Variation Of Material Parameters Research Articles

Estimating the Inf-Sup Constant in Reduced Basis Methods for Time-Harmonic Maxwell’s Equations

The reduced basis method (RBM) generates low-order models of parametrized partial differential equations. These allow for the efficient evaluation of parametrized models in many-query and real-time contexts. We use the RBM to generate low-order models of microscale models under variation of frequency, geometry, and material parameters. In particular, we focus on the efficient estimation of the discrete stability constant used in the reducced basis error estimation. A good estimation of the discrete stability constant is a challenging problem for Maxwell’s equations, but is needed to yield rigorous bounds on the model approximation error. We therefore test and compare multiple techniques and discuss their properties in this context.

Comparison of implicit and explicit hybridizable discontinuous Galerkin methods for the acoustic wave equation

SummaryWe describe implicit and explicit formulations of the hybridizable discontinuous Galerkin method for the acoustic wave equation based on state‐of‐the‐art numerical software and quantify their efficiency for realistic application settings. In the explicit scheme, the trace of the acoustic pressure is computed from the solution on the two elements adjacent to the face at the old time step. Tensor product shape functions for quadrilaterals and hexahedra evaluated with sum factorization are used to ensure low operation counts. For applying the inverse mass matrix of Lagrangian shape functions with full Gaussian quadrature, a new tensorial technique is proposed. As time propagators, diagonally implicit and explicit Runge–Kutta methods are used, respectively. We find that the computing time per time step is 25 to 200 times lower for the explicit scheme, with an increasing gap in three spatial dimensions and for higher element degrees. Our experiments on realistic 3D wave propagation with variable material parameters in a photoacoustic imaging setting show an improvement of two orders of magnitude in terms of time to solution, despite stability restrictions on the time step of the explicit scheme. Operation counts and a performance model to predict performance on other computer systems accompany our results. Copyright © 2015 John Wiley & Sons, Ltd.

Stress analysis of thick pressure vessel composed of functionally graded incompressible hyperelastic materials

The present paper develops stress analysis of functionally graded hyperelastic thick spherical shell subjected to internal and external pressure. Hyperelastic behavior is modeled by using modified neo-Hookean strain energy function with variable material parameters. The material constants of strain energy function are graded along the radial direction based on a power law function. Material inhomogeneity parameter (m) is a power in the mentioned power law function. Material constant of strain energy function calculated from experimental data by using Levenberg-Marquardt nonlinear regression method. Stress components and stretches of spherical shell have been obtained for axisymmetric radial condition. Following this, profiles of extension ratio and stress components are plotted as a function of radius of sphere in the undeformed configuration for different material inhomogeneity parameter (m). The obtained results show that the inhomogeneity properties of FGMs have a significant influence on the displacement, stretch and stresses distribution along the radial direction. Sensitivity of stress components and displacement field to applied pressure and outer to inner radius ratio of vessel (structure parameter) are also investigated and leads to the fact that outer to inner radius ratio has a great effect on the deformation field and stress components and is a useful parameter from a design point of view which can be tailored to specific applications to control the stress. Thus with selecting a proper m value and structure parameter (B/A), engineers can design a specific FGM hollow sphere that can meet some special requirements.

Analysis and optimization of In<sub>1-x</sub>GaxAsyBb<sub>1-y</sub> thermophotovoltaic cells under low radiator temperatures

In this paper,we investigated the heat to electricity conversion efficiency of In 1-x Ga x As y Sb 1-y radioisotope thermophotovoltaic (RTPV) converter with x=0.8 and y=0.18, taking account of the photons with energy below the cells bandgap using a comprehensive analytical process. This was done with a computer program designed for this reason, which allowed the computation of the cell performance under a variety of specified incident radiation spectra as well as a variety of material parameters. The results show that for an emissivity value of 0.78, a cell thickness of about 7µm with low front recombination velocity(700cm/s),a conversion efficiency greater than 29% can be obtained for radiator’s temperature of1300°k at ambient temperature. This efficiency will decrease as the cell temperature increase.

