Arbitrary Number Of Layers Research Articles

New analytical model for multi-layered composite plates with imperfect interfaces under thermomechanical loading

AbstractA new analytical model for thermoelastic responses of a multi-layered composite plate with imperfect interfaces is developed. The composite plate contains an arbitrary number of layers of dissimilar materials and is subjected to general mechanical loads (both distributed internally and applied on edges for each layer) and temperature changes, which can vary from layer to layer and along two in-plane directions. Each layer is regarded as a Kirchhoff plate, and each imperfect interface is described using a spring-layer interface model, which can capture discontinuities in the displacement and stress fields across the interface. Unlike existing models, the governing equations and boundary conditions are simultaneously derived for each layer by using a variational procedure based on the first and second laws of thermodynamics, which are then combined to obtain the global equilibrium equations and boundary conditions for the multi-layered composite plate. A general analytical solution is developed for a symmetrically loaded composite square plate with an arbitrary number of layers and imperfect interfaces by using a new approach that first determines the interfacial normal and shear stress components on one interface. Closed-form solutions for two- and three-layer composite square plates are obtained as examples by directly applying the general analytical solution. Numerical results for two-, three- and five-layer composite plates under different loading and boundary conditions predicted by the current model are provided, which compare well with those obtained from finite element simulations using COMSOL, thereby validating the newly developed analytical model.

Plasmon scattering at a junction in double-layer two-dimensional electron gas plasmonic waveguide

Abstract The scattering of plasmons at a junction within a double-layer two-dimensional electron gas plasmonic waveguide is studied via a full electromagnetic method. The dispersion relation is derived by utilizing the transfer matrix method and can be extended to the situation of an arbitrary number of layers. By numerically solving the dispersion equations, both the acoustic and optical plasmon modes are identified in this double layer system, and the unstable plasmon modes arising from plasmon coupling in different layers are discussed elaborately. Subsequently, the total fields are expanded with eigenmodes and matched at the interface to analyze the scattering characteristics at the junction. The results indicate that the total power of the plasmon mode is amplified when the electron fluid flows from a high concentration region to a low concentration region, and the amplification is more evident at a higher drift velocity. Additionally, we address the scattering of unstable plasmons caused by the two-stream instability and find that the transmitted plasmons are excited intensively at the incidence of the growing plasmon, leading to the plasmon amplification. The detailed examination of plasmon scattering at junction is the prerequisite for studying more complex structures of terahertz plasmonic devices and comprehending the corresponding amplification mechanism.

Efficient design of complex-valued neural networks with application to the classification of transient acoustic signals.

A paper by the current authors Paul and Nelson [JASA Express Lett. 3(9), 094802 (2023)] showed how the singular value decomposition (SVD) of the matrix of real weights in a neural network could be used to prune the network during training. The paper presented here shows that a similar approach can be used to reduce the training time and increase the implementation efficiency of complex-valued neural networks. Such networks have potential advantages compared to their real-valued counterparts, especially when the complex representation of the data is important, which is the often case in acoustic signal processing. In comparing the performance of networks having both real and complex elements, it is demonstrated that there are some advantages to the use of complex networks in the cases considered. The paper includes a derivation of the backpropagation algorithm, in matrix form, for training a complex-valued multilayer perceptron with an arbitrary number of layers. The matrix-based analysis enables the application of the SVD to the complex weight matrices in the network. The SVD-based pruning technique is applied to the problem of the classification of transient acoustic signals. It is shown how training times can be reduced, and implementation efficiency increased, while ensuring that such signals can be classified with remarkable accuracy.

Laser-induced ultrasound in multiple thin layers-An analytical solution.

