Stability Analysis Of Structures Research Articles

Fuzzy-stochastic stability analysis of soil-steel structures under uncertainty

Fuzzy-stochastic stability analysis of soil-steel structures under uncertainty

Critical lateral‐torsional buckling loads of porous orthotropic rectangular beams containing warping effects

AbstractDue to their elemental porosity, porous materials display individual mechanical properties, rendering them essential components in various engineering applications. So, this study investigates the lateral‐torsional buckling (LTB) sensitivity of porous orthotropic rectangular beams subjected to a concentrated load, including the warping effects. Porosity‐dependent material properties vary along the beam's height via four different porosity distribution patterns. The constitutive equations are obtained using the principle of virtual work based on the classical beam theory containing the warping effect, and the governing equations are solved by performing the Ritz method to obtain the critical LTB load. The porous orthotropic beams and the warping effects add complexity to the analysis. So, the influence of some parameters, such as porosity coefficients, porosity distribution patterns, orthotropy, height‐to‐width ratio, slenderness ratio, and warping coefficients, on the LTB characteristics of porous orthotropic rectangular beams are investigated in detail. The novelty of this study lies in its comprehensive LTB analysis of orthotropic rectangular beams under specific effects, such as porosity and warping factors. The findings offer valuable insights into the LTB characteristics of orthotropic porous beams, contributing to an improved comprehension of their structural behavior and facilitating the design of engineering structures. This study contributes to the composite materials and structural stability analysis, offering potential applications in many engineering domains.

Green synthesis of CaO nanoparticles from chicken eggshells: antibacterial, antifungal, and heavy metal (Pb2⁺, Cr2⁺, Cd2⁺ and Hg2⁺) adsorption properties

BackgroundChicken eggshells, a common poultry byproduct, are rich in calcium and provide a sustainable source for producing calcium oxide nanoparticles (CaO NPs). Their use in eco-friendly synthesis aligns with the growing emphasis on sustainable materials for environmental and biomedical applications. Objectives: This study develops an eco-friendly method for synthesizing CaO NPs from chicken eggshells, characterizes their physicochemical properties, and evaluates their antibacterial and antifungal activities. It also tests their effectiveness in removing heavy metal ions (Pb2⁺, Cr2⁺, Cd2⁺, and Hg2⁺) from aqueous solutions.MethodsCaO NPs were synthesized by calcining chicken eggshells at 700°C for 7 h. Comprehensive characterization included analysis of crystalline structure, morphology, optical properties, bandgap energy, chemical composition, and thermal stability. Antibacterial and antifungal activities were tested using the well-agar diffusion method. Batch adsorption experiments evaluated heavy metal ion removal under varying conditions of pH, temperature, stirring time, and adsorbent concentrationResultsThe synthesis produced spherical, single-crystal CaO NPs with diameters ranging from 5 to 30 nm and a crystalline size of approximately 20 nm. The nanoparticles had a bandgap energy of about 4.7 eV. Significant antibacterial activity was observed against Staphylococcus aureus, Klebsiella pneumoniae, and Escherichia coli, with increasing inhibition zones correlating with nanoparticle concentration. The CaO NPs also effectively inhibited Candida albicans. For efficient metal ion removal, the optimal conditions were found to be 30 min at pH 6 with 40 mg of CaO NPs at 25°C, achieving recovery rates of 98% for Pb2⁺, 97% for Cd2⁺, 97% for Cr2⁺, and 97% for Hg2⁺. For near-complete removal, extending the process to 70 min at pH 6 with 40 mg of CaO NPs at 45°C achieved the highest recovery rates: 99% for Pb2⁺, 98% for Cd2⁺, 99% for Cr2⁺, and 99% for Hg2⁺, though this approach involves higher energy and cost.ConclusionCaO NPs derived from chicken eggshells are effective antibacterial agents and adsorbents for heavy metal removal. These findings highlight their potential for sustainable applications in environmental and biomedical fields.

