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One of the key difficulties in applications of the effective media theories to real materials is the complex and "irregular" character of microstructures. However, in cases of moderate contrast between properties of the constituents, the sensitivity of the effective properties to microgeometries is much lower; it vanishes in the first approximation. The latter actually remains applicable at substantial (up to 70%–100%) contrast in properties. The effective elastic and conductive properties are considered as functions of property contrast between constituents. Whereas in the isotropic cases the Voigt–Reuss bounds provide guidance, in anisotropic cases these issues are less obvious. Two origins of effective anisotropies are discussed: (A) anisotropy of material constants and (B) geometric factors: non-random orientations of non-spherical inclusions. To the first order in contrast, the factor (A) is dominant, and factor (B) can be ignored (effective properties are independent of microgeometries, such as inhomogeneity shapes); the importance of factor (B) increases sharply with increasing contrast. For matrix composites (continuous matrices containing inhomogeneities), an interesting interplay takes place between the moderate contrast assumption and the non-interaction assumption (NIA). It shows that, in cases of moderate contrast, the NIA remains accurate at substantial concentrations. An application to monitoring fatigue of austenitic steel, whereby property contrast between the martensite and austenite phases is moderate, is discussed. Results of the second order in contrast, that are limited to the ellipsoidal inhomogeneities, are also given. [ABSTRACT FROM AUTHOR]

Discontinuous shear thickening in dense suspensions is accompanied by significant fluctuations in stress at a fixed shear rate. In this work, normal stress fluctuations are shown to have a one-to-one relationship with the formation and dissolution of local high-density regions. Namely, a burst in the force response corresponds to the spontaneous appearance of inhomogeneity. We observe that boundary conditions can significantly alter the spatiotemporal scale of these fluctuations, from short-lived to more sustained and enduring patterns. We estimate the occurrence frequency R and the average intensity Q of individual bursts/inhomogeneity events. The growth of R with the shear rate is the most rapid for the rigid boundary, whereas Q is nonmonotonic with confinement stiffness. Our results indicate that boundary conditions alter the development of inhomogeneity and thus the stress response under shear. [ABSTRACT FROM AUTHOR]

We investigate the temporal stability analysis of a two-layer flow inside a channel that is driven by pressure. The channel consists of a fluid layer overlying an inhomogeneous and anisotropic porous layer. The flow contains a Couette component due to the movement of the horizontal impermeable upper and lower walls binding the two layers. These walls of the channel move at an identical speed but in opposite directions. The flow dynamics for the porous medium are modelled by the Darcy-Brinkman equations, and the Navier-Stokes equations are employed to describe the motion within the fluid layer. The hydrodynamic instability of infinitesimal disturbance is investigated using Orr-Sommerfeld analysis. The corresponding eigenvalue problem is derived and solved numerically using the Chebyshev polynomial-based spectral collocation method. Results reveal that stability features are strongly affected by the axial and spatial permeability variations of the porous medium. Further, the ratio of the depth of the fluid layer to the porous layer and the strength of the Couette component play a crucial role. The destabilization of the perturbed system is noticed by strengthening the Couette flow component. The combined impact of increasing the anisotropy parameter and depth ratio, decreasing Darcy number, and reducing the inhomogeneity factor stabilizes the system. This facilitates us to have greater control over the instability characteristics of such fluid-porous configuration by suitably adjusting various flow parameters. The outcome will be beneficial in relevant applications for enhancing or suppressing the instability of perturbation waves, as preferable. [ABSTRACT FROM AUTHOR]

In this work, the electrical and photoelectric properties of the near-surface and surface layers of silicon doped by diffusion with chromium atoms were investigated. The formation of an anomalous concentration of charge carriers in these regions, as well as an anomalously low mobility, was revealed. The specific conductivity of the near-surface layer with a thickness of 1÷5 μm turned out to be equal to (1.6÷9.9)·10³ Ohm-1·cm-1. The inhomogeneity of the crystal under study was determined by the light probe method. [ABSTRACT FROM AUTHOR]

Sprite halos are diffuse glow discharges in the D-region ionosphere triggered by the quasi-electrostatic (QES) fields of lightning discharges. A three-dimensional (3D) QES model is adopted to investigate the effect of ionospheric electron density on sprite halos. The electron density is described by an exponential formula, parameterized by reference height (h') and sharpness (β), and the local inhomogeneity has a Gaussian density distribution. Simulation results indicate that the reference height and steepness of the nighttime electron density affect the penetration altitudes and amplitudes of normalized electric fields, as well as the altitudes and intensities of the corresponding sprite halos optical emissions. A comparison of the daytime and nighttime conditions demonstrates that the daytime electron density profile is not favorable for generating sprite halos emissions. Furthermore, the pre-existing electron density inhomogeneities lead to enhanced local electric fields and optical emissions, potentially offering a plausible explanation for the horizontal displacement between sprites and their parent lightning, as well as their clustering. [ABSTRACT FROM AUTHOR]

The spectral problem of determining the optimal distribution of mechanical properties of an arbitrary inhomogeneous body taking into account damping is investigated. The optimisation problem consists in finding the maximum first natural frequency. Damping is taken into account in the framework of the linear viscoelasticity model on the basis of the complex modules concept for the standard viscoelastic body model. The functions characterising the instantaneous and long-time modules are used as control functions. The problem formulation includes isoperimetric conditions that are imposed on the control functions and determine their average volume distribution. A Relye functional is constructed, and the optimality condition, which consists in the constancy of the potential energy, is found in a variational manner. As a model problem the problems of maximisation of the first natural frequency (bending and longitudinal vibrations) of a functionally graded cantilever beam with consideration of damping are considered. Analytical expressions for the laws of variation of the instantaneous and long-range modules are obtained. It is checked that the problem in the limiting case (when the relaxation time is equal to zero) is reduced to the elastic case. To determine the optimal value of the first natural frequency, a cubic equation is constructed and solved numerically. Asymptotic formulae for determining the optimal natural frequency at small values of relaxation time are obtained. Calculations have been carried out to evaluate the optimality of the obtained solution. For example, in comparison with the case of constant modules, the gain in the value of the first natural frequency is about 27% for the case of bending.

