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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

The role of surface forces in environment-enhanced cracking of brittle solids

Fracture initiation and propagation in brittle materials is promoted in surface-reactive (sorptive) environments, a phenomenon known as subcritical crack growth (SCG). Laboratory measured crack-propagation velocity vs. stress intensity factor relationships typically exhibit highly nonlinear, multi-stage characteristics that are sensitive to environmental factors such as adsorbate concentration and temperature. For practical purposes, empirical relationships (e.g., a power law) have been used to describe this complex phenomenon. However, how the overall SCG behavior emerges from the underlying fundamental processes near the crack tip, such as the interaction of the crack surfaces separated by only a few nanometers and mass transport within the nano-confined space, is still not well understood. This paper develops a mechanistic, surface-force-based fracture theory (SFFT) which integrates surface force models, fluid transport models, and linear elastic fracture mechanics to quantitatively explain the multi-stage characteristics of SCG in brittle solids. A numerical model is developed based on SFFT and solved through an implicit partitioned scheme for efficiency and modularity. The results are validated by Wiederhorn's data on crack propagation in soda-lime glasses at a wide range of relative humidity levels. We show that, for the first time, the entire range of an SCG curve can be captured by a single physics-based model. The predicted SCG curves reveal that the development of repulsive disjoining pressure behind the crack tip can be responsible for the reduced apparent fracture toughness in a sorptive environment. In conclusion, the shape of the SCG curve, and its changes with respect to the environment, is found to critically depend on the assumed transport models.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Robust Solar Receivers Using MAX Phase Materials

This work was supported by the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy under the Solar Energy Technologies Office Award Number 35928. The objective of the proposed effort was to develop and optimize additive manufacturing technologies for low-cost fabrication of high-temperature receivers using MAX phase-based materials (Ti 3 SiC 2 and Ti 3 AlC 2 ). MAX phase materials are a group of ternary metal carbides and nitrides where M stands for an early transition metal element, A is a group 13–16 element, and X is C and/or N. In Phase 1, the binder jetting additive manufacturing process was used to synthesize and characterize the Ti 3 SiC 2 MAX phase material. The typical process involved first producing a TiC preform using binder jetting followed by infiltration of the preform with silicon melt to form Ti 3 SiC 2 in situ. The reaction-infiltrated samples showed formation of MAX phase in the sample core; however, the surface showed cracking. Various process conditions—cooling rates, hold times, Si proportion, etc.—were varied to minimize the surface cracking. The fabricated MAX phase core was characterized by microstructure analysis and evaluations of mechanical properties such as hardness and thermal shock. In Phase 2, the focus included fabrication of Ti 3 SiC 2 MAX phase materials by spark plasma sintering (SPS) and synthesis of Ti 3 AlC 2 MAX phase materials by the Al melt infiltration process. It is expected that Al infiltration will not cause sample cracking, since Al does not expand during solidification. In addition, other processing approaches were investigated to fabricate the MAX phase materials, such as SPS with a graphite bedding approach for producing short-length Ti 3 AlC 2 MAX phase tubes for demonstration of prototypical Concentrating Solar Power receiver tubes. Fabricated samples underwent thermo-mechanical testing to validate the materials for the solar receiver application at temperatures >1000°C. In Phase 3, the effort focused on the development and optimization of the Ti-Al-C MAX phase composite material using the Al melt infiltration approach. We started with optimization of precursor powders and making preform structures by either pressing them in a die or using the binder jetting additive manufacturing process followed by Al melt infiltration. In addition, we investigated the formation of preform structures by cold isostatic pressing followed by Al melt infiltration for making Ti-Al-C MAX phase composite. Thermo-mechanical characterizations, such as creep, strength, and thermal shock, were conducted to establish the structures’ performance.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Employing Weibull Analysis and Weakest Link Theory to Resolve Crystalline Silicon PV Cell Strength Between Bare Cells and Reduced- and Full-Sized Modules

Weibull analysis and weakest link theory are employed to resolve the probability of crystalline silicon PV cell fracture when measured as bare cells and when stressed in reduced- and full-sized modules. Experimental results indicated that the characteristic cell strength is reduced by ~20% once packaged into the laminate of a one-cell module and loaded in four-point flexure (4PF). This experimental observation was shown consistent with a weakest link theory prediction that the strength limiting flaws reside on the surface of the cell's edge. Here, the analysis is ultimately extended to present the equivalent loading of four-cell modules by uniform pressure and 4PF and a uniformly loaded full-sized module and demonstrates that smaller, representative, modules must be loaded to a much higher level than their parent full-sized modules to achieve an equivalent probability for cell fracture.