Pattern of Partial Rear Contacts for Silicon Solar Cells

Partial rear contacts solar cells, which are passivated and locally contacted on their rear side, are widely used for their higher performances, especially in open-circuit voltage. If the distance in between two contacts has been optimized, the best geometry of a contact lattice remains unclear. So far, the most widely explored geometry is the square lattice. This work aims to explore, by the mean of numerical simulations on both PERL and PERT architectures, the consequences of different lattice geometries, and more specifically triangular and hexagonal patterns. This study was extended to the variation of a set of material and process parameters in order to observe the consequences on conversion efficiency for each contact pattern. Once the simulations performed, it has been demonstrated that even though these three geometries show the same optimal efficiency when varying the distance in between two contacts, the triangular contact pattern is clearly more robust with the variation of this distance, which makes it a good candidate for fully optimized solar cells. Moreover, the variation of material and process parameters shows the interest of the triangular contact pattern in case of degraded parameters.

How to decide between competing efficiency droop models for GaN-based light-emitting diodes

GaN-based light-emitting diodes (LEDs) exhibit a strong efficiency droop with higher current injection, which has been mainly attributed to Auger recombination and electron leakage, respectively. Thus far, the few reports on direct measurements of these two processes do not confirm their dominating influence on the droop unambiguously. Advanced numerical simulations of experimental characteristics are shown to validate one or the other explanation by variation of uncertain material parameters. We finally demonstrate how the comparative simulation of temperature effects enables a clear distinction between both models. Contrary to common assumptions, the consistently measured efficiency reduction of blue LEDs with higher ambient temperature eliminates electron leakage as primary cause of the efficiency droop in these devices.

Elastic parabolic equation solutions for oceanic T-wave generation and propagation from deep seismic sources.

Oceanic T-waves are earthquake signals that originate when elastic waves interact with the fluid-elastic interface at the ocean bottom and are converted to acoustic waves in the ocean. These waves propagate long distances in the Sound Fixing and Ranging (SOFAR) channel and tend to be the largest observed arrivals from seismic events. Thus, an understanding of their generation is important for event detection, localization, and source-type discrimination. Recently benchmarked seismic self-starting fields are used to generate elastic parabolic equation solutions that demonstrate generation and propagation of oceanic T-waves in range-dependent underwater acoustic environments. Both downward sloping and abyssal ocean range-dependent environments are considered, and results demonstrate conversion of elastic waves into water-borne oceanic T-waves. Examples demonstrating long-range broadband T-wave propagation in range-dependent environments are shown. These results confirm that elastic parabolic equation solutions are valuable for characterization of the relationships between T-wave propagation and variations in range-dependent bathymetry or elastic material parameters, as well as for modeling T-wave receptions at hydrophone arrays or coastal receiving stations.

Measuring the coating adhesion strength of electrodes for lithium-ion batteries

The coating adhesion strength of lithium-ion battery electrodes is a very important mechanical property, affecting the electrochemical life time of battery cells and the electrochemical handling during cell manufacturing. Hence the establishment of a standardized pull-off test with high reproducibility was long time overdue. The measurement setup is realized in a material testing machine. Machine and process parameters have been investigated to propose a reliable measurement procedure with a clearly specified parameter setup. Data acquisition rate (f), contact stress (σc), dwell time (td) and pull-off velocity (vpo) were identified to affect the adhesion strength measurement significantly. Finally electrodes with material and process parameter variations were manufactured to assess the applicability of the presented method. The impact of the amount of binder and its molecular weight as well as the influence of the dry mixing and the dispersing process on adhesion strength was verified and the differences can be clearly distinguished by the developed test method.

