Multilayered Plates Research Articles

A New Method for Measuring Multilayer Thickness Using a Chromatic Confocal Sensor

Multilayer transparent plates play a crucial role in industrial fields, such as optical lenses, electrodes, and solar panels, because of their superior optical and electrical properties. The thickness and uniformity of such plates are decisive for the quality of the final product. However, traditional contact measurement methods are inadequate in accuracy and pose the risk of damaging the plates, making nondestructive measurement of multilayer transparent plate thickness rather challenging. A new measurement technology is urgently needed. This study proposes a new method for the thickness measurement of multilayer transparent plates based on chromatic confocal sensor technology. First, we investigated the dispersive behavior of light in various media layers and derived theoretical measurement models for single-layer and multilayer transparent plate thicknesses. Subsequently, we designed and constructed a measurement system using a C-series chromatic confocal sensor and optical instruments and prepared a five-layer transparent sample consisting of quartz and air layers to confirm the feasibility of the method. The results of the experiment show that the proposed method can accurately measure the thickness of the five-layer sample with a maximum absolute error within 13 µm and a maximum relative error of 4.27%, thus proving its validity, precision, and stability. The results further indicate the high practicality and reliability of this technology in production environments, theoretically enabling the simultaneous measurement of up to 18 layers of the plate and offering broad application prospects in the industry.

Weak interface-induced repeated kinking of a central crack in a brittle multilayered plate under remote shear loading

Understanding the repeated kinking pattern of cracks is essential for controlling the complex fracture trajectories in multilayered composites. While previous studies have explored many aspects of fractures in layered materials, the conditions governing the repeated kinking behavior under basic loading modes remain largely unrevealed. This research elucidates the continual kinking condition for a central crack in a brittle, multilayered plate with closely-parallel weak interfaces under remote shear stresses. Using the strain energy release rate (SERR) ratio criterion, we analytically derived a closed-form solution to the condition through the equivalent crack concept. The solution specifies a value domain for the intersection angle and fracture toughness ratio of weak interfaces, where the load-guided direction competes closely with the weak interface-guided direction to shape the crack trajectory into a repeated kinking pattern. Our theoretical results, validated by a series of finite element (FE) simulations, clarify how closely-parallel weak interfaces induce repeated crack kinking in multilayered materials under remote shear loading. This research paves the way for the deeper understanding of intricate crack trajectories under mixed loads in various practical applications.

Vibration analysis of multilayer graphene origami-enabled metamaterial plates

Vibration analysis of multilayer graphene origami-enabled metamaterial plates

Accounting of imperfect interfaces in multilayer modeling

Multilayer systems are widely used in industry for their performances as compared with homogeneous materials. The layers are usually glued together but the bonding may be imperfect (air bubble, detachment). The interfaces are generally modeled as sliding or bonded. These two behaviors can be significantly different and the actual behavior is generally somewhere in between. The vibroacoustic behavior of the structure is thus modified by the imperfect interface. Several models have been implemented to describe the dynamic behavior of multilayer systems with imperfect interfaces. In this paper, we propose an analytical model of imperfect interfaces based on the Transfer Matrix Method (TMM). Two computations are performed in parallel (one with a perfectly bonded interface and the other with a sliding interface). Instead of mixing impedances or admittances matrices, a mixing law on the state variables is applied, resulting in an equivalent global matrix which can be coupled in any multi-layer. The model is compared in terms of the sound absorption or sound transmission loss with the existing ones and is applied on different classical multilayer systems with multi-layered solid plates and a multilayer composed of a porous layer with a heavy layer which is widely used in the automotive industry.