14 SOLAR ENERGY↗
DOE OSTI2025

You Only Look Once v5 and Multi-Template Matching for Small-Crack Defect Detection on Metal Surfaces

This paper compares the performance of Deep Learning (DL) and multi-template matching (MTM) models for detecting small defects. DL models extract distinguishing features of objects but require a large dataset of images. In contrast, alternative computer vision techniques like MTM need a relatively small dataset. The lack of large datasets for small metal-surface defects has inhibited the adoption of automation in small-defect detection in remanufacturing settings. This motivated this preliminary study to compare template-based approaches, like MTM, with feature-based approaches, such as DL models, for small-defect detection on an initial laboratory and remanufacturing industry dataset. This study used You Only Look Once v5 (YOLOv5) as the DL model and compared its performance against the MTM model for small-crack detection. The findings of our preliminary investigation are as follows: (i) YOLOv5 demonstrated higher performance than MTM in detecting small cracks; (ii) an extra-large variant of YOLOv5 outperformed a small-size variant; (iii) the size and object variety of the data are crucial in achieving robust pre-trained weights for use in transfer learning; and (iv) enhanced image resolution contributes to precise object detection.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Fatigue performance of laser powder bed fusion hydride-dehydride Ti-6Al-4V powder

We report hydride-dehydride (HDH) Ti-6Al-4V alloy with particle size distribution of 50–120 µm is laser powder bed fusion (L-PBF) processed using optimum processing parameters and a near-fully dense structure with a density of 99.9 % is achieved. Microstructural observations and phase analyses indicate formation of columnar β grains with acicular α/α' phases in as-built condition. The roughness of the as-fabricated samples is significant with an average roughness of R a = 15.71 ± 3.96 µm and a root mean square roughness of R rms = 108.4 ± 24.9 µm, however, both values are reduced to R a = 0.19 ± 0.04 µm and R rms = 4.9 ± 0.6 µm after mechanical grinding. Mechanical tests are carried out on as-fabricated specimens followed by stress relief treatment. All samples are tested to failure in fatigue, under fully-reversed tension-compression conditions of R = –1. The as-built samples failed from the surface with crack initiation mainly at micro-notches, whereas after mechanically grinding, crack initiation changed to subsurface defects such as pores. Minimizing surface roughness by mechanically grinding eliminates surface micro-notches which improves fatigue strength in the high cycle fatigue region. Fatigue notch factor calculations showed that the effect of surface roughness was significantly lower when HDH powder is used compared to standard spherical powder. X-ray diffraction analysis revealed an in-plane compressive stress, micro-strain and grain refinement on the surface of the mechanically ground samples. Fractography observations (macroscale) revealed a fully brittle fracture in the first stage of crack growth with a transition to a dominantly ductile fracture in the third stage of crack growth. On the other hand, at the micro scale, even the brittle fracture regions showed evidence of ductile fracture within the α' martensite laths.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Surface Stabilization with Fluorine of Layered Ultrahigh-Nickel Oxide Cathodes for Lithium-Ion Batteries