Evaluating the Impact of NPA Dynamics in Selected Indian Banks: A Fifteen-Year Comparative Study

Purpose: The purpose of this study is to investigate the impact on bank profitability, capital structure, and financial stability and trend analysis regarding non-performing assets [NPAs] performance in selected Indian public sector banks vis-à-vis that observed in private sector ones during fifteen years. Methodology: For this research, a quantitative methodological approach has been used, and for quantifiable data, annual reports from four select banks, which include two public sector banks [The Bank of Baroda, The State Bank Of India] as well as two private sector banks [ICICI Bank Ltd., Nainital bank], are analyzed for the period ranging 2008-09 to 2022-23. The analysis calculates Compound Annual Growth Rates [CAGR] and t-tests, Panel Regression models to determine the relationship between GNPA additions, reductions, and write-offs with closing balances. Findings: A major increase in GNPAs is observed in the research among Scheduled Commercial Banks. The public sector banks found an even larger dynamism in NPA growth rates than private sector banks, manifesting the fluctuation to a high degree. The study identifies GNPA addition, reduction, and write-off as key determinants of their respective closing balances. Even though there have been many policy initiatives, the public sector banks [PSBs] remain at a higher level of NPAs due to governance deficits and political interference. The effectiveness of these predictors on GNPA is also confirmed using the Random Effect Model, thus requiring improved risk management practices. Originality: The content of this article is guaranteed to be original.

Modeling obliquely incident seismic wave propagation in rocks via the FDM-DEM coupling scheme: Algorithms and applications

The incidence angle of seismic waves plays a pivotal role in the stability analysis of structures in near-field zones. Despite its importance, the application of obliquely incident seismic waves within models of discontinuous media has been limited. This study introduces a novel approach that integrates the oblique incidence of seismic waves into a coupled model employing both the Finite Difference Method (FDM) and the Discrete Element Method (DEM). We validate the accuracy of seismic wave propagation under oblique incidence in two FDM-DEM coupling models—overlapping coupling and interface coupling—through comparisons with theoretical solutions. For vertically incident seismic P-waves, both models yield similar results. However, under oblique incidence, the overlapping coupling model demonstrates superior accuracy, with a maximum error of approximately 4.217 %, compared to about 10 % in the interface coupling model. Our findings also show that while the relative sizes of particle diameter and overlap length minimally affect accuracy, the arrangement of particles markedly influences the results. Furthermore, we apply this method to a slope model to investigate the failure process, revealing that the nature of the sliding body shifts from tensile sliding to tensile ejection as the incidence angle increases.

Crack propagation process in double-flawed granite under compression using digital image correlation method and numerical simulation

The existence of flaws seriously weakens the rock strength, directly affects the crack expansion morphology, and indirectly affects the slope stability. In this study, uniaxial compression tests were carried out on double-flawed granite to investigate the effects of flaw angle on its compressive strength and crack coalescence based on DIC technology and PFC2D numerical simulation. The result indicates that the UCS values of flawed specimens at angles of 15°, 30°, 45°, and 60° are approximately 25.5–51.7% lower than that of the intact specimen. The failure strength of the double-flawed sample increases with the increase of flaw inclination angle, and the fracture morphology shifts from no expansion to split expansion. When the flaw tip strain of each flaw sample exceeded 0.6%, the stress concentration was generated at the flaw tip, and the sample began to appear macroscopic large cracks. DIC technique can well observe the crack initiation and propagation process, recording inclined shear strain bands at flaw tips, tensile strain bands in the middle of flaws, and tensile shear O-shaped strain ring in rock bridge areas. Numerical simulations using PFC2D software were carried out and showed a good agreement with the physical results. In addition, the effect of structural inclination on specimen failure strength is clearly explained by the theory of compressive damage based on the projected size of flaws. The deformation of rock mass is not a simple material deformation but is composed of material deformation and structural deformation. These experimental and numerical results enhance our understanding of crack initiation and coalescence characteristics, aiding in the analysis of rock structure stability in scenarios such as excavated underground openings, slopes, and tunneling construction, where pre-existing cracks or step-path fractures are pivotal to structural integrity.