Theoretical and numerical analysis of layered cylindrical pentamode acoustic cloak

As a newly-developed method, acoustic cloak made of pentamode materials is on its speedway to the promising potential application. However, physical fabrication of pentamode cloak with continuously varying material parameters can be a tough work, if not totally impossible. Layering is a natural compromise to bypass this quandary. Researches on layering effects of inertial cloak are ample. However, researches on layering pentamode acoustic cloak are relatively limited. Among these researches Scandrett extends the effective bandwidth through optimization of material parameters[2010 J. Acoust. Soc. Am. 127 2856, 2011 Wave Motion. 48 505].#br#The present work concerns the layering effects of pentamode acoustic cloak. By comparing with precedent results, the present paper has two major innovations: Firstly, cylinder is chosen to be the basic geometry. This is of obvious advantage since cylinder is the basic geometry of acoustic cloak's important potential host. Secondly, effects of layers' number and thickness distribution on the stealth effect are analyzed. The two are key parameters to be determined in the layering process. This paper is organized as follows: Firstly, analytical expression of the scattering pressure field of layered cloak is deduced by means of variables separation. In this process Fourier expansion plays a key role. And the harmonic assumption of the incident acoustic wave is made. Secondly, typical cases are calculated to verify the validation of the theoretical analysis. First let material parameters tend towards that of water, and compare the scattering field with that of the bare rigid object when the cloak is replaced by water. Second let the layering number goes to infinity, and compare the scattering field with that of the continuous cloak. Phenomena conforming with basic physical laws are observed. And validity of the theory and codes is confirmed. Thirdly, effects of layers' number and thickness distribution on the stealth character are theoretically and numerically analyzed. One can easily see from the computational results that a critical number N exists. When layers' number exceeds N, improvement of the stealth effect becomes less efficient by further adding layers' number. One can also see from the computational results that a wise distributional strategy that helps improve the stealth effect indeed exists. And the optimization iteration can be utilized to further improve it.#br#As a summary, the present paper concerns the layering process of cloaking. Qualitatively and quantitatively, several significant results are obtained. This paper offers a useful reference for future fabrication of realistic acoustic pentamode cloak.

Nondestructive Material Characterization in the Terahertz Band by Selective Extraction of Sample-Induced Echo Signals

Terahertz time-domain spectroscopy (THz-TDS) allows broadband noninvasive measurement of the optical parameters of various materials in the THz domain. The measurement accuracy of these parameters is highly influenced by the difficulty in distinguishing THz signals from unwanted signals such as noise, signal fluctuation, and multiple echoes, which directly affects material identification and characterization efficiency. We introduce a novel method that provides effective extraction and separation of THz signals from such undesired effects. The proposed algorithm was assessed through experiments that presented enhancement in material parameter evaluation, such as the decomposition of the sample-induced echoes (SIEs) from the complex THz sample signal with near-zero extraction error. Improved precision (\(\pm \)0.05\(\,\upmu \)m) was achieved in the determination of the sample thickness compared to that of the mechanical method (\(\pm \)10\(\,\upmu \)m). Furthermore, we could infer from the component concentration measurement results of a compound sample (44.2 % decrease in the root mean square concentration error) that the material parameter calculation accuracy had improved, proposing a means to enhance the ultimate nondestructive material evaluation performance.

PVDF–BaSrTiO3 nanocomposites for flexible electrical energy storage devices

We have explored the energy storage capability of Ba0·5Sr0 ·5TiO3 (BST)–polyvinylidene fluoride (PVDF) nanocomposites. Morphologically uniform BST colloidal nanocubes were prepared in high yield by a solvothermal method at temperatures as low as 150°C. As-synthesised BST nanocubes were used as fillers (35 vol%) in PVDF polymer matrix. The unique dielectric-polymer films show enhanced dielectric constant (>27) and enhanced electrical breakdown strength (Eb) (2·85 MV/cm). The resulting dielectric energy density for BST–PVDF is 9·7 J/cm3, which is a result of the interplay between dependencies of permittivity and breakdown strength on volume fraction. We propose that the strong nanoparticle–polymer matrix interfacial interaction is the main reason for the observed improved dielectric properties. This wet-chemical-assisted fabrication approach can be readily extended to other combinations of polymers and ceramics with concomitant improvement in properties. Key parameters of various materials (e.g. chemical composition, shape, size and surface reactivity) can be readily controlled in this method, opening up a new pathway to highly flexible macroelectronics.

