Isotropic Substrate Research Articles

Experimental and numerical implementation of auxetic substrate for enhancing voltage of piezoelectric sandwich beam harvester

To harvest energy from environment vibration, it is a good way to use piezoelectric material as a generator that converts mechanical strain to electrical charge. This paper aims to develop a numerical model to predict the performance of piezoelectric energy harvester in beam configuration in accordance to experimental test and then study the effect of implementing auxetic substrate. Two beams are manufactured using isotropic and auxetic substrates. Implementing auxetic substrate excites piezo in both in-plane directions leading to generate more charge while equivalent stress remains constant. Modal test and frequency sweep are done for these two types of beams. For updating the model, mechanical and coupling properties of components in beam studied and more effective parameters are selected and participated in optimization. Genetic algorithm is used for optimization and converged after seven generations. The updated model has maximum 1.6% error in natural frequency and 5.6% in voltage. With a fine adjustment of beam dimensions, natural frequencies are set to 50 Hz and performance of two beams are compared. With same amount of piezo material and same stress applied on, a 30% improvement on output voltage is observed.

Frictionless contact mechanics of an orthotropic coating/isotropic substrate system

This study has been performed to investigate the receding contact problem of a homogeneous orthotropic coating that is not bonded to a homogeneous isotropic substrate without any interfacial defects. The isotropic substrate is supported on a Winkler foundation. The problem is solved assuming that the contact between the rigid punch and orthotropic coating, and that between the orthotropic coating and isotropic substrate, are frictionless. Additionally, the effect of the body forces is neglected, and only compressive normal tractions can be transmitted through the interfaces. The contact analysis of the orthotropic coating, which is subjected to a contact load using a rigid cylindrical punch, is performed under plane strain conditions. The governing equations are analytically found using the theory of elasticity and Fourier integral transformation techniques. Subsequently, the governing equations are reduced to a system of two singular equations, wherein the unknowns are the contact stresses and contact widths. To numerically solve the resulting singular integral equations, Gauss-Chebyshev integration formulas are employed. It is analyzed the influence of the following parameters on the contact stresses and contact widths: orthotropicmaterial properties, punch radius, load ratio, Winkler foundation stiffness.

Dispersion of guided waves in stratified medium with a sandy layer

Dispersion analysis of acoustic guided waves, propagating in a stratified medium, containing an internal sandy layer in contact with the isotropic elastic substrate and the upper elastic isotropic layer, is developed by applying the modified Cauchy formalism coupled with the exponential fundamental matrices and the Thomson–Haskell transfer matrix method. The developed approach is suitable for analyzing dispersion properties of guided waves at the broad variation of the sandy parameter. Several phenomena, concerning anomalous dispersion of guided waves at varying sandy parameter, are observed, revealing the possibility of nondestructive evaluation of sandy layers within the upper crust.

Analytical determination of the complex refractive index and the incident angle of an optically isotropic substrate by ellipsometric parameters and reflectance.

An analytical solution for the determination of both angle of incidence (AOI) and the complex refractive index from combined ellipsometric and reflectometric measurements at optically isotropic substrates is presented. Conventional ellipsometers usually measure flat surfaces because the curvatures of the surface alter the reflected or transmitted light, which causes experimental errors due to the deviation of the incident angle. However, in real industrial applications, the shapes of samples are usually curved or even free-form. In this case, the knowledge of the AOI is essential. The proposed method provides a simple way to measure the AOI and the complex refractive index of nonplanar samples without extra or complicated hardware.

Harnessing the photonic local density of states in graphene moiré superlattices

In this work we investigate the electromagnetic local density of states (LDOS) near a twisted bilayer graphene (TBG) deposited over a general isotropic substrate. The band structure of the TBG is calculated within a tight-binding framework, and then used to determine the TBG's conductivity. The latter presents a nontrivial dependence upon the angle of twist, which shows up in the LDOS, allowing for a moir\'e pattern-dependent quantum emission. For some specific twist angles we show that it is possible to either enhance or decrease the LDOS by an order of magnitude at selected frequencies when compared to the monolayer. This impressive variation is explained in terms of the presence/absence of well defined surface plasmon polaritons (SPPs). Altogether our findings demonstrate that TBG is an alternative, versatile material platform for controlling spontaneous emission and enhancing light-matter interactions, and pave the way for further studies and applications of quantum emission in the emerging class of two-dimensional moir\'e materials.

