooth and Twisted-Tape-Inserted Tubes for Heat Transfer with NaCl/KCl/MgCl 2 Molten Salts by Principle of Entropy Generation Minimization

The entropy generation minimization principle is used as the criterion to optimize the flow and heat transfer of solar collectors and heat exchangers that use molten salts NaCl–KCl–MgCl 2 and KCl–MgCl 2 . The Gnielinski correlation for the Nusselt number versus Reynolds number, as well as the Moody friction factor given by Petukhov, was used for the calculation of the convective heat transfer coefficient and pressure loss due to friction in smooth tubes. For twisted-tap-inserted tube, equations of Nu and friction factor provided by Manglik and Bergles were used. The objective function, the entropy generation rate of the heat transfer system, was expressed as the function of Reynolds number, Prandtl number, heating flux, tube diameter, etc. As a result of the analysis, the optimum Reynolds number was determined and thereby to determine the optimum Nusselt number, convective heat transfer coefficient, friction factor, and tube diameter, which also allows the calculation of optimum flow velocity. The analysis was conducted in the fluid temperature range of 500–700 °C, which covers the operation temperature for supercritical CO 2 power cycles in concentrated solar power (CSP) system. Here, optimized results from the smooth tube and twisted-tap-inserted tube are compared, which is important to the design of solar receivers for CSP systems.

14 SOLAR ENERGY↗
DOE OSTI2023

ML-ACCEPT: Machine-Learning-enhanced Automated Circuit Configuration and Evaluation of Power Converters

This project, ML-ACCEPT, took a significant step toward achieving the first objective of the DIFFERENTIATE program: to help engineers to more rapidly and cost-effectively consider a wider range of more novel concepts before selecting an engineering-optimal architecture for high-fidelity detailed design and evaluation. Compared to existing methods, the ML-ACCEPT project investigated innovative technologies to make the design of power converters more cost-effective and time-efficient by i) integrating recent breakthroughs in ML, power electronics, simulation software, and optimization to research, develop, and developed a suite of ML-enhanced hypothesis generation tools for power converter design; and ii) facilitating the integration of the proposed software tools into existing power-converter design work-flows. Some existing tools for power-converter design have a certain level of intelligence to aid the design process, but to our knowledge none of them has ML-enhanced capability of automating the electrical circuit design process by selecting, configuring, and tailoring the individual components that enable available resources (e.g., high-voltage DC power) to be converted to the desired output (e.g., lower-voltage DC power with a desired voltage ripple), subject to application-specific (e.g., plasma generation and automotive applications) thermal and packaging considerations. The state-of-the-art circuit design of power converters is still heavily reliant on human experts to select the optimal topology and search for design parameters with human’s experience and intuitions, which can be very time-consuming, inefficient, and labor intensive. The team is composed of University of Michigan-Dearborn (UM-Dearborn), Lawrence Livermore National Laboratory (LLNL), Oak Ridge National Laboratory (ORNL), Modelon Inc., and lighthouse customers.

42 ENGINEERING↗
DOE OSTI2022

Vehicle-to-manufacturing (V2M) system: A novel approach to improve energy demand flexibility for demand response towards sustainable manufacturing

The U.S. manufacturing sector accounts for 77% of the industrial energy consumption, but its participation in demand response (DR) programs is largely lagged behind. The limited flexibility in production scheduling under high capacity utilization and the lack of DR schemes that incorporate energy demand flexibility measures are deemed as major barriers. In this study, a framework of the interactive vehicles-to-manufacturing (V2M) energy sharing system is proposed to improve the energy demand flexibility of the aggregated system and enhance the DR effectiveness for manufacturers. The V2M-based DR scheme aims to reduce the energy cost by load shifting through joint production and energy sharing control, which can eventually promote manufacturing DR implementation even under high capacity utilization requirements and dynamic real-time electricity prices. The V2M system is modeled based on a discrete-Markov chain considering the complex interconnections among various manufacturing resources and multi-directional energy flows among manufacturing facilities, electric vehicles, and the power grid. Based on the system model, a mixed-integer nonlinear programming (MINLP) problem is formulated to identify the optimal DR scheme. The effectiveness of the proposed approach is validated through comparisons with traditional manufacturing DR schemes. Finally, the results show that a 2.1 to 6.5 times energy demand flexibility improvement and an additional 4.7% to 6.9% energy cost reduction can be achieved by the proposed approach.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Observation of fully detached divertor integrated with improved core confinement for tokamak fusion plasmas