High-nickel layered oxide cathodes are key to meet the demands of the electric vehicle industry because of their high specific capacity. However, commercialization of these materials is hindered by critical challenges, such as phase transitions, particle cracking, aggressive surface reactivity, and thermal instability. Cation doping along with surface coating has proven to be an effective way to circumvent some of these issues to a large extent. Herein, fluorine coating is employed on a high-nickel Li[Ni 0.95 Mn 0.015 Co 0.02 Al 0.01 Mg 0.005 ]O 2 (NMCAM) cathode via a solution route. Detailed structural and electrochemical analyses indicate fluorine largely decorates the surface at low enough calcination temperatures. The cathode with 1 mol % fluorine coating exhibits a capacity retention of 71% after 500 cycles as compared to 59% for the control sample when cycled to a high cutoff voltage of 4.3 V in a full cell configuration with graphite anode. Post-mortem analysis of cycled electrodes reveals that surface reactivity is a major contributor to capacity fade as compared to particle cracking. Fluorine coating reduces surface reactivity and the depth to which rock-salt phase is formed on the surface during cycling. The thermal stability is also enhanced after fluorine coating as the material shows less heat release at high states of charge. Furthermore, this work demonstrates an effective, economical, and scalable way to stabilize the surface with fluorine and enhance the electrochemical performance of high-nickel cathodes.

25 ENERGY STORAGE↗
DOE OSTI2025

Mechanistic Insights Into Fatigue Life Enhancement of High‐Strength Steel via Ultrasonic Impact Treatment

In this work we explore the impact of Ultrasonic Impact Treatment (UIT) on the fatigue performance of high‐strength microalloyed steel commonly used in crankshaft applications. Building on prior observations of fatigue life improvement with UIT, this work focuses on unraveling the process–structure–performance relationships underpinning these enhancements. Microstructural analysis revealed significant grain refinement in the near‐surface layers, with deformation depth increasing at higher impact energies. This led to increased surface hardness and the development of deeper compressive residual stresses, particularly in samples treated with higher impact energy. Rotating bending fatigue testing showed a substantial improvement in fatigue life for UIT‐treated samples, with the endurance limit nearly doubling compared with untreated specimens. Fractographic analysis revealed a transition in crack initiation from surface defects in untreated samples to interior regions in UIT‐treated samples, characterized by the formation of noninclusion‐induced granular bright facets (GBFs). The observed fatigue enhancement is attributed to the synergistic effects of strain hardening and compressive residual stresses, which increase the surface crack threshold and promote interior crack initiation. This study provides new mechanistic insight into UIT‐induced fatigue resistance and interior failure behavior in high‐strength steels.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Strain-rate hardening enhances fatigue resistance of AlSi10Mg alloy at 350°C

The high cycle fatigue behavior of laser powder bed fusion processed AlSi10Mg has been investigated at 350 °C (T/T m ∼ 0.7). The alloy exhibited a fatigue strength of 30 MPa defined by runout after 10 7 cycles at a conventional loading frequency of 20 Hz, corresponding to a notable fatigue strength to ultimate tensile strength ratio of 0.73. The surprising fatigue resistance was attributed to the strain-rate hardening effect at high fatigue loading frequency relative to tensile loading rates at 350 °C. The strain-rate hardening effect was validated by performing ultrasonic fatigue tests (20 kHz loading frequency) with three orders of magnitude higher strain-rates than those at conventional loading frequency. The higher strain-rates in ultrasonic fatigue increased the magnitude of strain-rate hardening resulting in longer AlSi10Mg fatigue lives compared to fatigue at conventional frequency, thus confirming the strain-rate hardening effect. The fatigue crack initiation mechanism was strain-rate dependent. Post-mortem microstructural examination revealed intergranular cavitation inside clusters of fine equiaxed grains. The cavities interlinked with each other to initiate near-surface fatigue cracks at conventional frequency. Cavitation occurred to a lesser extent at the ultrasonic frequency. As a result, fatigue cracks initiated at pre-existing processing defects near the surface in ultrasonic fatigue samples. Finally, this investigation underscores the role of fine grain clusters in promoting high-temperature fatigue crack initiation and indicates a possible trade-off between printability via grain refinement and high-temperature fatigue resistance of additively manufactured alloys.