The potential of paper and paperboard as fiber-based materials capable of replacing conventional polymer-based materials has been widely investigated and evaluated. Due to paper’s limited extensibility and inherent heterogeneity, local structural variations lead to unpredictable local mechanical behavior and instability during processing, such as mechanical forming. To gain a deeper understanding of the impact of mechanical behavior and heterogeneity on the paper forming process, the Finite Element Method (FEM) coupled with continuum modeling is being explored as a potential approach to enhance comprehension. To achieve this goal, utilizing experimentally derived material parameters alongside stochastic finite element methods allows for more precise modeling of material behavior, considering the local material properties. This work first introduces the approach of modeling heterogeneity or local material structure within continuum models, such as the Stochastic Finite Element Method (SFEM). A fundamental challenge lies in accurately measuring these local material properties. Experimental investigations are being conducted to numerically simulate mechanical behavior. An overview is provided of experimental methods for material characterization, as found in literature, with a specific focus on measuring local mechanical material structure. By doing so, it enables the characterization of the global material structure and mechanical behavior of paper and paperboard.

Controlling repeated thermal cycling is one of the key mechanisms to design microstructures in the interlayer regions for narrow gap laser wire filling welding (NGLWFW) of austenite stainless steels. Herein, the optimization of process parameters for individual layers is tailored to customize the molten pool morphology during the NGLWFW process, facilitating precise control over the microstructure and, consequently, enhancing both mechanical properties and corrosion resistance of the joint. The results showed that the molten pool morphology acquired by simulation are obviously diverse from the bottom zone (BZ), middle zone (MZ) to upper zone (UZ) of the welded joint ascribed to the high heat accumulation effect, leading to the variation of microstructure. At BZ, the combination of smaller grain size and reduced dendrite spacing reduce the number of corrosion sites and promote the formation of a denser and more uniform corrosion product layer. Additionally, the diverse grain orientation, characterized by lower texture strength, facilitated a more uniform distribution of elements. Furthermore, the significantly higher content of δ-ferrite showing smallish shape disrupted the directional growth of austenite columnar grains, contributing to the excellent corrosion resistance observed at the BZ.

A 3D problem in linear elasticity is considered for a thin inhomogeneous layer subject to transverse compression. For the first time, the effect of arbitrary vertical inhomogeneity is elucidated. Two sets of boundary conditions along the faces of the layer are adapted for modelling transverse compression. Robust asymptotic formulae involving repeated integrals across the thickness are derived for displacements and stresses. As an illustration, numerical results are presented for the elastic moduli having a transverse parabolic variation. The obtained results have a potential to be implemented in modern technology, including manufacturing and design of functionally graded materials. [ABSTRACT FROM AUTHOR]

The potential of paper and paperboard as fiber-based materials capable of replacing conventional polymer-based materials has been widely investigated and evaluated. Due to paper's limited extensibility and inherent heterogeneity, local structural variations lead to unpredictable local mechanical behavior and instability during processing, such as mechanical forming. To gain a deeper understanding of the impact of mechanical behavior and heterogeneity on the paper forming process, the Finite Element Method (FEM) coupled with continuum modeling is being explored as a potential approach to enhance comprehension. To achieve this goal, utilizing experimentally derived material parameters alongside stochastic finite element methods allows for more precise modeling of material behavior, considering the local material properties. This work first introduces the approach of modeling heterogeneity or local material structure within continuum models, such as the Stochastic Finite Element Method (SFEM). A fundamental challenge lies in accurately measuring these local material properties. Experimental investigations are being conducted to numerically simulate mechanical behavior. An overview is provided of experimental methods for material characterization, as found in literature, with a specific focus on measuring local mechanical material structure. By doing so, it enables the characterization of the global material structure and mechanical behavior of paper and paperboard. [ABSTRACT FROM AUTHOR]

ABSTRACTIn this study, Al-Zn-Mg-Cu alloy components were prepared using wire arc additive manufacturing (WAAM). Through multi-scale characterisation technology, performance testing and slow strain rate tensile (SSRT) testing, the microstructure, mechanical properties and stress corrosion cracking (SCC) susceptibility of WAAM Al-Zn-Mg-Cu components were studied, revealing the generation mechanism of inhomogeneity and anisotropy. The results show that with the increase of WAAM thermal cycles, the matrix precipitates (MPs), grain boundary precipitates (GBPs) and precipitation-free zones (PFZ) evolve in different paths and increase to varying degrees, resulting in performance decrease and increase in stress corrosion susceptibility, so the inhomogeneity is mainly attributed to differences in precipitated phases. The Inter-layer inclined to the scanning direction and the Inner-layer inclined to the building direction led to anisotropy in tensile strength and SCC behaviour, so the anisotropy is mainly attributed to the grain orientation and fracture mode.

Inhomogeneities in the near-surface region of diffusion-doped silicon with manganese atoms were studied using the local photo-EMF method and photovoltage and photoconductivity signals were detected. It has been established that the inhomogeneous region is located at a depth of 3÷35 μm from the surface of the crystal. The magnitude of photo-EMF in these layers does not change monotonically from point to point. It was revealed that the photo-EMF spectra depend on the wavelength of the irradiated light, while the shape of the areas and their shift are related to the penetration depth of laser radiation. The photo-EMF signal increases to a depth of ~25 µm from the surface, then saturates and from ~30 µm smoothly decreases and completely disappears at a depth of ~40 µm. The magnitude of the internal electric field was determined using the Tauc method. A model of the structure of the near-surface region of diffusion-doped silicon with manganese is proposed.