Laser-induced ultrasound is based on the thermo-elastic conversion of absorbed short light pulses to pressure pulses. In the work presented here, laser-induced ultrasound in a planar structure of interconnected layers with variations in optical, thermal, and mechanical properties is studied. Layered structures can be used for generating wideband ultrasonic pulses specific to a chosen application. An analytical time-domain solution is derived for the resulting pressure transmitted from the layered structure. The solution is derived for an arbitrary number of layers with an arbitrary optical absorption profile. Free space Green's functions with image sources are used to derive the solution. A solution employing the Beer-Lambert law is also proposed. The simplification with reflections only at the boundaries is in agreement with previous published results. The spectral properties of the generated pulse are derived, where the effects of optical absorption coefficients and layer thicknesses are shown. The analytical solution is compared to one-dimensional (1D) simulations and a three-dimensional (3D) simulation, realised as a two-dimensional (2D) axially symmetric case, using the matlab toolbox k-Wave. The 3D simulation on-axis pressure agrees well with the 1D analytical solution when the diameter of the laser beam is larger by approximately 1 order of magnitude than the thickness of the planar layered structure.

Явные решения в проблеме звукоизоляции с использованием многослойных структур при нормальном прохождении волн

The problem of sound isolation at ultra-low frequencies (30–200 Hz) by using multilayered structures is con-sidered, taking into account the normal wave propagation and an arbitrary number of layers. It is assumed that the multilayered structure consists of parallel acoustic layers, connected to each other along vertical boundary lines; acoustic half-spaces (air) are located to the left and right of the structure. For the problem, we define the acoustic parameters of the structure. The wave equations of the harmonic process are described for the left and right half-spaces of the structure, using the Helmholtz equation and a system of linear algebraic equations with given boundary conditions. Besides, explicit analytical solutions are obtained to find the transmission coefficient (transparency coefficient), with an arbitrary number of layers. Examples of solution for low-frequency sound absorption for building structures with different numbers of layers of alternating building materials and air spaces are considered. The effectiveness of using mixed structures, in which air layers are sandwiched between high impedance layers, for low-frequency sound absorption has been confirmed by assessing the level of noise reduction.

Profiles of suction stress of layered soils under infiltration conditions and its applications

Suction stress is critical for understanding the hydrological and mechanical behavior of unsaturated soils in construction and engineering. Many soils encountered in these fields exhibit layering due to geological sedimentation or artificial reinforcement. This study establishes the vertical distributions of matric suction and degree of saturation for layered soils under one-dimensional (1D) steady-state seepage, using the Darcy law and constitutive relationships of unsaturated soils. A closed-form suction stress is derived for an arbitrary number of layers and soil types. Hypothetical layered soils with varying hydraulic properties at four infiltration rates are assessed. Results show that soil stratification affects the suction stress profiles, with the impact depending on infiltration rates, soil configuration, and layer thickness. Abrupt variations in suction stress occur at most layered interfaces due to differences in permeability between adjacent layers. The suction stress profiles can be used to evaluate the earth pressure and stability of layered slopes under seepage conditions. Several case studies of multi-layered slope failures in Southern Italy are presented to demonstrate the suitability of the proposed framework for evaluating the stability of layered slopes under rainfall conditions.

Optimal interply angle of bio-inspired composite curved panels with helicoidal fiber architecture

The exoskeleton structure of mantis shrimp’s dactyl clubs presents an extraordinary helicoidal reinforcement pattern, holding immense potential for revolutionizing fiber-reinforced composite materials. While extensive investigations have shed light on its unique advantages, the inherent nature of curved Bouligand structures remains incompletely comprehended. To elucidate these unexplored characteristics, the present study introduces a novel analytical model to efficiently calculate the interlaminar shear and normal stresses in helicoidal laminated curved beams under transverse loading. The analytical model systematically determines the optimal uniform fiber interply (pitch) angle for these bio-inspired structures with an arbitrary number of layers. The computational analysis revealed that achieving minimum interlaminar stresses always requires the precise orientation of π or 2π helicoids along the laminate thickness when the number of layers exceeds two. This theoretical discovery is remarkably identical to the study of stacked chitin fibrils in arthropod clubs reported in the literature. For a 37-ply composite, the flat and shallow-curved beam configurations primarily resulted in a 5° optimal pitch angle, while the deep-curved configuration yielded a 10° optimal angle. To validate the model, three-point bending testing were performed. Four fiber pitch angles were thoroughly examined, including the optimal and quad angles. The digital image correlation (DIC) technique was employed to analyze the structural responses and detect the onset of delamination. The numerical and experimental results demonstrated good consistency, exhibiting significant enhancement in the delamination resistance of up to 30 percent with the optimal angle.