Kinematic Stability Analysis of Anchor Cable Structures in Submerged Floating Tunnel under Combined Parametric–Vortex Excitation

The submerged floating tunnel is a marine transportation infrastructure that links two shorelines. The tunnel tube body’s buoyancy exceeds gravity, with anchoring ensuring equilibrium. Anchoring reliability is crucial. This study presents a three-way coupled kinematic model for the mooring structure, formulated on Hamilton’s principle and Kirchhoff’s assumption. It explores the impact of the tube body’s buoyancy-to-weight ratio and the sea current’s angle of incidence on mooring motion response. By solving the motion analysis model, Hill’s equation system is derived to assess the parameter instability of the anchor cable structure. The coefficient of excitation instability intervals for the submerged floating tunnel is determined and validated. The findings indicate the following: (1) Increasing the float-weight ratio reduces displacement response amplitudes in all directions, bringing downstream and transverse currents closer to their initial positions; (2) Changes in current direction angles result in decreased downstream excitation strength and increased transverse displacement response with the same excitation direction; (3) The instability interval visualization effectively predicts anchor cable structure instability under parametric excitation. Structures within the instability region are deemed unstable, while those outside are considered stable.

Analysis of failure mechanical behavior and structural stability of rock under dynamic load

Rock serves as a crucial source of building materials. Understanding the dynamic strength of rock under varying prestressed conditions is essential for evaluating structural stability and engineering design. This research investigates the strength and failure characteristics of sandstone under different impact velocities (v = 1m/s-5.5 m/s) and intermediate principal stresses (σ2 = 3/6/9/12 MPa) using a true triaxial Hopkinson pressure bar. The results show that as both impact velocity v and intermediate principal stress σ2 increase, the peak stress and peak strain of rock samples rise correspondingly. The strain rate of rock samples ranges from 40s−1 to 120s−1 under uniaxial impact and from 40s−1 to 100s−1 under triaxial impact, indicating more severe deformation without confining pressure. The degree of rock breakage is greater under uniaxial impact compared to triaxial impact, as evidenced by macroscopic damage patterns. Microscopic analysis shows that the internal crystal structure of the rock sample is mainly transgranular fracturing post-impact. Wave velocity tests pre- and post-impact show that increasing v exacerbates rock damage, while increasing σ2 mitigates it. A mechanical constitutive model for rock under triaxial conditions, considering dynamic load, prestress, and strain rate, has been developed and validated, with a fitting degree R2 exceeding 0.9. This study offers significant insights into the mechanical behavior of rock under different prestresses, diverging from conventional rock mechanics (prestress σ1≠σ2 = σ3 ≥ 0) by discussing the macroscopic and destructive behaviors of rock samples under different prestresses (σ1≠σ2≠σ3 ≥ 0) and providing a referential mechanical model for similar material studies.

Semi-analytical framework for modelling of surface heating and its impact on nonlinear stability of nanotube reinforced doubly curved porous fiber composite panels

In elevated temperatures, the stiffness of the panel deteriorates and can lead to loss of stability of structures. Hence, the stability analysis of thin-walled structures is a critical investigation in the thermal environment. Finding such criticality, the present semi-analytical study investigated the nonlinear stability behaviour of porous doubly curved thin-walled panels subject to surface heating like dome heating and localised heating. To improve the stiffness of the panel, the matrix is reinforced with carbon nanotubes (CNTs). Improper mixing of such nanoparticles can lead to agglomeration or bundling effect, which may reduce the structure's stiffness. Still, its investigation in surface heating can be an essential aspect that is found to be untouched by researchers for porous shell panels. The effective material properties of the three-phase composite panel are determined using the Eshelby-Mori-Tanaka (E-M-T) approach and the Chamis homogenisation technique. Using the variational principle, governing equations are derived and further simplified to non-linear algebraic equations using the Galerkin technique. Gibson and Ashby foam model is used to model cell structure. It is observed that a complete agglomerated state results in higher post-buckling strength, a continuous deformation path due to biaxial compression and curved geometry, and porosity of cellular structure distribution and cell walls are the important parameters to study the stability of panel in a thermal environment are the major conclusions drawn from the current study. Current investigation can be an important contribution towards modelling aircraft structure in supersonic airflow and furnace walls of thermal power plants subjected to localised heating.