The paper demonstrates the analysis of the stress and strain states of an inhomogeneous structure with an axial symmetrical spheroidal inclusion in an infinite solid under a remote uniform tension load derived from the conditions of the theory of elasticity. With respect to the inhomogeneous structure, the deformations produce constraints that require a complete 3-dimensional analysis in the z, r-coordinate system. The solution generates the stress state of the inclusion and at the interface of the matrix. Spheroidal inclusions in an uniform outer tension stress field deform self-similarly to a rather elongated spheroid. With respect to the compatibility condition and depending on the different elastic moduli and Poisson's ratios in the inclusion and matrix, the solution procedure leads to a system of two linear equations with the magnitudes of the two tractions as unknowns. In this way, the solution is shortened to a twofold statically indeterminate system. The analysis performed leads to an exact solution of the general spheroidal problem in a formulation of stress concentration factors considering the different stiffness parameters of inclusion and matrix. [ABSTRACT FROM AUTHOR]

Inhomogeneities in the near-surface region of diffusion-doped silicon with manganese atoms were studied using the local photo-EMF method and photovoltage and photoconductivity signals were detected. It has been established that the inhomogeneous region is located at a depth of 3÷35 μm from the surface of the crystal. The magnitude of photo-EMF in these layers does not change monotonically from point to point. It was revealed that the photo-EMF spectra depend on the wavelength of the irradiated light, while the shape of the areas and their shift are related to the penetration depth of laser radiation. The photo-EMF signal increases to a depth of ~25 μm from the surface, then saturates and from ~30 μm smoothly decreases and completely disappears at a depth of ~40 μm. The magnitude of the internal electric field was determined using the Tauc method. A model of the structure of the near-surface region of diffusiondoped silicon with manganese is proposed. [ABSTRACT FROM AUTHOR]

A rotating system that includes an initially stressed piezo-electric substrate was the subject of an analytical study of the SH waves. The substrate and vacuum bonding are in good contact with the corrugation, and the top border is treated as stress-free corrugation. About the upper barrier that is both electrically open as well as electrically short scenarios are taken into consideration. Dispersion equations for circumstances with a corrugated interface that are both electrically short as well as electrically open have been found. The SH wave characteristics through the framework suggested and circumstances dependent on different geometrical and physical factors have been investigated based on the numerical findings. The study looks at the simultaneous simulated outcomes of a number of physical factors that were produced in Mathematica 7 and include rotation, inhomogeneity, phase velocity, initial stress, and corrugated interface of SH wave distribution in a structure under discussion. The model under examination has potential applications in the creation of surface acoustic wave devices.

In this manuscript, we introduce a totally asymmetric simple exclusion process on a dynamic lattice with inhomogeneity to model motor-based long-range transport along microtubules (MTs) which exhibit cycles of growth, shortening and regrowth at their growing tips. By mean-field approximation and numerical simulations, we explore phase diagrams for the particle density near the dynamic end of the lattice as well as over the entire lattice. In particular, we find seven different phases for the density over the entire lattice and explore the corresponding phase diagram by analytical analysis. Interestingly, we find that the density may have a linear profile in part of the lattice. When the lattice has a defect, we separate the lattice into two subsystems: a right subsystem with fixed length and a defect in the middle and a left subsystem with dynamic length. When the right subsystem is in maximum-current phase, we calculate an analytical approximation of the density away from the boundaries and the defect site and the density is in association with the reduced hopping rate at the defect site; the density at the left side of the defect site serves as the effective entry rate of the left subsystem. We find that with defects, the linear profiles no longer appear at the left end of the left subsystem and only five possible phases could occur. This is a step-forward to a more comprehensive mathematical description of intracellular long-range transport of organelles along MTs with instability.

Along with the battery charge/discharge processes, the migration of the Li ions inevitably leads to an inhomogeneous distribution of the battery internal electrochemical and thermal characteristics, deteriorating the battery capacity and safety. In this work, the internal characteristics of a 20 Ah pouch LiFePO4 lithium-ion battery have been investigated based on a 3D electrochemical-thermal coupled model. It is found that the reduction of the particle size for either the cathode or anode would increase the battery capacity. Moreover, with the modulation of the thickness of cathode (Lpos) and convective heat transfer coefficient (h), the homogeneity of solid lithium concentration and temperature has been optimized. A relatively smaller Lpos and an h higher than the critical value should be adopted. From the aspect of thermal distribution, as the discharge rate increases, the irreversible reaction heat always dominates, while the proportion of ohmic heat among the total heat increases, and the high temperature region always locates on the inner sides of the tabs. The methodology proposed in this work could be applied to pouch batteries with more repeated cell units and larger sizes.

The present study investigated the inhomogeneity of microstructure and properties of hybrid laser-MIG welded 10-mm-thick 316L/AH36 joints. The study focused on the inhomogeneity of the laser zone, hybrid zone, and transition zone. The temperature field was simulated using ABAQUS and showed a higher cooling rate in the laser zone. As a result, the microstructure in the laser zone was dominated by martensite while that in the hybrid zone was composed of 84 % austenite and 16 % ferrite. The laser zone showed poorer impact toughness and corrosion resistance than the hybrid zone. However, the corrosion resistance of the whole weld was the worst. Because the inhomogeneous microstructure formed a galvanic couple that accelerated the corrosion process. This work indicated that the energy ratio (the ratio of laser to arc energy) should be considered in the welding of dissimilar thick steel to reduce the inhomogeneity in the two zones and obtain a desirable property balance among hardness, toughness, and corrosion resistance.