Weiskopf model for sandy materials: Rayleigh – Lamb wave dispersion

Rayleigh – Lamb wave propagation in a heterogeneous medium containing an upper sandy layer in a perfect contact with isotropic elastic substrate is analyzed by applying the modified Cauchy sextic formalism. It is also proved that sandy material is essentially anisotropic and should be modeled as an anisotropic material with the cubic symmetry. The performed numerical analysis revealed essential peculiarities with respect to dispersion of Rayleigh – Lamb waves. The observed discrepancy in dispersion portraits of media with sandy layer and with isotropic layer, may be important for the nondestructive evaluation of presence sandy layers in the upper Earth crust.

A new dispersive wave with Love-type waves in a microstructure due to an impulsive point source

The crux of the present study is to analyze the dispersion characteristics of the Love-type wave in a micropolar elastic stratum overlying a functionally graded transversely isotropic substrate. An influencing impulsive point source is considered at the interfacial surface. Non-traditional boundary conditions at the common interface of the stratum and substrate are enforced due to the consideration of micropolarity in the stratum. The micropolar effect in the stratum asserts the existence of a new type of dispersive wave, besides the conventional Love-type wave. Green’s function comes in handy as an effective mathematical tool to derive the dispersion equations of both the Love-type wave and the new type of dispersive wave. Validity conditions for both the dispersive waves are established, and a common range of existence is also identified. The result of the Love-type wave is reduced to validate with the classical result of the Love wave. It is noted that without the consideration of micropolarity, the new type of dispersive wave ceases to exist. A detailed study is carried out through graphical illustrations to highlight the obscured characteristics of the Love-type wave and the new type of dispersive wave in response to the various influencing parameters, namely, micropolar parameter, functional gradients, and anisotropy.

Numerical and Experimental Investigation of the Opposite Influence of Dielectric Anisotropy and Substrate Bending on Planar Radiators and Sensors.

The simultaneous influences of the substrate anisotropy and substrate bending are numerically and experimentally investigated in this paper for planar resonators on flexible textile and polymer substrates. The pure bending effect has been examined by the help of well-selected flexible isotropic substrates. The origin of the anisotropy (direction-depended dielectric constant) of the woven textile fabrics has been numerically and then experimentally verified by two authorship methods described in the paper. The effect of the anisotropy has been numerically divided from the effect of bending and for the first time it was shown that both effects have almost comparable but opposite influences on the resonance characteristics of planar resonators. After the selection of several anisotropic textile fabrics, polymers, and flexible reinforced substrates with measured anisotropy, the opposite influence of both effects, anisotropy and bending, has been experimentally demonstrated for rectangular resonators. The separated impacts of the considered effects are numerically investigated for more sophisticated resonance structures—with different types of slots, with defected grounds and in fractal resonators for the first three fractal iterations. The bending effect is stronger for the slotted structures, while the effect of anisotropy predominates in the fractal structures. Finally, useful conclusions are formulated and the needs for future research are discussed considering effects in metamaterial wearable patches and antennas.

A theoretical study on the growth of low-dimensional nanocrystals on isotropic substrates

We present a theoretical model describing the growth of low-dimensional nanocrystals with various shapes on liquid surfaces. The characteristic aggregation of deposited atoms is primarily resulted from the property of isotropic and free-sustained substrates. In the subsequent growth process, the atoms diffuse along preferential growth direction after they meet and then the low-dimensional nanocrystal forms gradually. The variety of nanocrystal morphology is attributed to the deviation of seed crystal size or growth direction in the initial stage caused by inhomogeneous deposition conditions. The dependence of nanocrystal length and growth rate during the growth process was discussed, and the results are in good agreement with the experimental findings.