Stability Analysis Method of a Hierarchical Control Structure Microgrid Based on a Small-Signal Model and Hopf Bifurcation Theory

To the oscillation and stability problem caused by multi-scale and broadband electromagnetic dynamics among many isomerized power electronic devices in a microgrid, a small-signal model of hierarchical control structure microgrid and stability analysis method based on oscillation trajectories are proposed. Moreover, a hierarchical control structure is used as the research object in microgrid, and the analysis is performed based on the small-signal model and Hopf bifurcation theory. First, the small-signal model of the hierarchical control structure microgrid is established, combining the dominant eigenvalue and participation factor analysis methods, to analyze the influence of the controller and related sensitive parameters on the dynamic performance of the system. Then, based on the small-signal model and Hopf bifurcation theory, a stability analysis method based on oscillation trajectories is proposed. The relationship between different oscillation modes and limit cycles in the microgrid system and the influence of the sag control parameter values on the oscillation trajectory and stability domain of the system are researched on. Combining Hopf bifurcation theory and oscillation trajectory to delineate the stable domain of parameter trajectories, the influence of secondary control on the system stability is analyzed under different oscillation trajectories and load disturbances, revealing the corresponding relationship between the state trajectories of different oscillation modes and system stability of a hierarchical control structure microgrid. Based on the proposed oscillating trajectories, the stability analysis method has sufficient universality for studying the impact of system stability, establishing the parameter selection standards for the design of microgrids. Finally, according to the verification results, the correctness and applicability of above methods are verified.

Stress-dependent Mohr–Coulomb shear strength parameters for intact rock

Rock strength is imperative for the design and stability analysis of engineering structures. The Mohr–Coulomb (M-C) criterion holds significant prominence in geotechnical engineering. However, the M-C criterion fails to accurately capture the nonlinear strength response and neglects the critical state of rocks, potentially leading to inaccuracies in the design phase of deep engineering projects. This study introduces an innovative stress-dependent friction angle and cohesion (SFC) for the M-C criterion to capture the nonlinear strength responses of intact rocks, spanning from non-critical to critical states (brittle to ductile regions). A novel method for determining these stress-dependent parameters at each corresponding σ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma_{3}$$\\end{document} is initially introduced. Subsequently, an examination of the confinement dependency of the friction angle and cohesion is conducted, leading to the derivation of the SFC model. The SFC-enhanced M-C criterion, utilizing parameters obtained from triaxial tests under lower σ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma_{3}$$\\end{document}, demonstrates the capability to delineate the complete non-linear strength envelope from brittle to ductile regions. Validation through triaxial test data confirms that the predictions of the SFC-enhanced M-C criterion accurately correspond to the strength characteristics of the tested rocks.

Microscopic deformation mechanism and characteristics of carbonaceous slate during the creep process

Carbonaceous slate exhibits a significant creep deformation that seriously affects the construction and operation of underground projects. To investigate the microstructural changes characteristics and reveal the microscopic deformation mechanism of the carbonaceous slate during the creep process, multiple methods were performed, including the triaxial creep test, SEM and MIP. The following conclusions were drawn: The rock samples underwent three stages during the creep test: microporosity closure at a low-stress level, material densification at an intermediate stress level, and microcracks emerging and expanding to failure at the high stress. The creep deformation was particularly significant in the first and third processes. The lamellar particles are compressed or bent under stress in parallel and vertical directions, showing the anisotropic properties of deformation. The deformation of the rock sample is related to the angle between the bedding and the orientation of major principal stress, and the effect of the anisotropy decreases with the increased stress level. The sprouting and expansion of microfractures occur at high-stress levels, showing pressure dissolution of mineral particles, migration of very fine particles, and cement damage between lamellar particles. Finally, the horizontal samples formed a combined rupture surface composed of the laminar surface and the fracture surface intersecting it, showing brittle damage, while the vertical samples formed a fracture surface parallel to the laminar surface, showing a ductile damage pattern. Those results could provide the basis for a further understanding of the mechanical properties of carbonaceous slate and the improvement of its creep model and parameters. It was significant for the stability analysis and deformation prediction of engineering structures using numerical simulation.