Stochastic Dynamic Analysis of Structures with Spatially Uncertain Material Parameters

This paper investigates the uncertainty quantification in structural dynamic problems with spatially random variation in material and damping parameters. Uncertain and locally varying material parameters are represented as stochastic field by means of the Karhunen–Loève (KL) expansion. The stiffness and damping properties of the structure are considered uncertain. Stochastic finite element of structural modal analysis is performed in which modal responses are represented using the generalized polynomial chaos (gPC) expansion. Knowing the KL expansions of the random parameters, the nonintrusive technique is employed on a set of random collocation points where the structure deterministic finite element model is executed to estimate the unknown coefficients of the polynomial chaos expansions. A numerical case study is presented for a cantilever beam with random Young's modulus involving spatial variation. The proportional damping constants are estimated from the experimental modal analysis. The expected value, standard deviation, and probability distribution of the random eigenfrequencies and the damping ratios are evaluated. The results show high accuracy compared to the Monte-Carlo (MC) simulations with 3000 realizations. It is also demonstrated that the eigenfrequencies and the damping ratios are equally affected from material uncertainties.

Determination of yield stress from nano-indentation experiments

Abstract The aim of this paper is to investigate the possibilities of getting information on the initial yield stress Y from nano-indentation experiments with sharp indenters. Berkovich indenters have been used for the experiments and the data evaluation was performed by using two expanding cavity models (ECM) described in the literature, one for elastic-perfectly plastic, and one for power law work hardening materials. To characterize the ECMs, finite element simulations with extensive material parameter variations together with substantial experimental data are used. As a first result, the possibilities of determining Y using the introduced ECMs can be shown for the simulated materials (Fig. 3) and the presented selection of real specimens. Furthermore, the restriction of the ECMs to materials where the yield behavior obeys the von Mises yield criteria is discussed. In doing so it is shown that the indentation work, which can be determined directly from the indentation force–displacement curves, represents a useful quantity to assess the applicability of an ECM to a particular material.

Large‐scale mechanical buckle fold development and the initiation of tensile fractures

AbstractTensile failure associated with buckle folding is commonly associated to the distribution of outer arc extension but has also been observed on fold limbs. This study investigates whether tensile stresses and associated failure can be explained by the process of buckling under realistic in situ stress conditions. A 2‐D plane strain finite element modeling approach is used to study single‐layer buckle folds with a Maxwell viscoelastic rheology. A variety of material parameters are considered and their influence on the initiation of tensile stresses during the various stages of deformation is analyzed. It is concluded that the buckling process determines the strain distribution within the fold layer but is not solely responsible for the initiation of tensile stresses. The modeling results show that tensile stresses are most dependent on the permeability, viscosity, and overburden thickness. Low permeability (<10−19 m2), high viscosity (≥1021 Pa s), and low overburden pressure can explain tensile failure at the fold hinge. Tensile stresses in the limb of the fold cannot (in general) be explained by buckling. Rather, it develops due to a combination of compression and erosional unloading. The modeling results show that erosion of high permeability rocks can explain the generation of tensile stresses at significant depths (∼2 km) both at the hinge of the fold and throughout the limb of the fold. This study shows that tensile stresses and associated failure within buckle folds is directly dependent on the distribution of material parameters but moreover to the strain history of the geologic system.

Analyses of cracks in thick stiffened plates repaired with single-sided composite patch

This study investigated the effect of composite patches applied to thick stiffened plates with single-sided repairs. A simplified analytical model was derived to predict the reduction in the mode I strain energy release rates resulting from the single-sided composite patches. Finite element analyses were also conducted to compute the mode I strain energy release rates with and without composite patches, and their results were compared to the analytical model prediction. Furthermore, changes in the location of the neural axis with single-side patches were examined with their effects on the effectiveness of the patch repair with variations in both material and geometric parameters of the patch and plate. The neutral axis location in the patched plate played an important role to influence the effectiveness of the composite patch.