The solution of the nonlinear (NL) vibration problem of the interaction of laminated plates made of exponentially graded orthotropic layers (EGOLs) with elastic foundations within the Kirchhoff–Love theory (KLT) is developed using the modified Lindstedt–Poincaré method for the first time. Young's modulus and the material density of the orthotropic layers of laminated plates are assumed to vary exponentially in the direction of thickness, and Poisson's ratio is assumed to be constant. The governing equations are derived as equations of motion and compatibility using the stress–strain relationship within the framework of KLT and von Karman-type nonlinear theory. NL partial differential equations are reduced to NL ordinary differential equations by the Galerkin method and solved by using the modified Lindstedt–Poincaré method to obtain unique amplitude-dependent expressions for the NL frequency. The proposed solution is validated by comparing the results for laminated plates consisting of exponentially graded orthotropic layers with the results for laminated homogeneous orthotropic plates. Finally, a series of examples are presented to illustrate numerical results on the nonlinear frequency of rectangular plates composed of homogeneous and exponentially graded layers. The effects of the exponential change in the material gradient in the layers, the arrangement and number of the layers, the elastic foundations, the plate aspect ratio and the nonlinearity of the frequency are investigated. [ABSTRACT FROM AUTHOR]

The current study examines the behavior of an SH wave traveling over a functionally graded magneto-elastic substrate arrangement. At the substrate-vacuum interface, two irregularities with different shapes—rectangular and parabolically shaped—are considered in electrically and magnetically open cases and electrically and magnetically short cases. A study is also done on the combined impact of inhomogeneity, depth source, and irregularity. With the help of the Fourier transform, inverse Fourier transform, and perturbation technique, complex frequency relation has been derived for each type of irregular interface. The results’ key characteristics are highlighted. In order to know the impact of the parameters involved, a particular model consisting of BaTiO3- CoFe2O4 magneto-electro-elastic material has been taken. The findings were presented in the form of graphs, which were created using Mathematica 7. Graphs are plotted for variations in wavenumber and phase velocity. This calculation model could be the ideal match for laminated FGMEE structures utilized as surface acoustic wave devices since the variation of the film's magneto-electromechanical characteristics changes gradually with depth and throughout the production process (SAW). As a result, it can serve as a theoretical foundation for the design of high-performance SAW devices. [ABSTRACT FROM AUTHOR]

For large-scale device fabrication, information about film inhomogeneities is crucial for high fabrication yield. In this work, inhomogeneities in two-inch diameter heavily boron-doped nanocrystalline diamond (BNCD) films have been studied. Two BNCD films were grown using chemical vapour deposition (CVD) with different boron-to-carbon (B/C) ratios. Their superconducting properties were measured as a function of distance from the centre of the film. The critical temperature (Tc) and critical magnetic field (Hc2) decreased radially outwards from the centre for both films. Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM) and scanning electron microscopy (SEM) were done on the samples to pinpoint the underlying explanation for the observed behaviour. Raman spectroscopy suggested a reduction in boron concentration and diamond purity over both films while moving radially outwards from the centre. XPS data from both films, however, did not show similar behaviours to that observed from the Raman data for the B/C ratios or diamond content. The AFM scans and SEM analysis showed a decreasing grain size further away from the film centre irrespective of the B/C ratio. This is due to the film being thinner at the edges when compared with the centre of the film. Raman analysis showed that the film with the higher B/C ratio had a higher diamond purity across the film. As expected, the film with a higher B/C ratio showed a more robust superconducting behaviour. The observed reductions in boron concentration, diamond purity, film thickness and decreased grain sizes are responsible for the diminishing superconductivity at the edge of the films.

Decreasing the freezing time of the cold storage heat exchanger was an effective way to reduce the risk of cold chain breakage and the fluctuation of cold chain temperature. A validated unsteady mathematical model of the cold storage heat exchanger was established to analyze the transient evolution of temperature, velocity, ice distribution, and heat transfer coefficient for different diameters of heat transfer tubes and coolant temperatures. The results showed that there were four stages of temperature in the cold storage heat exchanger, namely the primary cooling stage, the freezing stage, the secondary cooling stage, and the constant temperature stage. The ice fraction distribution and the heat transfer coefficient were inextricably linked to the water's natural convection. The average heat transfer coefficient decreased with decreasing coolant temperature and increasing heat transfer tube diameters. The freezing time decreased with the coolant temperature and the diameter of the heat transfer tubes decreasing. The tendency of the inhomogeneity of ice distribution first increased with the ice fraction up to 0.75 and then decreased with the ice fraction over 0.75. The inhomogeneity decreased with the coolant temperature increasing when the diameter of the heat transfer tubes was greater than 2 mm.

The microstructure and performance homogeneity of 80 mm thick ultra-wide 7B50-T7751 plate with different widths and thicknesses were studied by means of mechanical testing machine and scanning electron microscope, and the fatigue properties were compared and discussed with 7050-T7451 plate. The results show that the ultra-wide 7B50-T7751 plate has excellent mechanical properties. In L and LT directions, the tensile yield strength of 1/2 thickness reaches up to 568 MPa and 545 MPa, and the tensile strength reaches up to 612 MPa and 591 MPa, the compressive yield strength reaches up to 575 MPa and 587 MPa, the fracture toughness in L-T direction and T-L direction reaches 30.16 MPa·m1/2 and 26.47 MPa·m1/2, respectively. The ultra-wide thick plate exhibits certain anisotropy at different width positions, the performance homogeneity in LT direction tends to be better than in L direction. Performance at different width positions with 1/4 thickness shows little difference, while the performance at the edge of 1/2 thickness is better than that of the center. No obvious texture exhibits at 1/4 thickness, however, the main textures at the center of 1/2 thickness are S texture and Brass texture, and the main textures at the edge are R texture, S texture and Brass texture. When the stress ratio is 0.06, the T-L anti-fatigue crack growth rate performance of ultra-wide 7B50-T7751 thick plate is better than 7050-T7451 plate with the same thickness. The fatigue limit of LT smooth sample (Kt=1) is about 7.6% inferior than that of 7050-T7451 plate, while the fatigue limit of notch sample (Kt=3) is about 3.7% higher.