Numerical Study of Ballistic Performance in Level III SiC Ceramic Multilayered UHMWPE Ballistic Plates

This study investigates the ballistic resistance of composite plates composed of a silicon carbide (SiC) strike face and ultra-high molecular weight polyethylene (UHMWPE) layers against 7.62 mm NATO caliber projectiles using Ansys Explicit Dynamics. Five ballistic plate samples were numerically modeled, featuring 40 to 60 UHMWPE layers and a 4 mm SiC strike face. The simulation assessed the plates' response, including backface signature, bullet penetration depth, absorbed kinetic energy, and deformation mechanisms. The findings revealed that increasing the UHMWPE thickness reduces both the backface signature and bullet penetration depth. Plates with 50 to 60 layers of UHMWPE met level III NIJ standards, demonstrating lower backface signatures and bullet penetration compared to those with 40 or 45 layers. Thicker UHMWPE layers were associated with reduced deformation, with the plate featuring 60 layers of UHMWPE and an overall thickness of 25 mm emerging as the optimal configuration for level III ballistic protection.

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.

A quasi-3D SinZZ model-driven multi-field Chebyshev FEM for nonlinear vibration control in multilayer multiferroic composite plates

This paper presents an advanced numerical method for modeling and mitigating nonlinear vibrations in thin multilayered fiber-reinforced multiferroic composite plates, addressing complex multi-physical interactions. The proposed methodology leverages a multi-physical coupling Chebyshev finite element formulation, utilizing high-order shape functions derived from Chebyshev polynomials. By integrating the strengths of spectral element methods and Legendre spectral finite element methods, this approach effectively overcomes challenges such as shear locking and spurious zero energy modes while ensuring high convergence rates in multi-physical problems. A quasi-3D refined model, incorporating the Murakami zig-zag model and sinusoidal shear deformation theory, is employed to accurately capture the nonlinear Von Kármán strain–displacement relationship and the magneto-electro-elastic coupling in multilayer structures with thickness-dependent material properties. To suppress nonlinear vibrations, the study utilizes a closed-loop multiphysical Chebyshev finite element model for time-domain analysis of viscoelastically damped systems, employing the Golla–Hughes–McTavish model. The results underscore the significant influence of multiferroic properties and the strategic distribution of ferroelectric fibers within the substrate on the dynamic behavior of the plate. The numerical validation, supported by rigorous verification, demonstrates the robustness of the proposed method in effectively simulating and controlling multilayer fiber-reinforced multiferroic composite plates. Additionally, this research highlights the potential for significant vibration reduction through semi-active damping mechanisms, offering valuable insights for practical applications in industries where precision and stability are critical.

In Vitro evaluation of probiotic properties of lactic acid bacteria strains isolated from juçara fruit native to the Atlantic Forest

Lactic acid bacteria (LAB) are the microorganisms most commonly used as probiotics. Since probiotic benefits are strain-dependent, there is a continuous need for research into new cultures with probiotic properties. Fruits such as juçara (Euterpe edulis Martius), a palm species from the Atlantic Forest threatened with extinction, are rich niches for microorganisms, including LAB. This study investigated the probiotic properties of Lactococcus lactis J7 and Leuconostoc pseudomesenteroides JF17 strains isolated from juçara fruits native to the Atlantic Forest. Probiotic characteristics, such as tolerance to simulated gastrointestinal fluids or juices, hydrophobicity, autoaggregation, coaggregation properties, inhibition of pathogenic microorganisms, and technological properties were evaluated. The survival rate of L. lactis J7 and L. pseudomesenteroides JF17 decreased after exposure to simulated gastrointestinal conditions; however, L. lactis J7 was more resistant, maintaining viability at the end of the enteric phase of 6.07 ± 0.16 log CFU mL-1. The J7 strain also exhibited the highest values in hydrophobicity (12.55 ± 0.52%), autoaggregation (25.63 ± 0.75%), and coaggregation capacity with E. coli ATCC 25922 (21.52 ± 0.98%) and S. Enteritidis ATCC 13076 (22.68 ± 1.01%). Both J7 and JF17 strains demonstrated antimicrobial activity, confirmed by the multilayer agar plate system. Additionally, the growth of the strains was temperature-dependent, and they were able to thrive in high concentrations of sodium chloride (6%). Thus, L. lactis J7 is a promising probiotic candidate for the development of functional products. Nevertheless, further studies using animal models are necessary to explore the properties of these probiotic bacteria. Novel strains isolated from fruits should be studied to broaden the application of probiotic microorganisms in the development of foods and medicines.