Valleytronics in bulk MoS2 with a topologic optical field.

The valley degree of freedom1-4 of electrons in materials promises routes towards energy-efficient information storage with enticing prospects for quantum information processing5-7. Current challenges in utilizing valley polarization are symmetry conditions that require monolayer structures8,9 or specific material engineering10-13, non-resonant optical control to avoid energy dissipation and the ability to switch valley polarization at optical speed. We demonstrate all-optical and non-resonant control over valley polarization using bulk MoS2, a centrosymmetric material without Berry curvature at the valleys. Our universal method utilizes spin angular momentum-shaped trefoil optical control pulses14,15 to switch the material's electronic topology and induce valley polarization by transiently breaking time and space inversion symmetry16 through a simple phase rotation. We confirm valley polarization through the transient generation of the second harmonic of a non-collinear optical probe pulse, depending on the trefoil phase rotation. The investigation shows that direct optical control over the valley degree of freedom is not limited to monolayer structures. Indeed, such control is possible for systems with an arbitrary number of layers and for bulk materials. Non-resonant valley control is universal and, at optical speeds, unlocks the possibility of engineering efficient multimaterial valleytronic devices operating on quantum coherent timescales.

Universal three-dimensional finite element for analyzing of elastic inhomogeneous shells under thermomechanical loads

The work is devoted to the development of a new modification of the finite element intended for the calculation of inhomogeneous composite shells of thin and medium thickness. The element is constructed on the basis of a universal three-dimensional isoparametric 8-node multilayer finite element of a continuous medium. The layers of the modified finite element are made of composite materials reinforced with continuous unidirectional fibers. Within the framework of a finite element model of a multilayer shell of stepwise variable thickness, a technique for modeling the properties of a unidirectional fibrous composite material has been developed, based on a method for structuring material inhomogeneities iby thickness and by plan. The shell can consist of an arbitrary number of layers of varying thickness bonded into a single piece. Each layer can have its own type of material: traditional or composite. Effective physical and mechanical characteristics of the layer material are determined using known micromechanical methods for predicting the thermoelastic constants of a fiber composite through the known physical characteristics of the matrix and fiber. The fibrous material of the layer is presented as homogeneous transversely isotropic with planes of isotropy normal to the direction of reinforcement. Additional variable parameters of the "basic" universal finite element are supplemented with new attributes that determine the thermoelastic properties of the composite components. The new parameters are related to the choice of the type of fibrous composite material in the layer of the finite element, to the setting of structural micromechanical parameters of its components, and to the setting of the reinforcement orientation angle. This allows the calculations to use both traditional and fiber-composite materials in layers of inhomogeneous shells. Numerical examples demonstrate the effectiveness of the developed approach.

A hybrid finite difference level set–implicit mesh discontinuous Galerkin method for multi-layer coating flows

A mathematical model and numerical framework are presented for computing multi-physics multi-layer coating flow dynamics, with applications to the leveling of multi-layer paint films. The algorithm combines finite difference level set methods and high-order accurate sharp-interface implicit mesh discontinuous Galerkin methods to capture a complex set of multi-physics, incorporating Marangoni-driven multi-phase interfacial flow and the transport, mixing, and evaporation of multiple dissolved species. In particular, we develop several numerical methods for this multi-physics problem, including: high-order local discontinuous Galerkin methods for Poisson problems with Robin boundary conditions on implicitly-defined domains, to capture solvent evaporation; finite difference surface gradient methods, to robustly and accurately incorporate Marangoni stresses; and a coupled multi-physics time stepping approach, to incorporate all the different solvers at play including quasi-Newtonian fluid flow. The framework is applicable to an arbitrary number of layers and dissolved species; here, we apply it in a variety of settings, including multi-solvent evaporative paint dynamics, the flow and leveling of multi-layer automobile paint coatings in both 2D and 3D, and an examination of interfacial turbulence within a multi-layer matter cascade. Our results reproduce several phenomena observed in experiment, such as the formation of Marangoni plumes and Bénard cells. We also use the model to study the impact of long-wave deformational surface modes on immersed interfaces as well as the emergence of the final multi-layer film profile.