Investigating Elastic Anisotropy of 4H-SiC Using Ultra-High Q Bulk Acoustic Wave Resonators

Hexagonal 4H-silicon carbide (4H-SiC) is a transversely isotropic substrate garnering interest for precision MEMS devices such as resonant gyroscopes. This paper investigates the elastic anisotropy of 4H-SiC by utilizing capacitive bulk acoustic wave (BAW) resonators with ultra-high mechanical quality factors ( $Q$ ) enabled by phononic crystals. We directly measure the value of $C_{66}$ using Lame mode resonators for the first time and numerically fit the values of $C_{11}$ and $C_{12}$ using BAW elliptical modes in center-supported solid disk resonators. We compare (0 0 0 1) 4H-SiC to (1 1 1) Si, another in-plane isotropic material and validate (0 0 0 1) 4H-SiC’s superior robustness to fabrication and design variations. Measurement of in-plane BAW elliptical modes in multiple disk resonators with as-born frequency splits as low as 3 ppm reveal (0 0 0 1) 4H-SiC’s transverse isotropy across process corners. Lame mode resonators display a temperature coefficient of frequency (TCF) three times lower compared to its Si counterpart. Finally, this paper provides a modified set of elastic constants for 4H-SiC with a view towards monocrystalline SiC MEMS devices. [2020-0254]

Static stiffness of rigid foundation resting on elastic half-space using a Galerkin boundary element method

In this work, a simple and effective numerical model is proposed for studying flexible and rigid foundations in bilateral and frictionless contact with a three-dimensional elastic half-space. For this purpose, a Galerkin Boundary Element Method for the substrate is introduced, and both surface vertical displacements and half-space tractions are discretized by means of a piecewise constant function. The work focuses on a transversely isotropic substrate having the plane of isotropy parallel to the half-space boundary, hence the relationship between vertical displacements and half-space reactions is given by Michell solution, reducing to Boussinesq solution for an isotropic half-space. Several numerical tests are performed for showing the effectiveness of the model, on one hand by determining vertical displacements of flexible rectangular foundations subjected to vertical pressures, on the other hand by accurately determining the translational and rotational stiffness of rigid rectangular and L-shaped foundations. Particular attention is given to the determination of the center of stiffness in case of unsymmetrical foundations, since it turns out to be not coincident with foundation area centroid.

Large-scale spontaneous self-organization and maturation of skeletal muscle tissues on ultra-compliant gelatin hydrogel substrates

Cellular self-organization is the fundamental driving force behind the complex architectures of native tissue. Yet, attempts at replicating native tissue architectures in vitro often involve complex micro-fabrication methods and materials. While impressive progress has been made within engineered models of striated muscle, the wide adaptation of these models is held back by the need for specific tools and knowhow. In this report, we show that C2C12 myoblasts spontaneously organize into highly aligned myotube tissues on the mm to cm scale, when cultured on sufficiently soft yet fully isotropic gelatin hydrogel substrates. Interestingly, we only observed this phenomenon for hydrogels with Young’s modulus of 6 kPa and below. For slightly more rigid compositions, only local micrometer-scale myotube organization was observed, similar to that seen in conventional polystyrene dishes. The hydrogel-supported myotubes could be cultured for multiple weeks and matured into highly contractile phenotypes with notable upregulation of myosin heavy chain, as compared to myotubes developed in conventional petri dishes. The procedure for casting the ultra-soft gelatin hydrogels is straight forward and compatible with standardized laboratory tools. It may thus serve as a simple, yet versatile, approach to generating skeletal muscle tissue of improved physiological relevance for applied and basic research.