Based on the model of in-plane oscillations of inhomogeneous prestressed plates, the new inverse problems of identifying the components of the prestress tensor via acoustic response probing are considered for the plates with and without holes and inclusions; the prestress components are assumed to be functions of two coordinates. Prestresses were set as a result of solving auxiliary problems of static loading of plates by some initial mechanical load. To solve the main and auxiliary problems of calculating the plates’ displacement functions, a finite element (FE) scheme was developed based on the derived corresponding weak problem statements, implemented in the form of software systems in the FE package FreeFem++. Rectangular plates clamped along one face, both solid and having a hole or a rigid insert, were considered. Inverse problems of identification of three prestress functions depending on two coordinates are formulated on the basis of additional data about the acoustic response on the non-clamped edges of the plates as a result of considering several sets of probing loads at several frequencies. In view of the nonlinearity of the inverse problems under study, an iterative approach was developed to solve them, which combines solving the direct problems for current approximations of the desired functions and the determination of the corresponding corrections from the operator equation built at each iteration. To solve the operator equation, a projection method has been employed that allows one to present the corrections in the form of expansions in terms of some smooth given functions and reduce the problem solution to the study of ill-conditioned SLAEs with respect to sets of the expansion coefficients using the A. N. Tikhonov method. The results of computational experiments on the simultaneous identification of two-dimensional prestress fields corresponding to various types of initial actions on the considered plates are discussed.

Sprite halos are diffuse glow discharges in the D-region ionosphere triggered by the quasi-electrostatic (QES) fields of lightning discharges. A three-dimensional (3D) QES model is adopted to investigate the effect of ionospheric electron density on sprite halos. The electron density is described by an exponential formula, parameterized by reference height (h’) and sharpness (β), and the local inhomogeneity has a Gaussian density distribution. Simulation results indicate that the reference height and steepness of the nighttime electron density affect the penetration altitudes and amplitudes of normalized electric fields, as well as the altitudes and intensities of the corresponding sprite halos optical emissions. A comparison of the daytime and nighttime conditions demonstrates that the daytime electron density profile is not favorable for generating sprite halos emissions. Furthermore, the pre-existing electron density inhomogeneities lead to enhanced local electric fields and optical emissions, potentially offering a plausible explanation for the horizontal displacement between sprites and their parent lightning, as well as their clustering.

A 3D problem in linear elasticity is considered for a thin inhomogeneous layer subject to transverse compression. For the first time, the effect of arbitrary vertical inhomogeneity is elucidated. Two sets of boundary conditions along the faces of the layer are adapted for modelling transverse compression. Robust asymptotic formulae involving repeated integrals across the thickness are derived for displacements and stresses. As an illustration, numerical results are presented for the elastic moduli having a transverse parabolic variation. The obtained results have a potential to be implemented in modern technology, including manufacturing and design of functionally graded materials.

The differences in the microstructure, grain orientation, texture type, aging nano precipitate phase distribution and mechanical properties of 160 mm 7050-T7651 aluminum alloy extra-thick plate at different thickness positions were studied by means of metallographic microscope, scanning electron microscope, transmission electron microscope and mechanical tensile test. The results show that from the surface to the center of the plate, the content of the second phase particles in the microstructure decreases, but the size increases; The surface layer of the plate is mainly composed of small angle grain boundaries. The proportion of small angle grain boundaries ranges from 79% to 85%, while the proportion of small angle grain boundaries in the center of the plate is about 58%, which is a decrease of 26.6% to 31.8% compared to the proportion of small angle grain boundaries on the surface layer of the plate; The surface layer of the plate is mainly characterized by {001}shear texture, accounting for 3.64%. As the thickness increases, the content of deformation texture components gradually increases. The mechanical properties of the plate in the thickness direction show a trend of first decreasing and then increasing along the thickness surface-center-surface direction, and the optimal positions for mechanical properties are all located at the surface of the plate.

The vibration behavior of moderately-thick inhomogeneous orthotropic cylindrical shells under clamped boundary conditions based on first-order shear deformation theory (FOSDT) is investigated using an analytical approach. The basic relationships for cylindrical shells composed of inhomogeneous orthotropic materials are established, and then partial differential equations of motion are derived in the framework of FOSDT. The analytical expression for frequency is found for the first time using the special approach for clamped boundary conditions. After checking the accuracy of obtained expressions, the effects of shear stress, orthotropy ratio and inhomogeneity on frequency values are examined in detail.

In this study, an optical investigation in a wide spectral range of polymer-like (SiOxCyHz) thin films deposited by plasma-enhanced chemical vapor deposition (PECVD) is presented. The primary focus is on assessing the homogeneity of the grown films. Within the PECVD, it is possible to alter the properties of the deposited material by continually adjusting deposition process parameters and hence allow for the growth of inhomogeneous layers. However, as shown in this study, the growth of homogeneous layers could be similarly challenging. This challenge is especially pronounced at the beginning of the deposition process, where it is necessary to consider the influence of the substrate among other factors, as even slight variations in the deposition conditions can lead to the formation of inhomogeneous layers. Several series of polymer-like thin films were deposited onto silicon substrates with the goal of producing homogeneous layers, i.e. all deposition parameters were held constant. These samples were optically characterized with a special interest in homogeneity, especially at the beginning of the growth. It was found that initial inhomogeneous growth is always present. The thickness of the initial inhomogeneous part was found to be surprisingly large.

The analysis of the bending behavior of rotating porous disks with exponential thickness variation consisting of viscoelastic functionally graded material is illustrated. The study of bending in the porous disk was done using the first-order shear deformation theory. The porous disk is under the effect of a combination of mechanical stresses and thermal distribution. All material factors for the porous disk change across the thickness as a power law of radius. To solve the mathematical structure by using the semi-analytical technique for displacements in the porous disk, and then to treat the structure model with viscoelastic material by the correspondence principle and Illyushin's approximation manner. Numerical outcomes including the effect of porosity parameter, inhomogeneity factor, and relaxation time are presented with three different sets of boundary conditions for the solid and hollow disks. A comparison between porous and perfect disk with numerous values of porosity parameters and different inhomogeneity factors have been shown to emphasize the importance of complex mathematical structure in modern engineering mechanical designs. [ABSTRACT FROM AUTHOR]