Multilayered Inhomogeneous Beams under Torsion and Bending: An Analytical Study of Energy Dissipation

The present theoretical paper is devoted to the problem of energy dissipation in multilayered inhomogeneous beam structures of visoelastic behaviour. In particular, our attention is concentrated on studying the energy dissipation for the case of a beam that is loaded simultaneously in torsion and bending. Both torsion and bending moments which are applied on the beam change with time so that the angles of twist and rotation of the beam end vary continuously with time. The viscoelastic mechanical behaviour of the beam under torsion is treated by a viscoelastic model that has two linear springs and a linear dashpot. The model is under time-dependent shear stress. The viscoelastic behaviour of the beam under bending is modelled in a similar way. An analytical approach of deriving the energy dissipation is applied. The approach treats a multilayered beam that has an arbitrary number of layers of different thicknesses and material properties. The layers are longitudinally inhomogeneous. An investigation of the energy dissipation is carried-out to clarify the effect of the parameters of the time-dependent bending and torsion moments, the material inhomogeneity and the beam size on the energy dissipation.

Generation a solution to the equations of elasticity theory for a layered strip basing on the principle of compressed mappings

A systematic presentation of the modified classical semi-inverse SaintVenant method as an iterative one is given on the example of generating a solution to the differential equations of elasticity theory for a long layered strip. The firstorder differential equations of the plane problem are reduced to the dimensionless form and replaced by integral equations with respect to the transverse coordinate, just as it is done in the Picard method of simple iterations. In this case, a small parameter appears in the integral equations before the integral sign as a multiplying factor, which is used to ensure convergence of solutions in accordance with the Banach’s principle of compressed mappings. The equations and elasticity relations are converted to a form that enables to calculate the unknowns consecutively, so that the unknowns being calculated in one equation are the inputs for the next equation, and etc. Fulfillment of the boundary conditions at the long edges leads to ordinary differential equations for slowly and rapidly changing singular components of the solution with sixteen effective stiffness coefficients that are defined by integrals from the given ones as a stepped function of Young's moduli for each layer. Integrating of these ordinary differential equations makes it possible to obtain the formulas for all the required unknowns of the problem, including transverse stresses that are not defined in the classical theory of the beam and solutions of the edge effect type, and to fulfill all the boundary conditions for the elasticity theory problem. The solution of three boundary value problems of the strip elasticity theory is provided such as for a two-layer strip with layers of the same thickness and different thicknesses, and a strip with an arbitrary number of layers. Formulas for all unknowns of the problem are obtained.

A Semi-Analytical Model of Contaminant Transport in Barrier Systems with Arbitrary Numbers of Layers

In regions with sanitary landfills, unsuitable liner designs can result in significant soil and groundwater contamination, leading to substantial environmental remediation costs. Addressing this challenge, we propose a semi-analytical model for solute transport that uses the advection–dispersion–reaction equation in a multi-layered liner system. A distinctive feature of our model is its ability to account for infiltration velocity, arbitrary numbers of layers, thin layers such as geomembranes, and mass flow. We validated our model against existing published models and applied it to a case study of a real sanitary landfill in the capital of Brazil. Through parametric analyses, we simulated contaminant transport across various layers, including the geomembrane (GM), geosynthetic clay liner (GCL), soil liner (SL), and compacted clay liner (CCL). The analyses showed the importance of choosing the most appropriate construction system based on the location and availability of materials. Considering toluene contamination, a GM molecular diffusion coefficient (DGM) greater than 10−13 m2 s−1 exhibited similar efficiency when compared with CCL (60 cm thick). In addition, the results showed that the liner system may have the same efficiency in changing SL (60 cm thick) for a GCL (1 cm thick).