Analysis of interfacial imperfections and electro-mechanical properties on elastic waves in porous piezo-composite bars

The main intention of this research work is to carry out an investigation regarding the mechanical and electrical characteristics of shear wave propagation in a porous piezoelectric material (PPEM) bounded by fiber-reinforced medium (FRM) and elastic half-space. The interface between two different media has been considered mechanically imperfect. The mechanical displacement and electric potential are obtained for respective medium by solving coupled electromechanical field equations. After that, the required expression of dispersion has been established using the relevant boundary conditions. For the purpose of validation, the obtained result is reduced to fairly match with the classical Love wave equation in an isotropic elastic layer and substrate (i.e., in the absence of upper surface, piezoelectricity, porosity, imperfection parameter) For the propose of numerical calculation, four sets of porous piezoelectric materials are considered namely, PZT-1, PZT-5H, PZT-7 and BaTiO3. Notable effects of various parameters involved in proposed structure such as piezoelectric, dielectric, reinforcement and interfacial imperfect on phase velocity with respect to frequency have been observed. In this regard, the numerical computation and graphical demonstration have been carried out. Moreover, first three different modes of SH-wave have also been reported.

Mathematical study on the reflection and refraction phenomena of three-dimensional plane waves in a structure with floating frozen layer

A physically realistic mathematical problem has been modelled to discuss the reflection and refraction phenomena of three-dimensional (3-D) plane waves. The considered composite structure comprises of water layer of finite width lying between isotropic and ice substrate has been considered. The mathematical analysis pertaining to this problem has been addressed analytically. The closed form expressions for reflection and refraction coefficients of different reflected and refracted waves are derived. Mathematical expressions for the energy share associated with the various waves are also enlisted in a very concise form in connection with the reflection and refraction coefficients. The effects of various polar and azimuthal angles have been exhibited on the reflection and refraction coefficients. The energy conservation law is established to validate this model. Numerical examples and computations have been performed to illustrate the results of this model graphically. Further, as a particular case of the present problem, the deduced results are compared and validated with the pre-established classical results.

Dynamic response of an irregular heterogeneous anisotropic poroelastic composite structure due to normal moving load

The present study is concerned with the dynamic response of an anisotropic composite structure due to a normal moving load on its irregular rough surface. The composite structure is comprised of an irregular incompressible heterogeneous transversely isotropic fluid-saturated poroelastic layer lying over a transversely isotropic substrate. The mathematical formulation of this structure gives rise to a boundary value problem with specified boundary conditions, and the perturbation method has been used to tackle the irregular surface problem. The expressions for the induced shear and normal stresses in layer and substrate of the composite structure are derived analytically in closed form due to the moving load. As a special case of the problem, the deduced expressions of the induced stresses are validated with the pre-established and standard results. The effect of several substantial parameters such as vertical depth, heterogeneity parameter, porosity parameter, frictional coefficient, irregularity depth, and irregularity factor on the induced shear as well as normal stresses of the layer and substrate has been delineated graphically by the numerical computation. Moreover, a comparative study of the various types of irregularity, namely rectangular irregularity, parabolic irregularity and no irregularity (regular boundary surface) on the induced shear and normal stresses in the layer and, substrate, is carried out by means of graphs, and some considerable peculiarities are outlined.

Torsional surface wave propagation in a transversely isotropic FG substrate with piezoelectric over-layer within surface/interface theory

Propagation of the torsional surface waves in a medium consisting of a functionally graded (FG) substrate bonded to a thin piezoelectric over-layer has been analytically formulated in the mathematical framework of surface/interface elasticity theory. In the cases where the wavelength and/or the thickness of the over-layer are comparable to the surface/interface characteristic length, then the surface/interface effects are not negligible. It is assumed that the over-layer is made of hexagonal 622 crystals with a single axis of rotational symmetry coinciding with the axis of polarization. The half-space is made of an FG transversely isotropic material in which the elasticity tensor and the mass density vary linearly with depth. Accounting for the surface/interface effects, the pertinent dispersion relation is derived analytically and verified for five different limiting cases of the proposed problem. The effect of the inhomogeneity parameters of the FG half-space and the surface/interface parameters on the dispersion relation is studied numerically, and the results are compared with those obtained from the classical theory.

A low-dimensional crystal growth model on an isotropic and quasi-free sustained substrate**Project supported by the National Natural Science Foundation of China (Grant Nos. 11374082 and 51671048) and the Ten Thousand Talents Plan of Zhejiang Province of China (Grant No. 2018R52003).