Monitoring and diagnosing the battery status in real‐time are of utmost importance for clarifying failure mechanism, improving battery performance, and ensuring safety, particularly under fast charging conditions. Recently, advanced operando techniques have been developed to observe changes in the microstructures of lithium deposits using laboratory‐scale cell designs, focusing on understanding the nature of Li metal electrodes. However, the macroscopic spatial inhomogeneity of lithium electroplating/stripping in the prototype pressurized pouch cells has not been measured in real‐time under practical conditions. Herein, a new noninvasive operando technique, spatial pressure mapping analysis, is introduced to macroscopically and quantitatively measure spatial pressure changes in a pressurized pouch cell during cycling. Moreover, dynamic spatial changes in the macroscopic morphology of the lithium metal electrode are theoretically visualized by combining operando pressure mapping data with mechanical analyses of cell components. Additionally, under fast charging conditions, the direct correlation between abrupt capacity fading and sudden increases in spatial pressure distribution inhomogeneity is demonstrated through comparative analysis of pouch cells under various external pressures, electrolyte species, and electrolyte weight to cell capacity (e/c) ratios. This operando technique provides insights for assessing the current battery status and understanding the complex origin of cell degradation behavior in pressurized pouch cells. [ABSTRACT FROM AUTHOR]

For a given class of materials, universal deformations are those that can be maintained in the absence of body forces by applying only boundary tractions. Universal deformations play a crucial role in nonlinear elasticity. To date, their classification has been accomplished for homogeneous isotropic solids following Ericksen's seminal work, and homogeneous anisotropic solids and inhomogeneous isotropic solids in our recent works. In this paper we study universal deformations for inhomogeneous anisotropic solids defined as materials whose energy function depends on position. We consider both compressible and incompressible transversely isotropic, orthotropic, and monoclinic solids. We show that the universality constraints—the constraints that are dictated by the equilibrium equations and the arbitrariness of the energy function—for inhomogeneous anisotropic solids include those of inhomogeneous isotropic and homogeneous anisotropic solids. For compressible solids, universal deformations are homogeneous and the material preferred directions are uniform. For each of the three classes of anisotropic solids we find the corresponding universal inhomogeneities—those inhomogeneities that are consistent with the universality constraints. For incompressible anisotropic solids we find the universal inhomogeneities for each of the six known families of universal deformations. This work provides a systematic approach to study analytically functionally-graded fiber-reinforced elastic solids. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Materials Engineering / Cailiao Gongcheng is the property of Journal of Materials Engineering Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Realising an ideal lithium-ion battery (LIB) cell characterised by entirely homogeneous physical properties poses a significant, if not an impossible, challenge in LIB production. Even the slightest deviation in a process parameter in its production leads to inhomogeneities and causes a deviation in performance parameters of LIBs within the same batch. The greater the number and/or intensity of inhomogeneities, the more they need to be avoided. Severe inhomogeneities (defects), such as metal particle contamination, significantly impact the cell's performance. Besides electrical measurements, image-based measurement methods can be used to identify defects and, thus, ensure the production quality and safety of LIBs. While the applicability of computed tomography (CT) as an image-based measurement method for detecting defects has been proven, the limitations of this method still need to be determined. In this study, a systematic analysis of the capabilities of CT imaging was conducted. A multilayer pouch cell without an electrolyte was reassembled with several defects on one of the middle anodes. To investigate the boundaries of CT, defects such as a partial and complete removal of the coating, a cut, or a kink, as well as particle contaminations of various sizes and materials (aluminium, copper, iron) were chosen. By comparing the CT images of the cell using laser scanning microscope images of the defective anode, it could be proven that all selected defects except the kink were detectable. [ABSTRACT FROM AUTHOR]

Faber series are used extensively in the application of complex variable methods to two-dimensional elasticity theory, for example, in the mechanical analysis of composite materials where Faber series representations of complex potentials lead to convenient expressions for the corresponding displacement and stress distributions. In many cases, the use of the Faber series is combined with conformal mapping techniques which "transfer" a boundary value problem defined in the elastic body (physical plane) to a simpler problem posed in an imaginary plane characterized by the conformal mapping. In several instances in the literature, however, little attention has been paid to the domain of definition of the Faber series in the imaginary plane leading often to misunderstandings and erroneous conclusions regarding the concept and feasibility of the use of the Faber series. In this paper, we present a thorough and rigorous examination of the representation of the Faber series in both the physical (occupied by the material) and imaginary (defined by the conformal mapping) plane. In addition, we show that replacing a truncated Faber series by a truncated Taylor series does not induce any additional errors in the numerical analysis of the corresponding boundary value problem. We anticipate that the discussion in this paper will help clarify any existing misinterpretations regarding the application of the Faber series and help further extend their use to a range of problems in composite mechanics. [ABSTRACT FROM AUTHOR]

The current work examines shear wave propagation in inhomogeneous functionally graded orthotropic media (FGOM) with imperfect contacts. The intermediate stratum is assumed to be viscous FGOM, while the upper and lower FGOMs have been endowed with initial stress. Closed-form displacement fields have been derived for both the layers and half space. The derivation process involves employing the interfacial stress-displacement continuity condition, which accounts for sliding and loosely bonded parameters, in conjunction with the requirement of a stress-free upper interface and a bounded lower half space. Special cases of previously published results in the literature were used to validate the analytical form of the dispersion relation. The study also includes a mathematical analysis of the dispersion equation as well as numerical computations for the presented geophysical model to characterize the impact of initially stressed parameters, inhomogeneity parameters, dissipation factor, and the effect of interface imperfectness on shear wave velocity. Notably, the study emphasizes the effect of sliding interface on the propagation of SH waves at the lower contact. The current finding adds to our understanding of shear wave propagation dynamics in elastic inhomogeneous functionally graded materials, which can help with earthquake engineering design and execution. [ABSTRACT FROM AUTHOR]

Large magnetic resistance has been widely considered due to its many applications in various fields, including the manufacture of magnetic sensors. An important case of this type of resistance is the linear magnetoresistance caused by the inhomogeneity of charge distribution. The magnetoresistance of heterogeneous conductors is simulated by the two-dimensional resistance network model. In the network model, the resistance unit of a homogeneous circular disk with four current terminals and the potential difference between the terminals is considered, and the currents and potential differences are connected to each other by means of the impedance matrix, and the magnetic field is perpendicular to the lattice. In this work, we study and investigate the changes in magnetoresistance for a network including two subsystems with different resistances with a diagonal arrangement. The results show that the changes in the magnetic resistance of the heterogeneous system depend on the resistance ratio of the two materials as well as the location of the boundary between them. In addition, it was observed that for large values ​​of the resistance ratio or high inhomogeneity, there is the possibility of the existence of a peak of resistance variation.