A shear-lag model for laminated beams with extreme modulus mismatch between layers

Multilayer laminated beams, comprised of alternating stiff and soft layers, are widely used in flexible electronics and photonics. These structures exhibit complex mechanical behaviors that deviate from the Euler–Bernoulli beam theory under conditions of extreme inter-layer modulus mismatch. Extending beyond prior studies on trilayer beams, we present an analytical framework for laminated beams with arbitrary number of layers subjected to various bending conditions, and validate our theory with finite element analysis. We define an equivalent flexural rigidity, exploring its dependence on position and deformation, and systematically examine the impact of the number of layers, applied deformation, layer properties, and the layer aspect ratio.

Explicit thermal analysis of inhomogeneous multilayer cylinders using the direct integration method

A technique for analyzing two-dimensional thermal fields in hollow cylinders is presented when the cylinders are assembled of a number of perfectly connected coaxial layers made of dissimilar materials exhibiting arbitrarily continuous radial variation of their thermophysical properties. Making use of the direct integration method allows for reducing the original heat conduction equation with stepwise variable coefficients to the integral equations of the second kind with solution constructed through the resolvent-kernel technique in the form of explicit dependences on the applied thermal loading on the inner and outer circumferences of the cylinders and the internal heat sources. This approach allows for constructing a solution from the “single-solid” standpoint and thus is efficient for an arbitrary number of layers exhibiting inhomogeneous properties. On the other hand, the application of this technique does not involve the generalized-derivative apparatus typical for the use of single-solid methods. The applicability of the proposed solution for the verification of homogenization models for stratified cylinders is demonstrated by the considered case studies.

New analytical model for thermomechanical responses of multi-layered structures with imperfect interfaces

A new analytical model is developed for thermomechanical responses of multi-layered structures with an arbitrary number of layers and subjected to general thermal and mechanical loading. The formulation is based on an extended Bernoulli–Euler beam theory and a slip-interface model. The former includes Poisson’s effect and covers both the plane stress and plane strain deformations, and the latter allows slipping between two adjacent layers but no jump in the normal displacement or traction. An analytical solution for a multi-layered structure under general thermomechanical loading is derived by using a new approach that first determines one interfacial shear stress and the curvature of the deformed structure. To illustrate the newly developed model, three example problems for two-, three- and five-layer structures respectively are analytically solved by directly applying the new model. In all three cases, the solutions are obtained in closed-form expressions by considering both temperature changes and mechanical loads including body forces, distributed normal and shear stresses on the top and bottom surfaces, and normal forces, transverse shear forces and bending moments at the two ends, unlike existing ones. It is shown that the current solution for two-layer structures recovers an existing solution without considering Poisson’s effect and mechanical loading and the classical solution of Timoshenko for perfectly bonded bi-metal thermostats as two special cases. The closed-form solution for five-layer structures with imperfect interfaces is derived here for the first time. In addition, numerical results are provided for five- and seven-layer transistor stacks to quantitatively demonstrate the new model. It is found that the current results for the five-layer transistor stack agree well with those obtained by others, thereby further validating the new model.

An Exact Solution to the Linearized Richards Equation for Layered Media With Flexible Initial Condition

AbstractSrivastava and Yeh (1991, https://doi.org/10.1029/90WR02772) derived an exact solution to the linearized Richards equation (LRE) for two‐layer medium infiltration using the Laplace transform (LT) method with a particular initial condition assumed, making the most pioneering contribution to the derivation of exact solutions to the layered‐medium LRE (i.e., ES‐LMLREs). However, the LT method is unsuitable for deriving an ES‐LMLRE that considers either an arbitrary initial condition or an arbitrary number of layers, or both, preventing further progress in developing ES‐LMLREs. Adopting a new solution strategy, namely a conjunctive use of the variable separation method and the transfer matrix method, we develop a novel exact layered‐medium‐LRE infiltration solution, overcoming the above difficulties. First, the proposed solution is successfully validated against the Srivastava‐Yeh solution. As a feature‐demonstration example, a layered‐medium water absorption process is simulated, and our solution well captures how the heterogeneity of hydraulic parameters affects the dynamics of this process. Moreover, the proposed solution is a valuable benchmark for related numerical models.