Additive manufacturing↗
DOE OSTI2023

Microstructural Insights into Performance Loss of High-Voltage Spinel Cathodes for Lithium-ion Batteries

Spinel-structured LiNi x Mn 2-x O 4 (LNMO), with low-cost earth-abundant constituents, is a promising high-voltage cathode material for lithium-ion batteries. Even though extensive electrochemical investigations have been conducted on these materials, few studies have explored correlations between their loss in performance and associated changes in microstructure. Here, down to the atomic scale, the structural evolution of these materials is investigated upon the progressive cycling of lithium-ion cells. Transgranular cracking is revealed to be a key feature during cycling; this cracking is initiated at the particle surface and leads to the penetration of electrolytes along the crack path, thereby increasing particle exposure to the electrolyte. The lattice structure on the crack surface shows spatial variances, featuring a top layer of rock-salt, a sublayer of a Mn 3 O 4 -like arrangement, and then a mixed-cation region adjacent to the bulk lattice. The transgranular cracking, along with the emergence of local lattice distortion, becomes more evident with extended cycling. Further, phase transformation at primary particle surfaces and void formation through vacancy condensation is found in the cycled samples. All these features collectively contribute to the performance degradation of the battery cells during electrochemical cycling.

25 ENERGY STORAGE↗
DOE OSTI2024

Development of Graphite Thermal and Mechanical Modeling Capabilities in Grizzly

Nuclear-grade graphites are used extensively in the core designs of multiple types of advanced nuclear reactors. In the reactor environment, graphite is exposed over long durations to extreme conditions, including high temperatures, radiation and potentially molten salt and oxygen. Exposure to these conditions can cause several degradation mechanisms in graphite, including nonuniform volumetric strains induced by irradiation and thermal expansion, which lead to stresses that can compromise the performance of graphite components. Evaluating component integrity, predicting component performance over the reactor lifetime, and developing design standards all require robust tools for predicting fracture initiation and propagation in graphite structural components in nuclear reactors. This report documents progress in an ongoing effort to develop modeling and simulation tools in the Grizzly code for predicting the performance of graphite exposed to reactor conditions. Recent developments include a set of thermal and mechanical models that now include the IG-110, NBG-18, and H-451 graphite grades. Improvements have also been made to a nonlinear damaged plasticity model applicable to predicting damage under tension and compression to quasibrittle materials, including graphite. In addition, enhancements have been made to the extended finite element method implementation targeted at simulating graphite fracture. These include new capabilities for crack nucleation in the interior of a solid body, improved treatment of crack nucleation on free surfaces, and more robust modeling approaches for crack growth approaching free surfaces or other cracks.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Spontaneous mesostructure formation produces optically transmissive Ni–P films that are catalytically active for the photoelectrochemical hydrogen evolution reaction

Ni–P films that are catalytically active for the hydrogen-evolution reaction were electrodeposited onto photoactive Si substrates between 20 °C and 80 °C from an aqueous solution. Ni–P films deposited at 20 °C and exposed to acidic environments spontaneously developed deep cracks. A substantial increase in optical transmission to the semiconducting substrate resulted without affecting the catalytic performance of the film. In contrast, Ni–P films deposited at 80 °C only developed minor surface-level cracks and did not exhibit a substantial increase in optical transmission. During electrodeposition of the Ni–P films at low temperatures, the uptake of parasitically evolved hydrogen generated partially defective Ni–P, causing crack formation. Increases in the temperature of the electrodeposition bath increased the faradaic efficiency of Ni–P deposition and consequently reduced the uptake of parasitically generated hydrogen. The defective Ni–P films were converted to a crack-resistant material by thermally desorbing the excess hydrogen that was absorbed during the low-temperature electrodeposition process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Stabilizing High–Nickel Cathodes with High–Voltage Electrolytes

Electrolytes connect the two electrodes in a lithium battery by providing Li + transport channels between them. Advanced electrolytes are being explored with high-nickel cathodes and the lithium-metal anode to meet the high energy density and cycle life goals, but the origin of the performance differences with different electrolytes is not fully understood. Here, the mechanisms involved in protecting the high-capacity, cobalt-free cathode LiNiO 2 with a model high-voltage electrolyte (HVE) are delineated. The kinetic barrier posed by a thick surface degradation layer with poor Li + -ion transport is found to be the major contributor to the fast capacity fade of LiNiO 2 with the conventional carbonate electrolyte. In contrast, HVE reduces the side reactions between the electrolyte and the electrodes, leading to a thinner nano-interphase layer comprised of more beneficial species. Crucially, the HVE leads to a different surface reorganization pathway involving the formation of a thinner nanoscale LiNi 2 O 4 spinel phase on the LiNiO 2 surface. Finally, with a high 3D Li + -ion and electronic conductivity, the spinel LiNi 2 O 4 reorganization nanolayer preserves fast Li + transport across the cathode–electrolyte interface, reduces reaction heterogeneity in the electrode and alleviates intergranular cracking within secondary particles, resulting in superior long-term cycle life.