In this note we study the response of an inhomogeneous body, whose material moduli depend on the density and the mechanical pressure, that is described by an implicit constitutive relation between the Cauchy stress and the right Cauchy–Green tensor. Such a constitutive relation is relevant to the study of the deformation of porous elastic solids as the porous structure varies and the local density changes. The boundary value problems of a plate of such a material subject to uniaxial and bi-axial extension and compression are considered. We find that regions that are more porous, and thus of lower macroscopic density, have the propensity to fail than regions of higher density, in the sense the load carrying capacity decreases, when other measures such as the stress are comparable.

While usually we don't know complete geometrical and physical information on the occurred inhomogeneity, but in order to study the related phenomena, continuum mechanics theory as well as exiting energy-based models need direct information from the desired system in order to A General Approach to the Mechanical Analysis of Continuous Local Inhomogeneity Using Continuum Mechanics Theory and A New General Energy-Based- Modelapply the field equations. Of course, theories and ideas based on the unification of mechanics and thermodynamics can offer other solutions. This paper establishes a general energy based model to study effects of local inhomogeneity on the mechanical behavior of materials using thermodynamic laws with a new deviation as well as new approach to the total energy. In fact, the main goal is that the established model can be used with a wide range of applications and appropriate accuracy, both theoretically and experimentally, while not getting involved with excessive computational complexity. It can be noted that the extracted formulations develop possibility to study inhomogeneity effects on the mechanical behavior without any more limiting conditions. In addition, due to that study of the stored and dissipated energy, usually, has the main role in the investigating of the inhomogeneity effects on the mechanical behavior, also the point of view in the presented model is in complete agreement to provide the conditions for this study directly. Therefore, the prediction possibility of the inhomogeneity effects on the mechanical behavior will be provided with the smallest volume of needed calculations. Also, due to that the structure and properties of the inhomogeneity are unknown usually, the formulations aren't dependent to these knowledge directly, and can be analyzed theoretically and experimentally to study the homogeneity part, as a known material. In the following, feasible processes are studied using extracted formulations. To validate the equations, a rectangular material shape with local inhomogeneity is considered, and extracted equations are developed for that. To consider our mean on the stored and dissipated energies, it is assumed that the homogeneity part of material has viscoelastic behavior, and the equations are developed to Maxwell and Kelvin viscoelastic models in different homogeneity parts of the body. In the following, classical continuum mechanic theory due to elasticity theory is used, and the field equations are developed to the considered body. Finally, results are discussed, compared as well as their differences, and corresponding capabilities for functional completion are discussed. Finally, the fundamental equivalence of the results is studied, and matching of the results between continuum mechanics theory and extracted formulations is shown.

Abstract Monitoring and diagnosing the battery status in real‐time are of utmost importance for clarifying failure mechanism, improving battery performance, and ensuring safety, particularly under fast charging conditions. Recently, advanced operando techniques have been developed to observe changes in the microstructures of lithium deposits using laboratory‐scale cell designs, focusing on understanding the nature of Li metal electrodes. However, the macroscopic spatial inhomogeneity of lithium electroplating/stripping in the prototype pressurized pouch cells has not been measured in real‐time under practical conditions. Herein, a new noninvasive operando technique, spatial pressure mapping analysis, is introduced to macroscopically and quantitatively measure spatial pressure changes in a pressurized pouch cell during cycling. Moreover, dynamic spatial changes in the macroscopic morphology of the lithium metal electrode are theoretically visualized by combining operando pressure mapping data with mechanical analyses of cell components. Additionally, under fast charging conditions, the direct correlation between abrupt capacity fading and sudden increases in spatial pressure distribution inhomogeneity is demonstrated through comparative analysis of pouch cells under various external pressures, electrolyte species, and electrolyte weight to cell capacity (e/c) ratios. This operando technique provides insights for assessing the current battery status and understanding the complex origin of cell degradation behavior in pressurized pouch cells.

The mathematical modeling of the stability problem of nanocomposite cylindrical shells is one of the applications of partial differential equations (PDEs). In this study, the stability behavior of inhomogeneous nanocomposite cylindrical shells (INH-NCCSs), under combined axial compression and hydrostatic pressure in the thermal environment, is investigated by means of the first-order shear deformation theory (FSDT). The nanocomposite material is modeled as homogeneous and heterogeneous and is based on a carbon nanotube (CNT)-reinforced polymer with the linear variation of the mechanical properties throughout the thickness. In the heterogeneous case, the mechanical properties are modeled as the linear function of the thickness coordinate. The basic equations are derived as partial differential equations and solved in a closed form, using the Galerkin procedure, to determine the critical combined loads for the selected structure in thermal environments. To test the reliability of the proposed formulation, comparisons with the results obtained by finite element and numerical methods in the literature are accompanied by a systematic study aimed at testing the sensitivity of the design response to the loading parameters, CNT models, and thermal environment. [ABSTRACT FROM AUTHOR]