Structural Stability and Mechanical Analysis of PVC Pipe Jacking under Axial Force

Structural Stability and Mechanical Analysis of PVC Pipe Jacking under Axial Force

Enhanced Hoek-Brown (H-B) criterion for rocks exposed to chemical corrosion

Underground constructions often encounter water environments, where water–rock interaction can increase porosity, thereby weakening engineering rocks. Correspondingly, the failure criterion for chemically corroded rocks becomes essential in the stability analysis and design of such structures. This study enhances the applicability of the Hoek-Brown (H-B) criterion for engineering structures operating in chemically corrosive conditions by introducing a kinetic porosity-dependent instantaneous mi (KPIM). A multiscale experimental investigation, including nuclear magnetic resonance (NMR), X-ray diffraction (XRD), scanning electron microscopy (SEM), pH and ion chromatography analysis, and triaxial compression tests, is employed to quantify pore structural changes and their linkage with the strength responses of limestone under coupled chemical-mechanical (C-M) conditions. By employing ion chromatography and NMR analysis, along with incorporating the principles of free-face dissolution theory accounting for both congruent and incongruent dissolution, a kinetic chemical corrosion model is developed. This model aims to calculate the kinetic porosity alterations within rocks exposed to varying H+ concentrations and durations. Subsequently, utilizing the generalized mixture rule (GMR), the kinetic porosity-dependent mi is formulated. Evaluation of the KPIM-enhanced H-B criterion using compression test data from 5 types of rocks demonstrated a high level of consistency between the criterion and the experimental results, with a coefficient of determination greater than 0.96, a mean absolute percentage error less than 4.84%, and a root-mean-square deviation less than 5.95 MPa. Finally, the physical significance of the porosity-dependent instantaneous mi is clarified: it serves as an indicator of a rock’s capacity to leverage the confining pressure effect.

Scalable Analysis of Dipole Moment Fluctuations for Characterizing Intermolecular Interactions and Structural Stability.

Accurately predicting protein-ligand interactions is essential in computational molecular biochemistry and in silico drug development. Monitoring changes in molecular dipole moments through molecular dynamics simulations provides valuable insights into dipole-dipole interactions, which are critical for understanding protein structure stability and predicting protein-ligand binding affinity. In this study, we propose a novel method to monitor changes in the interangle between dipole vectors of residue molecules within proteins and ligand molecules, aiming to evaluate the strength and consistency of interactions within the complex. Additionally, we extend the concept of positional root-mean-square fluctuation (RMSF), commonly used for protein structure stability analysis, to dipole moments, thus defining dipole moment RMSF. This enables us to analyze the stability of dipole moments for each residue within the protein and compare them across residues and between binding and non-binding complexes. Using the CRBP1-retinoic acid complex as our model system, we observed a significant difference in the interangle change of dipole moments for the key residue at the residue-level between the non-binding and binding complexes. Furthermore, we found that the dipole moment RMSF value of the non-binding complex was substantially larger than that of the binding complex, indicating greater dipole moment instability in the non-binding complex. Leveraging the concept of scalability inherent in the calculation of dipole moment vectors, we systematically expanded the residues within the protein's primary secondary structure. Our dipole moment analysis approach can provide valuable predictive insights into complex candidates, especially in situations where experimental comparisons are challenging.

Preparation of Calcium-Binding Peptides Derived from Mackerel (Scomber japonicus) Protein and Structural Characterization and Stability Analysis of Its Calcium Complexes.

The purpose of this study was to prepare mackerel peptides (MPs) with calcium-binding capacity through an enzyme method and to investigate the potential role they play in improving the bioavailability of calcium in vitro. The calcium-binding capacity, degree of hydrolysis (DH), molecular weight (MW), and charge distribution changes with the enzymolysis time of MPs were measured. The structural characterization of mackerel peptide-calcium (MP-calcium) complexes was performed using spectroscopy and morphology analysis. The results showed that the maximum calcium-binding capacity of the obtained MPs was 120.95 mg/g when alcalase was used for 3 h, with a DH of 15.45%. Moreover, with an increase in hydrolysis time, the MW of the MPs decreased, and the negative charge increased. The carboxyl and amino groups in aspartic (Asp) and glutamate (Glu) of the MPs may act as calcium-binding sites, which are further assembled into compact nanoscale spherical complexes with calcium ions through intermolecular interactions. Furthermore, even under the influence of oxalic acid, MP-calcium complexes maintained a certain solubility. This study provides a basis for developing new calcium supplements and efficiently utilizing the mackerel protein resource.