A new crystal growth theoretical model is established for the low-dimensional nanocrystals on an isotropic and quasi-free sustained substrate. The driven mechanism of the model is based on the competitive growth among the preferential growth directions of the crystals possessing anisotropic crystal structures, such as the hexagonal close-packed and wurtzite structures. The calculation results are in good agreement with the experimental findings in the growth process of the low-dimensional Zn nanocrystals on silicone oil surfaces. Our model shows a growth mechanism of various low-dimensional crystals on/in the isotropic substrates.

Dielectric Anisotropy Sensor Using Coupled Resonators

In this article, a new approach is proposed for the measurement of the uniaxial anisotropic dielectric constant of different planar samples by means of a single sensor. The sensor is based on a couple of straight-line coupled resonators in microstrip technology that can be excited in odd and even propagation modes. This sensor is designed on an isotropic substrate at the design frequency. Due to the electric field configuration specific for each mode, it is possible to relate these modes to the dielectric constant in two different directions (parallel and perpendicular) of a dielectric material placed on top of the sensor. This technique is used for the successful characterization of the dielectric constant anisotropic of anisotropic dielectrics (FR4, Rogers 4350B, and Arlon Diclad 880), and the isotropic material PTFE.

Retroreflex ellipsometry for isotropic substrates with nonplanar surfaces

Ellipsometry is a widely-used and highly-accurate method for characterizing materials and thin films, though conventional ellipsometry restricts the geometric shape of samples to flat or nearly flat surfaces. For nonplanar surfaces, the beam path of the reflected or transmitted light will be altered owing to the curvature of the surfaces. The concept of retroreflex ellipsometry was developed at Fraunhofer IOSB to overcome the limitation of conventional ellipsometry via a retroreflector (retroreflective sheet). However, prior information regarding the samples is still necessary. In this paper, retroreflex ellipsometry is combined with reflectance measurements to derive the optical properties for isotropic substrates with nonplanar surfaces using the reflectance R and the ellipsometric data (Ψ, Δ) without prior knowledge of incident angles. The experimental results show that this retroreflex ellipsometry prototype has excellent accuracy and precision for the full Mueller matrix measurement and is capable of measuring refractive indices of nonplanar surfaces.

Love-type waves in couple-stress stratum imperfectly bonded to an irregular viscous substrate

The focus of the present study is on analysing the characteristics of a Love-type wave through a layered structure constituted of a size-dependent microstructure solid and a viscous solid. Heterogeneous material with microstructural features is requisite when dimensions of the heterogeneous material are comparable to the length scale of the microstructure and the state of stress needs to be redefined in a non-local manner. To frame the model geometrically, we have considered a layered structure comprised of a couple-stress stratum, imperfectly bonded to an irregular transversely isotropic viscoelastic substrate. Two differently shaped irregularities are considered, in two different cases, at the stratum–substrate interface, viz. rectangular and parabolically shaped. Expressions of frequency equations of Love-type waves associated with these cases are established using a suitable mathematical treatment. The established frequency equations are in complex form, of which the real coefficient imparts the frequency curve whereas the imaginary coefficient represents the attenuation curve. The derived frequency equations are reduced to a perfectly bonded classical elastic isotropic layered structure without irregularity and found to fairly match with the classical results of Love waves. Phase velocity and attenuation coefficient profile of the Love-type wave is manifested graphically with the aid of certain numerical computations. To unravel the effect of anisotropy, numerical data of two distinct transversely isotropic rocks are taken into account, viz. Mesavarde Clay Shale and Taylor Sandstone. Parametric traits of various influencing parameters, in particular, characteristic length, irregularity parameter, bonding parameter, and viscosity parameters, are manifested graphically. A comparative analysis of distinct shaped irregularities and other key parameters on phase velocity and attenuation coefficient of a Love-type wave is among the major concerns of the study. The study may prove handful for some engineering problems dealing with microstructure and an irregular viscous solid.