A modified bond-based peridynamic approach for rigid projectile perforation on concrete slabs

Peridynamic (PD) has a unique advantage in describing the crack growth and fragmentation of brittle materials. Concerning the dynamic behaviors and failure patterns of concrete slabs under projectile perforations, a modified bond-based PD approach maintaining both the easy implementation and computational stability characteristics was firstly developed from the following three aspects, (i) a rate-dependent PD constitutive model was proposed for describing the dynamic behaviors of concrete; (ii) a progressive damage criterion considering the tension-compression anisotropy, softening behavior, and strain rate effect of concrete was incorporated to more accurately reproduce the damage and failure of concrete; (iii) an improved micro-modulus function related to bond length was introduced to reveal the internal length effect of bond force. Then, numerical simulations of projectile perforation on concrete slabs by utilizing the developed modified bond-based PD approach, as well as the corresponding sensitivity analyses of discretization parameters including horizon size and particle spacing were performed. Based on the recommended horizon size and particle spacing, the predicted residual velocity of projectile and failure patterns of concrete slabs exhibited an excellent agreement with the test data. Furthermore, by comparisons of the traditional bond-based PD and classical finite element methods, the superiority of developed approach in describing the perforation damage of concrete targets against projectile impact was demonstrated. Finally, the modified bond-based PD approach was employed to blind simulate the projectile normal and oblique perforating multi-layered spaced concrete target plates. It was found that the modified PD model reasonably predicted the terminal ballistic trajectory, deflection angle, and residual velocity of projectile, as well as the failure patterns of target plates. The present work provides a new way to predict the terminal ballistic effect of projectile and dynamic behaviors of concrete slabs.

A novel mixture rule for multi-layer plates with thermal bending and twisting effects applied to FOCoS devices

A novel approach for reducing the simulation time of highly complex fan-out chip on substrate (FOCoS) structures was developed. Based on the Uflyand-Mindlin plate theory and using the multi-layer plate technique, we have successfully obtained the effective elastic and thermal expansion constants incorporating with the effects of bending and twisting for a two-layer plate structure. The newly developed approach was then applied to simulate, by the finite element method, a variety of cases commonly encountered in practice, such as a slightly asymmetric substrate, an extremely asymmetric rigid structure, and an extremely asymmetric soft structure, with a maximum error of only 3 μm. Remarkably, applying the present mixture rule to simulate the complete FOCoS structure has resulted in an error of only 10 μm with up to 75 % of reduction in the number of mesh elements. The present approach, hence, provides an effective and reliable means for simulating the ever increasingly important FOCoS structures in the rapidly evolving information technology applications.

Vibroacoustic suppression of sandwich plates with imperfect acoustic black hole

Acoustic black holes (ABHs) have recently been revealed as an effective vibration-control technology. However, owing to their disadvantages such as low stiffness, structural discontinuity and manufacturing difficulties, ABHs are limited in terms of their practical application. Therefore, a multilayer composite sandwich plate with filled imperfect-ABH (F-IABH) is proposed in this study to attenuate the vibration and sound radiation of the multilayer sandwich plate, as well as to enhance its bearing capacity and maintain its topological continuity. The structural-damping characteristics and vibroacoustic response of F-IABH are determined using a semi-analytical wave propagation model developed based on symplectic and discrete radiation model methods. The accuracy and effectiveness of the analytical model are validated using the finite-element method. The results show that the F-IABH can achieve broadband vibration-attenuation and noise-reduction effects, and their vibration and noise reduction effects are significantly better than those of ABH structures. Additionally, the wave-damping characteristics of uniform, ABH, and F-IABH plates are analyzed. The results show that the wave damping of the F-IABH plate is much higher than that of the uniform plate, and that it generates more propagative waves to dissipate energy. Additionally, the damping-attenuation characteristics of each wave in the F-IABH and ABH plates exhibit similar variations. However, owing to the large variation range of the wave-mode damping characteristics of the F-IABH plate, the control effect of the latter on structural vibration and acoustic radiation is more significant than that of the ABH plate.