Integration of divertor detachment with a high-performance (β N ~ 3, β p > 2, H 98 ~ 1.5) core plasma has been demonstrated in DIII-D high-β p (poloidal beta) plasmas associated with a sustained core internal transport barrier (ITB) and an H-mode edge transport barrier (ETB). Such good core-edge integration has been achieved for both neon and nitrogen seeding, for both favorable and unfavorable B-field directions, independently from the impurity puffing locations, though these variations play important roles on divertor characteristics. Compared to the standard H-mode plasmas, the high-β p plasma exhibits a much wider window of detachment compatible with high confinement core. Fully detached divertor plasmas with low plasma temperature (Te < 5 eV), low particle flux, and low heat flux across the entire divertor target plate were obtained by using nitrogen seeding. This detached high-β p plasma is compatible with a newly developed detachment control system which can help optimize the nitrogen gas flow rate. Several features, i.e., the high edge safety factor in the high-β p scenario, impurity injection, closed divertor and reduced heating power requirement due to the high confinement, facilitate the achievement of full divertor detachment at lower density. Instead of degrading global performance, the divertor detachment facilitates the access to an even stronger ITB at large radius with a relatively weak ETB through self-organized synergy between ITB and ETB, leading to sustained high confinement. The strengthening of the large-radius ITB compensates for the ETB degradation associated with divertor detachment. In addition, a weak ETB naturally has smaller edge localized modes (ELMs). In particular, with neon injection, a long-period no-ELM H-mode phase has been achieved simultaneously with high-performance core and partially detached divertor plasmas. Furthermore, these results demonstrate the possibility of integrating excellent core plasma performance with an effective divertor solution, an essential step toward steady-state operation of reactor-grade plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Improving AHU Performance by Minimizing Approach Temperature, Reducing Air Maldistribution, and Efficiently Handling Sensible and Latent Loads (Phase 1 Interim Final Technical Report)

Residential air handling units (AHUs) have stayed the same in form and efficiency for the past 30+ years, with incremental improvements made to address safety, functionality, and energy-efficiency. The purpose of this research in Phase I, Topic 9a: Next Generation Residential Air Handlers, was to improve AHU performance by minimizing heat exchanger (HX) approach temperature, reducing air maldistribution, and developing alternative system configurations which more efficiently handle sensible and latent loads. In this research Optimized Thermal Systems (OTS) developed, modeled, and evaluated multiple alternative system concepts. A dual vapor compression system separate sensible and latent cooling (SSLC) concept was studied to inform work on alternative concepts and to show best-case performance benefit. System concepts included ejector enhanced vapor compression cycles, desiccant assisted dehumidification, dual evaporator SSLC, and alternative AHU HX configurations. A dual vapor compression system showed COP improvement of 20%, however, required additional components, increased unit size, and increased cost. Two types of ejector enhanced vapor compression cycles with dual evaporators improved system COP by 9 to 11%, and reduced AHU losses by as much as 18%, with design changes limited to the AHU, no unit physical size increase, and a moderate increase to system first cost. Desiccant assisted air-conditioning required increased air flow rate resulting in higher fan power and the desiccant wheel increased sensible heat load leading to increased compressor power and reduced system COP. Dual evaporator cycles were found to degrade performance due to increased expansion losses. Optimized single slab HX designs used in place of the traditional A-coil HX led to 44–49% reduction in aluminum, 47–60% less refrigerant charge, and improved HX velocity distribution.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Data-Driven Modeling of a High Capacity Cryogenic System for Control Optimization

The Cryogenic Moderator System (CMS) is responsible for maintaining a steady flow of cold neutrons for numerous physics experiments at the Spallation Neutron Source (SNS) in Oak Ridge National Laboratory (ORNL). Sudden losses in beam power, known as beam trips, cause a major disturbance to the CMS due to large step changes in cooling demands. Ongoing efforts on upgrading the neutron beam power from 1.4 to 2.0MW are expected to generate larger transients that can further strain the CMS subsystems if they are not properly controlled. To manage such disturbances, four flow valves and one electric heater are adjusted by five decentralized proportional-integral-derivative (PID) controllers. However, the original PID gains were calibrated empirically based only on tracking performance and not based on disturbance rejection. To address this issue without compromising current CMS operations, a control-oriented model was developed to recalibrate the PID controllers offline. The zero-dimensional (0-D) model was based on simple physics-based principles and data-driven system identification techniques. The CMS was broken into several subsystems for analysis, each of which corresponds to a parametric model tied to the thermodynamic states of the working fluid. The model parameters were identified using the nonlinear least squares method where the residuals were calculated from available sensor data. Simulation results show that the proposed model can capture the dynamics of the CMS at steady state and during beam trips.

Maldonado Puente, Bryan↗
DOE OSTI2022

Coordinated operation of pumped-storage hydropower with power and water distribution systems

Small pumped-storage hydropower (PSH) units have gained popularity as distributed energy storage options that can provide flexibility to the operation of power distribution systems. Optimal operation of small PSH units is not only dependent on the energy storage provided to power distribution system, but also on the inflow and outflow of water from and to the water distribution system. Here, in this context, this paper develops an optimization model for coordinated operation of PSH units with power and water distribution systems. The proposed model optimizes the operation of water tanks, variable-speed pumps and PSH in pumping and generating modes to minimize the operation cost of power distribution system, while respecting the power flow constraints of power distribution and hydraulic constraints of water distribution system. Appropriate electricity tariffs are implemented to avoid additional expenses in water distribution system that can be enforced by its coordinated operation in favor of power distribution system. The proposed model is implemented on a 33-bus and a 123-bus test power distribution system connected to a 16-node test water distribution system. Results demonstrate the effectiveness of proposed model in tapping PSH flexibility to reduce the operation cost of power and water distribution systems, while meeting the power and water demands.