A meshless method for axisymmetric problems in continuously nonhomogeneous saturated porous media

A meshless method based on the local Petrov–Galerkin approach is proposed to analyze 3-d axisymmetric problems in porous functionally graded materials. Constitutive equations for porous materials possess a coupling between mechanical displacements for solid and fluid phases. The work is based on the u–u formulation and the incognita fields of the coupled analysis in focus are the solid skeleton displacements and the fluid displacements. Independent spatial discretization is considered for each phase of the model, rendering a more flexible and efficient methodology. Both displacements are approximated by the moving least-squares (MLS) scheme. The paper presents in the first time a general meshless method for the numerical analysis of axisymmetric problems in continuously nonhomogeneous saturated porous media. Numerical results are given for boreholes in continuously nonhomogeneous porous medium with prescribed misfit and exponential variation of material parameters in the excavation zone.

Augmented MPM for phase-change and varied materials

In this paper, we introduce a novel material point method for heat transport, melting and solidifying materials. This brings a wider range of material behaviors into reach of the already versatile material point method. This is in contrast to best-of-breed fluid, solid or rigid body solvers that are difficult to adapt to a wide range of materials. Extending the material point method requires several contributions. We introduce a dilational/deviatoric splitting of the constitutive model and show that an implicit treatment of the Eulerian evolution of the dilational part can be used to simulate arbitrarily incompressible materials. Furthermore, we show that this treatment reduces to a parabolic equation for moderate compressibility and an elliptic, Chorin-style projection at the incompressible limit. Since projections are naturally done on marker and cell (MAC) grids, we devise a staggered grid MPM method. Lastly, to generate varying material parameters, we adapt a heat-equation solver to a material point framework.

Numerical study on screening of surface waves using a pair of softer backfilled trenches

Vibration screening effectiveness of a pair of in-filled trenches is numerically studied under conditions of plane strain using PLAXIS 2D in a linear elastic, isotropic, and homogeneous half-space acted upon by a steady-state vertical excitation. Barrier efficiency is analyzed in terms of reduction of vertical and horizontal vibration components with respect to the variations in barrier geometry and in-fill material parameters. The geometric features are normalized with respect to Rayleigh wavelength of vibration in soil. The in-fill trench material is considered to be softer and accordingly assigned lower shear wave velocities than the half-space. Non-dimensional design charts are developed and the key parameters participating in wave screening process are identified. Some recommendations are made regarding the optimal selection of these parameters. Comparison with a few published results shows close agreement. Such an isolation scheme may be advantageous in circumstances where a single trench requires unrealistic depth.

Bending of sparklers

A new equation is proposed to explain the curvature of spent sparklers. We found the state of a segment of the sparkler to depend strongly on the state of its spent segments. The equation is nearly able to produce the sparkler shape for a range of lengths and for all elevation angles. The method proposed here is likely to explain any phenomena in nature related to an evolving length scale associated with some material that becomes progressively stiff or dry, such as the growth of resin exuded from trees. The equation can produce a very rich spectrum of shapes by varying material parameters (density, temperature-dependent strength), heating temperature, elevation angle and gravitational acceleration. This might provide new insights into explaining many shapes in nature or man-made structures.

Edge states and topological properties of electrons on the bismuth on silicon surface with giant spin-orbit coupling

We derive a model of localized edge states in the finite width strip for two-dimensional electron gas formed in the hybrid system of bismuth monolayer deposited on the silicon interface and described by the nearly-free electron model with giant spin-orbit splitting. The edge states have the energy dispersion in the bulk energy gap with the Dirac-like linear dependence on the quasimomentum and the spin polarization coupled to the direction of propagation, demonstrating the properties of topological insulator. The topological stability of edge states is confirmed by the calculations of the $Z_2$ invariant taken from the structure of the Pfaffian for the time reversal operator for the filled bulk bands in the surface Brillouin zone which is shown to have a stable number of zeros with the variations of material parameters. The proposed properties of the edge states may support future advances in experimental and technological applications of this new material in nanoelectronics and spintronics.