Finite element analysis of the electro-mechanical coupling effects in piezoelectric laminated structures

This study utilized the COMSOL Multiphysics software to conduct finite element analysis on the piezoelectric coupling effect of the composite layer structure. The article begins by introducing the basic principles and history of the piezoelectric effect, emphasizing the importance and widespread application of piezoelectric materials in the field of smart materials. Subsequently, it defines in detail the models of bimorph piezoelectric beams and multilayer composite piezoelectric plates, and conducts potential verification. The bimorph piezoelectric beam model uses PVDF material, and the potential distribution is monitored by boundary probes, confirming the influence of the quantity and distribution of sensor electrodes on voltage distribution. The multilayer composite piezoelectric plate model combines a Si non-piezoelectric semiconductor layer with a PZT-4 piezoelectric material layer, demonstrating the in-plane distribution of potential under lateral mechanical loads. This study not only verifies the reliability of COMSOL software in piezoelectric coupling analysis but also provides an in-depth understanding of the behavior and performance of piezoelectric materials in complex environments.

An analytic solution for bending of multilayered structures with interlayer-slip

Layered structures are prevalent in both natural environments and engineered composite materials. The elastic bending behavior of these structures is primarily governed by properties of their abundant interfaces. While the behavior of two- and three-layered beams has been extensively studied, this research shifts the focus to the impact of elastic shearing at interfaces on the deflection of multilayered structures comprising a substantial number of layers. We present an analytical solution indicating that the bending properties of multilayered beams and plates are nonlinearly dependent on interfacial stiffness. Denoting Se as the effective bending stiffness of an n-layered beam of length L, and S0 as the bending stiffness of a perfectly bound counterpart, we arrive at SeS0=11+(n2−1)tanhαLαL where αL represents a dimensionless parameter related to geometry and material properties. The analytical solutions, validated through finite element simulations, highlight the substantial variations in stiffness across different layered structures. This solution could also be instrumental in assessing interfacial damage and delamination in lamellar composites.

Tunable bandgaps of guided waves by periodic shunting circuits in multilayered piezoelectric plates

The multi-mode and dispersion characteristics of guided waves in plate bring great challenges to the manipulation of guided waves and controlling vibration and noise. In this study, the Stroh formalism is developed to establish a theoretical model for deriving the dispersion relations of guided waves in a multilayered piezoelectric plate. The dispersion characteristics under different electrical boundary conditions introduced by periodic shunting circuits are discussed to reveal the influences of external circuits on guided wave propagation. The proper shunting circuit is not only the key point to obtain the specific frequency of bandgap, but also the effective method to control the bandwidth. Furthermore, for the separation of symmetric and anti-symmetric modes of guided waves, the multilayered piezoelectric plate with a mirror plane is studied by using an equivalent model. Results indicate that the propagation behaviors of guided waves in multilayered piezoelectric plates can be interpreted by developed Stroh formalism, and their bandgaps can be effectively manipulated by periodically external circuits. The tunable bandgaps in this work could be helpful for designing smart devices of wave isolation based on multilayered piezoelectric plate.

Triple filtration robot (T-robot) based on functionally graded multilayer antiviral environment-friendly (F-MAX) system for pathogen purification in confined space

The improved abstract which especially take the suggestions above can be seen as follow:This study addresses the challenge of pathogen regulation in confined spaces by introducing the T-robot, an innovative air filtration robot featuring the F-MAX multilayer composite plate. Designed to capture a wide range of pollutants, including harmful viruses and bacteria, the T-robot significantly enhances air quality. The experimental setup used magnesium phosphate cement, electrostatically charged melt-blown fabric, and eco-friendly materials such as lithium brine by-product magnesia. Key results include a virus removal rate of 99.99% and an antibacterial rate of 98%.The F-MAX system combines multiple layers, each targeting specific particles, with features like the self-healing Desert Rose (DR) coating and high-speed air circulation. The T-robot's high filtration efficiency and sustainable design make it superior to traditional methods, suitable for both commercial and residential use. Its durability and advanced filtration capabilities help reduce airborne contaminants, creating healthier living spaces and demonstrating a commitment to a sustainable future.