25 ENERGY STORAGE↗
DOE OSTI2024

Critical role of slags in pitting corrosion of additively manufactured stainless steel in simulated seawater

Abstract Pitting corrosion in seawater is one of the most difficult forms of corrosion to identify and control. A workhorse material for marine applications, 316L stainless steel (316L SS) is known to balance resistance to pitting with good mechanical properties. The advent of additive manufacturing (AM), particularly laser powder bed fusion (LPBF), has prompted numerous microstructural and mechanical investigations of LPBF 316L SS; however, the origins of pitting corrosion on as-built surfaces is unknown, despite their utmost importance for certification of LPBF 316L SS prior to fielding. Here, we show that Mn-rich silicate slags are responsible for pitting of the as-built LPBF material in sodium chloride due to their introduction of deleterious defects such as cracks or surface oxide heterogeneities. In addition, we explain how slags are formed in the liquid metal and deposited at the as-built surfaces using high-fidelity melt pool simulations. Our work uncovers how LPBF changes surface oxides due to rapid solidification and high-temperature oxidation, leading to fundamentally different pitting corrosion mechanisms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Experimental system for studying temperature gradient-driven fracture of oxide nuclear fuel out of reactor

Temperature gradients in ceramic light water reactor (LWR) uranium dioxide (UO 2 ) nuclear fuel pellets generate thermal stresses that cause fractures in the fuel beginning early in the life of fresh fuel. The combination of heating due to fission and forced convective cooling on the exterior of LWR fuel rods generates a temperature profile that is difficult to replicate outside the reactor environment. In the present study, a state-of-the-art experimental set-up using electrical heating to replicate fission heating was built and surrogate fuel materials such as ceria (CeO 2 ) were used to validate the system. Cracking experiments were conducted on these surrogates by inducing reactivity-initiated-accident (RIA) like temperature gradients in the pellets via induction and direct resistance heating. Induction heating was done using copper coils and molybdenum susceptors which heated the surrogates to a threshold temperature that is sufficiently high for the fuel material to conduct current. Thereafter, direct resistance heating was used by a D.C. power supply to introduce volumetric heating to replicate LWR operating conditions analogous to fission heating. The pellets were held against nickel electrodes and mounted on a boron nitride test-stand. All the tests were carried out in a stainless-steel vacuum chamber. Simultaneous real-time dual imaging of the surrogate pellet surface has been implemented using an optical and infrared camera system which will be mounted along axial and perpendicular directions to the pellet surface respectively. A beam-splitter was used to split the incoming radiation from the sample into two halves. While one of the beams is transmitted from the splitter through a bandpass filter to obtain optical images, the other beam is reflected from the splitter to the thermal camera to capture full field temperature gradients of the as fabricated pellet surface during crack initiation and propagation. In the current series of tests, a 2-color pyrometer was used for recording and comparing the surface and centerline temperatures of the surrogate pellets in lieu of the thermal camera. A LabVIEW data acquisition system has been set up for collecting useful data during experiments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