A 3D-Based Modeling and Analysis of an Artificial Palm Tree for Video Surveillance Activities

A study on the 3-D modeling and analysis of an artificial palm tree structure capable of housing a camera was made. The proposed system's design, simulation, and virtual testing were done using SolidWorks software. This work's primary objective was an aesthetically pleasing and functional solution that integrates with the urban landscape while providing an enhanced concealed security system. The natural form of a palm tree was incorporated into the artificial palm tree structure. The hidden camera ensures optimal coverage without compromising the overall appearance and presence of the device. This is so because, in the Nigerian situation, Miscreants will pull down the structure if they know of its presence. A detailed analysis of the system's structural integrity and stability was achieved using a 3D model of the artificial palm tree structure. Factors such as wind load, weight distribution, and material strength are considered to ensure the design can cope with environmental conditions. Virtual simulations allow for the maximization of the structure, ensuring it complies with safety standards, and the results of VonMise's stress show that the materialsselected for the design are suitable for the work.

Weighted Mostar invariants of chemical compounds: An analysis of structural stability

The concept of the weighted Mostar invariant is a mathematical tool used in chemical graph theory to study the stability of chemical compounds. Several recent studies have explored the weighted Mostar invariant of various chemical structures, including hydrocarbons, alcohols, and other organic compounds. One of the key advantages of the weighted Mostar invariant is that it can be easily computed for large and complex chemical structures, making it a valuable tool for studying the stability of a wide range of chemical compounds. This notion has been utilized to build novel approaches for forecasting chemical compound stability, such as machine learning algorithms. The focus of the paper is to demonstrate the weighted Mostar indices of three specific nanostructures: silicon dioxide (SIO2, poly-methyl methacrylate network (PMMA(s)), and melem chains (MC(h)). The authors seek to provide the findings of their investigation of these nanostructures using the weighted Mostar invariant.

Physics informed machine learning based applications for the stability analysis of breakwaters

ABSTRACT One of the key aspects in designing and stability analysis of breakwater structures is predicting the stability number of their armour blocks. This study presents a novel approach called physics informed deep neural network, for the stability analysis of rubble-mound breakwaters. The present work makes two main contributions. Firstly, it proposes a method for creating hybrid combinations of theoretical models or physical models and deep neural network architectures, leveraging the advantages of both physics and data. This framework incorporates the output of physics-based simulations and observational features into a hybrid modelling setup. Secondly, the framework employs physics-based loss functions in the learning objective of these deep neural networks, which not only demonstrate lower errors on the training set but also adhere to the established physical relations. The proposed study may have the potential to address the existing limitations in this field and provide better accuracy in estimating the stability number.

Electronic structure of double perovskite SrTi0.5Co0.5O3: order, disorder, and vacancy effects

In this study, we investigate the electronic structure of the ordered/disordered double perovskite SrTi0.5Co0.5O3 (STCO) using density functional theory (DFT) and the full-potential linearized augmented plane wave method. Detailed structural and magnetic stability analysis revealed that Sr2TiCoO6 crystallizes in the tetragonal I4/m space group, in which Co4+ and Ti4+ ions are distributed in an alternating arrangement along three directions. Notably, Sr2TiCoO6 exhibits a half-metallic property and exhibits ferromagnetic (FM) behavior, originating from the Co4+-O2--Ti4+ bonds and the high spin state of cobalt. Additionally, a chemical/magnetic stability analysis was carried out to identify the ground state structure in disordered STCO. The investigation identified a two-dimensional-like configuration (referred to as STC5FM) characterized by ferromagnetic order. This particular arrangement represents the most chemically stable layered configuration, featuring a maximal occurrence of Co–O–Co chains. Thus, Co4+ ions exhibit an intermediate spin state following Goodenough-Kanamori-Anderson rules of ferromagnetic mechanism. Interestingly, this structure also displays ferromagnetism at room temperature, accompanying with semiconductor properties. The study also explored the impact of oxygen vacancies. Remarkably, the ferromagnetic attributes remain robust even in the presence of oxygen vacancies. Moreover, a transition from semiconductor to metal behavior becomes evident under these conditions.