Hamiltonian formalism for bistable-multilayered plates under non-mechanical stimuli

Bistable multilayered plates have attracted significant attention as morphing and adaptive structures, renowned for their unprecedented exceptional performance. However, accurately predicting both their shape and internal stresses poses formidable challenges due to their geometrically nonlinear nature. For the first time, this paper introduces a Hamiltonian formalism aimed at achieving high-resolution analysis of nonlinear multilayered plates subjected to non-mechanical stimuli, including hygro-thermo-electro-magneto-elastic responses. A canonical system is strategically developed to compute membrane behaviors, yielding symplectic dual differential equations for in-plane field variables. This method elegantly decouples out-of-plane variables from the full-state vector, leading to an exact analytical solution in the membrane problem. To predict the bending behaviors, the first variation of the Hamiltonian energy density function, expressed as a power series of the transverse deflection, ensures flexural equilibrium. The power series effectively captures all admissible out-of-plane deformations, enabling a smooth transition between linear and nonlinear plate responses, including pitchfork bifurcation and limit points. The validity and accuracy of the proposed method are rigorously assessed through convergence tests and satisfaction of boundary conditions across various equilibria, ranging from monostability to bistability. It is cross-verified with high-fidelity finite-element methods (FEM), showing excellent agreements in both deformations and stress resultants. This research presents a physics-based methodology that unveils a parametric interplay between in-plane and out-of-plane field variables, serving as an efficient approach for analyzing adaptive and morphing structures.

A quadrilateral non-classical microplate element considering the voltage effect

A quadrilateral non-classical Mindlin element that incorporates voltage effects was introduced for examining the bending and free vibration of piezoelectric multilayer plates. The model was developed to examine multilayer plates in the presence of voltage effects. Hamilton’s principle was initially employed to formulate the equation of motion for a multilayer Mindlin plate, considering both size and voltage effects. The equations of motion were resolved through the Galerkin’s method. The suggested element is a rectangular element featuring four-nodes, each possessing 15 degrees of freedom, accounting for both bending and stretching deformations. This element meets the requirements for C0 continuity and C1 weak continuity, and incorporates size and voltage effects. The results were examined with both experimental and analytical data. Upon investigating the voltage effect, it was found that the stiffness matrix depends on both the magnitude and sign of the voltage. Furthermore, it has been demonstrated that the natural frequencies of higher modes are less affected by voltage variations compared to lower modes. In the end, the model was compared to experimental results obtained from a multilayer microcantilever.

On the vibrational analysis of small-scale flexoelectric multi-layer plates based on the modified porous EP-FG formulations

On the vibrational analysis of small-scale flexoelectric multi-layer plates based on the modified porous EP-FG formulations

A fast and efficient pseudo-direct identification method for orthotropic elastic properties of multi-layered composite plates

New types of laminated composites are continuously being developed to meet various requirements involved in engineering applications. Before mass production of these new composite materials can take place, it is necessary to identify their elastic properties. Although current identification methods based on vibration tests and optimization algorithms are highly accurate, their high computation cost is a drawback. To address this issue, this paper proposes a new method to identify orthotropic elastic properties of multi-layered composite plates. The proposed method is based on the Modal Stability Procedure, using the experimental vibration frequencies and corresponding numerical mode shapes of structures. It converges after only two or three iterations without requiring an optimization algorithm. Therefore, the computational cost of the proposed method is significantly lower than that of optimization-based methods. The effectiveness and robustness of this method are demonstrated through three examples with different material, stacking sequences, and geometries including curved plate.

Design of an aperiodic Cr/C reflective multilayer quarter-wave plate at the carbon K-edge

An aperiodic Cr/C reflective multilayer quarter-wave plate is designed and optimized at the carbon K-edge, by implementing both the genetic algorithm (GA) and the non-dominated sorting genetic algorithm II (NSGA-II). The performance is demonstrated using test free electron laser (FEL) pulses simulated by GENESIS to convert the imperfect linearly polarized light to circular polarization; the characteristics are verified by a numerical analysis of the Stokes parameter of the FEL pulses before and after penetration through the multilayer.