A Lizard-inspired Tube Inspector (LTI) Robot

This final report summarizes the research findings of the current project. This project is a collaboration between New Mexico State University (NMSU) as a lead (Recipient) and Arizona State University (ASU) as a Co-Recipient. Tubular structures are common components of boilers and heat exchangers in power plants. Over time, these components may suffer corrosion, cracks, and stress-corrosion cracks in either the body or the welded connections. A single tube leakage can cause an outage of several weeks. Regular inspection is a key safety factor when ensuring that power plants are maintained in reliable, operational condition. This inspection, however, is challenging, time-consuming, and in many cases impossible due to accessibility issues and safety concerns. Recent developments in robotic-based inspection can offer a great solution. Hard-to-reach places can be inspected without overhauling the unit, saving time and cost. Although several robots have been designed and implemented successfully for inspecting power plant components, in particular tubular structures, their mobility and flexibility are limited. Most of these robots use wheels for mobility which reduces their maneuverability of these robots. Moreover, they usually use magnets to attach to tubes which will not work on tubes with non-ferromagnetic materials. These robots usually carry measurement tools for a particular non-destructive testing (NDT) method such as ultrasound testing (UT) that requires a couplant to perform a point-by-point (scanning) inspection of the tubular structure. In this project, we developed a versatile lizard-inspired tube inspector (LTI) robot with embedded inspection sensing components for tube inspection which removes the need for point-by-point scanning of tube surface for crack and corrosion detection. Inspired by a “lizard”, the novelty of the current project is the integration of couplant-free ultrasound sensing and transmission, advanced data-driven defect detection and imaging, and friction-based mechanical mobility components in a single robot to eliminate a need for smooth surfaces and simple geometry for mobility and scanning. The LTI robot could replace the wheel-based approach with friction-based mobility to significantly increase the flexibility and maneuverability of the robot. The LTI robot can get into a power plant unit, such as a boiler, from a small area allowing it to access a component of interest for inspection (e.g., move on OD, curved and flat surfaces, non-ferromagnetic or ferromagnetic materials, and tubes with rough surfaces and complex geometries). Additionally, an advanced data-driven method using ultrasound data was pioneered to allow the robot to detect defects in the entire area between the robot’s multi-functional mobility system (grippers). Integrating a couplant-free ultrasound sensing in the robot’s grippers as well as using advanced data-driven methods allowed the LTI to detect defects in the entire cross-section of a tube using its grippers when stationary and when mobile.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2021

Integrating Electromagnetic Acoustic Transducers in a Modular Robotic Gripper for Inspecting Tubular Components

Tubular structures are critical components in infrastructure such as power plants. Throughout their life, they are subjected to extreme conditions or suffer from defects such as corrosion and cracks. Although regular inspection of these components is necessary, such inspection is limited by safety-related risks and limited access for human inspection. Robots can provide a solution for automatic inspection. The main challenge, however, lies in integrating sensors for nondestructive evaluation with robotic platforms. As part of developing a versatile lizard-inspired tube inspector robot, in this study the authors propose to integrate electromagnetic acoustic transducers into a modular robotic gripper for use in automated ultrasonic inspection. In particular, spiral coils with cylindrical magnets are integrated into a novel friction-based gripper to excite Lamb waves in thin cylindrical structures. To evaluate the performance of the integrated sensors, the gripper was attached to a robotic arm manipulator and tested on pipes of different outer diameters. Two sets of tests were carried out on both defect-free pipes and pipes with simulated defects, including surface partial cracking and corrosion. The inspection results indicated that transmitted and received signals could be acquired with an acceptable signal-to-noise ratio in the time domain. Moreover, the simulated defects could be successfully detected using the integrated robotic sensing system.

Materials Science↗
DOE OSTI2024

Stress intensity factor models using mechanics-guided decomposition and symbolic regression

The finite element method can be used to compute accurate stress intensity factors (SIFs) for cracks with complex geometries and boundary conditions. In contrast, handbook solutions act as surrogate SIF models that provide significantly faster evaluation times. However, the development of conventional surrogate SIF models relies on manual development based on low-order parameterizations. This limits surrogate model accuracy and generalizability. Here, in this paper, we develop a framework for the automated development of mechanics-guided handbook SIF solutions by using interpretable machine learning via genetic programming for symbolic regression (GPSR). Formalizing the mechanics-based approach of Raju and Newman, SIF training data is decomposed into multiple subsets. This decomposition enables parallel GPSR model development of subfunctions, each of which accounts for specific geometrical corrections with respect to a known analytical model. Using this mechanics-based approach with GPSR allows for equations to be learned with improved accuracy and reduced complexity relative to the Raju Newman equations while maintaining the inherent interpretability of mathematical expressions. In this paper, we present equations that match the complexity of the Raju Newman equations while having reduced error, as well as equations with similar errors and reduced complexity.

42 ENGINEERING↗