On the strength of many-layer fiber-reinforced plates

In Kolpakov and Rakin (2021), the concept of a representative model for multilayer plates was introduced. It was shown that a three-layer representative plate model provides us with complete information about the local stress-strain state (SSS) in a multilayer plate formed from an arbitrary number of layers. In this paper, it is shown that for a many-layer plate (the number of layers is more than 300), the periodicity cell problems (PCPs) corresponding to in-plane (tension/shear) make the main contribution to the local SSS. On one hand, it is a similarity with the uniform plate. On another hand, the solutions to the PCPs corresponding to in-plane (tension/shear) for fiber-reinforced plate are very different from the solutions corresponding to uniform plate.If the number of layers is less than 60, it is necessary to take into account the solutions to the bending/torsion cell problem. In both cases, it is necessary to take into account the skin-boundary layers (which occurs both in tension/shear and bending/torsion PCPs).Using the idea of a representative model, we construct a homogenized strength criterion (HSC) for fiber reinforced plates. As a result of the complex form of the local stress-strain stale in the components of composite, the HSC is built as a computer procedure. Since the representative model is low-dimension one, the procedure is fast.In general, the failure surface is a 5-dimensional surface in 6-dimensional space. For a multilayer plate, the strength criterion depends on three variables (three combinations of tension/shear and bending/torsion). In this case, the failure surface is a 2D surface in 3D space and can be visualized. In multilayer plates, we find many similarities with the classical theory of plates, but at the same time we clearly see quantitative and qualitative differences between multilayer plates and classical information plates. In particular, we see that the maximum of the local stress in composite plate occurs not at the top/bottom surfaces of the plate, but in the deep of the plate.

Shear wave transmissivity and wave-induced vorticity diffusion through conversion scattering to slow-shear diffusion wave

In the poroelasticity theory of de la Cruz and Spanos, fluid shearing within the viscous boundary layer, i.e. fluid vorticity, manifests as an independent process, namely the diffusive slow shear wave. Quantifying its impact on elastic wave propagation remains a research challenge. We analyse the transmissivity of a horizontally polarized shear wave travelling across a stack of porous fluid-saturated layers. The fluid shearing developed at each contact is captured, in a macroscopic sense, through conversion scattering into this diffusive slow shear wave. Generalizing the reflectivity method for elastic waves to the poroelastic case, we develop semi-analytical results for an arbitrary number of layers. We find that the conversion scattering into this diffusion wave reduces the shear wave amplitude, and this reduction accumulates with the number of layers. In the limit when the layer thickness corresponds to the pore diameter, the resulting wave quality factor is close to the predictions of previously reported attempts to capture the fluid vorticity. However, our approach is distinctively different since it is purely based on a wave-theoretic analysis of interacting waves, acknowledging vorticity diffusion as an independent process, thereby avoiding the problems arising when incorporating a pore-scale phenomenon in a macroscopic wave propagation theory.

A closed-form model for layered snow slabs

Abstract. We propose a closed-form analytical model for the mechanical behavior of stratified snow covers for the purpose of investigating and predicting the physical processes that lead to the formation of dry-snow slab avalanches. We represent the system of a stratified snow slab covering a collapsible weak layer by a beam composed of an arbitrary number of layers supported by an anisotropic elastic foundation in a two-dimensional plane-strain model. The model makes use of laminate mechanics and provides slab deformations, stresses in the weak layer, and energy release rates of weak-layer anticracks in real time. The quantities can be used in failure models of avalanche release. The closed-form solution accounts for the layering-induced coupling of bending and extension in the slab and of shear and normal stresses in the weak layer. It is validated against experimentally recorded displacement fields and a comprehensive finite-element model indicating very good agreement. We show that layered slabs cannot be homogenized into equivalent isotropic bodies and reveal the impact of layering on bridging with respect to weak-layer stresses and energy release rates. It is demonstrated that inclined propagation saw tests allow for the determination of mixed-mode weak-layer fracture toughnesses. Our results suggest that such tests are dominated by mode I when cut upslope and comprise significant mode II contributions when cut downslope. A Python implementation of the presented model is publicly available as part of the Weak Layer Anticrack Nucleation Model (WEAC) software package under https://github.com/2phi/weac (last access: 28 March 2023) and https://pypi.org/project/weac (last access: 28 March 2023, Rosendahl and Weißgraeber, 2022).