13 HYDRO ENERGY↗
DOE OSTI2024

Percheron Power Archimedes Screw Turbine Analysis (Abstract)

The development of the Percheron Power (Percheron) composite Archimedes screw turbine (AST) is based upon employing newly developed theoretical mathematical models for optimizing the water volume carried through the AST for a given diameter, combined with minimizing efficiency losses due to bypass flow and friction. The key feasibility issues associated with producing the composite blades will be to understand the strength, fatigue, and wear performance of the AST blades and associated components, and how these factors change along the length of the turbine. To get to this understanding of material property requirements, Percheron needs free-surface computational fluid dynamics (CFD) models of the AST designs and to perform interactive modeling between the turbine blade optimization and component design based on finite element method stress analysis (FEA). The workscope and analyses requested by Percheron in the Small Business Voucher (SBV) program are well aligned with PNNL capability and recent work experience in performing CFD and FEA analysis for hydropower and marine energy turbines. The CFD analysis will provide estimates of power, efficiency, and surface forces on the blades. The forces on the blade will be transferred to the FEA analysis that will be used to evaluate the material stresses. The CFD and FEA analyses will be repeated for different AST designs provided to PNNL by Percheron. The work conducted in this SBV project will complement the existing Percheron FOA project by providing better defined parameters for design and material selection for the turbine unit prior to manufacture of initial test units.

42 ENGINEERING↗
DOE OSTI2023

Parametric and Sensitivity Analysis of a Steam Generator Model Using Python and Machine-Learning Tools

For this study, we used Python and machine-learning tools to perform a comprehensive parametric and sensitivity analysis on a steam generator (SG) model. (The Python model was based on a previously completed MATLAB framework for the Holtec SMR-160 SG.) We investigated the influence of various input parameters (e.g., heat transfer coefficient [HTC], Nusselt number, and heat exchanger effectiveness) on the system’s output. With machine-learning tools such as the Risk Analysis Virtual Environment (RAVEN), which was developed at Idaho National Laboratory, we were then able to perform an automated analysis of the SG inputs’ effect on the HTC. The analysis results give valuable insights into the performance and optimization of SG systems. We found the inlet mass flow rate (MFR) to have the greatest impact on the HTC, followed closely by the inlet temperature, and then pressure. Shifting of the input parameters causes the location of the maximum HTC along the SG length to change incrementally. The cold leg (CL) MFR was also found to impact the HTC magnitude as well as the location of the maximum HTC. At between 0.4–0.9 of the total SG length, the input parameters experience maximum impact on the HTC, leading us to suggest that sensors be efficiently placed on the SG so as to closely and effectively monitor thermal-hydraulic properties during reactor operation. We also found that the sensitivity data calculated manually agrees with the RAVEN – based data, confirming the same range of maximum sensitivity. However, the RAVEN-based analysis showed that cold leg pressure and hot leg temperature have a greater impact on the heat transfer coefficient than the mass flow rate, implying that a manual sensitivity study taking only two samples is not accurate.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2025

A phase-field fracture formulation for generalized standard materials: The interplay between thermomechanics and damage

Accurately modeling fracture of ductile materials poses open challenges in the field of computational mechanics due to the multiphysics nature of their failure processes. Integrating the interplay between thermodynamics and damage into ductile fracture models is vital for predicting critical failure modes. Here, in this paper, we develop a versatile phase-field (PF) framework for modeling ductile fracture, taking into account finite-strain elasto-plasticity. The framework stems from a variational formulation of constitutive relations for generalized standard materials (GSMs), whose response is described by a Helmholtz free energy and a dissipation pseudo-potential. Its variational structure is based on a minimum principle for a functional that expresses the sum of power densities for reversible and irreversible processes. By minimizing this functional with a constraint on a von Mises yield function, we derive the evolution equation for the equivalent plastic strain and an associative flow rule. This constrained optimization problem is analytically solved for a wide class of thermo-viscoplasticity models. The key innovations of the current work include (i) a cubic plastic degradation function that accounts for a non-vanishing damage-dependent yield stress, (ii) closed-form expressions of the Helmholtz free energy and dissipation pseudo-potential for three thermo-viscoplasticity models, (iii) an extended Johnson–Cook plasticity model with a nonlinear hardening law, and (iv) a plastic work heat source that depends on the plastic degradation function and a variable Taylor–Quinney (TQ) coefficient. The capabilities of the proposed framework are tested with the aid of four ductile fracture problems, including the Sandia Fracture Challenge. In each of these problems, we examine the evolution of relevant field variables such as the PF order parameter, the equivalent plastic strain, the temperature, and the internal power dissipation density, in addition to the overall structural response quantified by the force–displacement curve. These numerical studies demonstrate that the proposed framework effectively represents ductile fracture, yielding computational results that exhibit good agreement with experimental data.

36 MATERIALS SCIENCE↗