The Li intercalation reaction exhibits non-uniform behavior along the thickness direction of the electrode in a Li-ion battery. This non-uniformity, or intra-layer inhomogeneity (ILIH), becomes more serious as the charging and discharging speed increases. Substantial ILIH can lead to Li plating and the emergence of inhomogeneous inner stress, resulting in a decrease in battery service life and an increase in battery safety risks. In this study, an operando optical observation was conducted based on the color change reaction during Li intercalation in the anode. Subsequently, we introduce a novel quantitative method to assess ILIH in commercial Li-ion batteries. A specific ILIH value ( K I L I H ) is first used in this article for ILIH characterization. An analysis of K I L I H at different charging and discharging rates was conducted, alongside the exploration of K I L I H -SOC trends and their underlying mechanisms. The proposed method exhibits favorable mathematical convergence and physical interpretability, as supported by the results and mechanism analysis. By enabling the assessment of ILIH evolution in response to SOC and (dis)charging rate variations, the proposed method holds significant potential for optimizing fast charging protocols in commercial batteries and contributing to the development of refined electrochemical battery models in future research. [ABSTRACT FROM AUTHOR]

Simple Summary: Our study aims to understand mysterious parts of our DNA, known as ultra-conserved non-coding elements. Found in the genomes of mammals and other vertebrates, these long (300 nucleotides, on average) DNA fragments have remained unchanged for hundreds of millions of years, despite numerous mutations happening within them. We do not yet know the function of these elements, but their extraordinary evolutionary stability could help us devise new approaches to preventing harmful mutations that lead to cancer and genetic disorders. We sought to discover why ultra-conserved non-coding elements are so resistant to change by studying their smaller building blocks, called dinucleotides, which play a crucial role in the shape and structure of DNA. Using a bioinformatics approach, we compared the differences in arrangement of dinucleotides in the ultra-conserved non-coding elements to the rest of the human genome. Our study revealed unique patterns within the ultra-conserved non-coding elements sections that distinguish them from the rest of our genetic code. Long human ultra-conserved non-coding elements (UCNEs) do not have any sequence similarity to each other or other characteristics that make them unalterable during vertebrate evolution. We hypothesized that UCNEs have unique dinucleotide (DN) composition and arrangements compared to the rest of the genome. A total of 4272 human UCNE sequences were analyzed computationally and compared with the whole genomes of human, chicken, zebrafish, and fly. Statistical analysis was performed to assess the non-randomness in DN spacing arrangements within the entire human genome and within UCNEs. Significant non-randomness in DN spacing arrangements was observed in the entire human genome. Additionally, UCNEs exhibited distinct patterns in DN arrangements compared to the rest of the genome. Approximately 83% of all DN pairs within UCNEs showed significant (>10%) non-random genomic arrangements at short distances (2–6 nucleotides) relative to each other. At the extremes, non-randomness in DN spacing distances deviated up to 40% from expected values and were frequently associated with GpC, CpG, ApT, and GpG/CpC dinucleotides. The described peculiarities in DN arrangements have persisted for hundreds of millions of years in vertebrates. These distinctive patterns may suggest that UCNEs have specific DNA conformations. [ABSTRACT FROM AUTHOR]

In this study, the stability of inhomogeneous nanocomposite cylindrical shells (INCCSs) under hydrostatic pressure in a thermal environment is presented. The effective material properties of the inhomogeneous nanocomposite cylindrical shell are modeled on the basis of the extended mixture rule. Based on the effective material properties, the fundamental relations and stability equations are derived for thermal environments. In this process, the first-order shear deformation theory (FSDT) for the homogeneous orthotropic shell is generalized to the inhomogeneous shell theory. This is accomplished using the modified Donnell-type shell theory. The analytical expressions are obtained for hydrostatic buckling pressure of INCCSs in the framework of FSDT and classical shell theory (CST) by obtaining a solution based on Galerkin's procedure. The numerical examples presented include both comparisons and original results. The last section shows the influences of carbon nanotube (CNT) models, volume fraction, and shell characteristics on the hydrostatic buckling pressure in the thermal environment. [ABSTRACT FROM AUTHOR]

The vibration behavior of moderately-thick inhomogeneous orthotropic cylindrical shells under clamped boundary conditions based on first-order shear deformation theory (FOSDT) is investigated using an analytical approach. The basic relationships for cylindrical shells composed of inhomogeneous orthotropic materials are established, and then partial differential equations of motion are derived in the framework of FOSDT. The analytical expression for frequency is found for the first time using the special approach for clamped boundary conditions. After checking the accuracy of obtained expressions, the effects of shear stress, orthotropy ratio and inhomogeneity on frequency values are examined in detail. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Aeronautical Materials is the property of Editorial Board of Journal of Aeronautical Materials and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The inhomogeneity of microstructures and mechanical properties in an as-quenched thin specification NM450TP wear-resistant steel plate were quantitatively investigated. The results show that the microstructures exhibit inhomogeneous distribution through the thickness and the area percentage of martensite and ferrite grains varies regularly through the thickness, and the content of ferrite on the top surface of the plate is found to be two times that of ferrite at the core location and more than that of ferrite at the bottom surface. In addition, the steel plate exhibits the obvious anisotropy of tensile properties, the tensile strength paralleling to the rolling direction is lower than that along the transverse direction while the elongation paralleling to the rolling direction is better than that along the transverse direction. The result indicates that the deformation degree of prior austenite grains during hot rolling and the content of martensite after quenching dominate the mechanical properties while the ferrite content is not the main factor affecting the plasticity. The findings provide experimental evidences and lay a theoretical foundation for analyzing the subsequent processing. [ABSTRACT FROM AUTHOR]

In this work, we investigate the magnetic soliton profile and propagation properties of ultrashort waves in one-dimensional deformed ferrite. A generalized variable-coefficient (1+1)-dimensional ultrashort wave model is obtained by employing the multi-scale expansion method and short-wave approximation. Using numerical simulations, we examine the impact of multiple inhomogeneities on the transmission of magnetic solitons, which arise from local and periodic deformations. Our results indicate that the localized inhomogeneity alter the velocity of magnetic solitons, allowing for the manipulation of their acceleration or deceleration. Periodic type deformation inhomogeneities, on the other hand, provide the magnetic solitons with a period-like external potential that converts its transmission mode to a controlled oscillation.