Arbitrary Material Properties Research Articles

Nonlinear transient coupled thermo-electromechanical dynamic responses of the piezoelectric structure with the high-order temperature-dependent material properties

This work aims to study the nonlinear transient coupled thermo-electromechanical dynamic responses of the piezoelectric structure with the high-order temperature-dependent material properties. The multi-field coupling nonlinear model is established based on the non-Fourier thermoelasticity theories by introducing the function of high-order temperature dependency of the arbitrary material property. The virtual work principle and the nonlinear finite element approach are proposed to investigate the two-dimensional case of the orthotropic rectangular piezoelectric plate of the crystal class mm2 subjected to the zonal transient heating loads. The influences of the high-order temperature-dependent material parameters on the structural responses and wave propagations are discussed.

Thermoelastic bending analysis of thick functionally graded sandwich plates with arbitrary graded material properties using a novel quasi-3D HSDT

Thermoelastic bending analysis of thick functionally graded sandwich plates with arbitrary graded material properties using a novel quasi-3D HSDT

Construction of the differential surface admittance operator with an extended Fokas method for electromagnetic scattering at polygonal objects with arbitrary material parameters

This article presents a novel method to accurately simulate electromagnetic scattering at homogeneous polygonal cylinders with arbitrary material properties. A single source equivalence approach is invoked, allowing to substitute the background medium for the inner material of the scatterer, provided an equivalent surface current density is introduced. We construct the pertinent differential surface admittance operator by means of the Fokas method, establishing a map between the known Dirichlet boundary values and their unknown Neumann counterparts. However, to allow for lossy materials, we extend the Fokas method to complex wavenumbers. The novel formalism, employing pulse-shaped local basis functions, natively supports combined magnetic and dielectric contrast, accurately captures the skin effect, and is conveniently integrated in traditional boundary integral equation formulations. The correctness and versatility of our technique are verified for various examples by means of analytical validation and through comparison with a Poggio-Miller-Chan-Harrington-Wu-Tsai approach, a volume integral equation method and a commercial solver.

An efficient analytical method to obtain the homogenised frequency-independent elastic material properties of cross-laminated timber elements

Cross-Laminated Timber (CLT) is a renewable, sustainable, and cost-efficient building element that has been growing in popularity in recent years. To improve one of CLT’s weaknesses, its suboptimal noise and vibration isolation performance, computationally efficient, accessible, and extensible CLT vibro-acoustic models are required. An effective approach to achieve such models is the homogenisation of layered materials. This paper presents a validated homogenisation method based on First-order Shear Deformation Theory (FSDT) that obtains the frequency-independent elastic material properties of CLT. This method is applicable to arbitrary linear elastic material properties, orientations, and stacking sequences of the layers. The homogenised material properties are utilised with FSDT Equivalent Single-Layer (ESL) models that are readily implemented with many finite element method codes to calculate the vibro-acoustic behaviour of CLT elements, even including thickness resonance effects when applied with an appropriate model. The presented homogenisation method for CLT is validated in a numerical study by comparing the mechanical mobilities of ESL models against layerwise dynamic models. The numerical study is conducted based on an experimentally validated 5-ply model for 2- to 7-ply CLT plates with proportionally increasing thicknesses and three idealised boundary conditions. The frequency-independent material properties also allow for the graphical exploration of the anisotropic nature of CLT and the calculation of the universal anisotropic index. The flexibility of the homogenisation method, combined with its ready implementation in already widely implemented FSDT models, can have an application and impact beyond the vibro-acoustic considerations of CLT into the general mechanical modelling of CLT as it is implemented in ever more advanced applications.

Dynamic bearing capacity of point fixed corrugated metal profile sheets subjected to blast loading

Blast loading scenarios and the corresponding hazards have to be evaluated for infrastructure elements and buildings especially at industrial sites for safety and security issues. Point fixed corrugated metal sheets are often applied as façade elements and can become a hazard for humans if they are pulled off. This paper investigates the dynamic bearing capacity of such structural members in terms of their general bending behavior in the middle of the span and pull-out behaviors at the fixing points. The elements are fixed at two sides and the load transfer is uniaxial. An experimental series with static and dynamic tests forms the basis to identify the predominant failure modes and to quantify the maximum stress values that can be absorbed until the investigated structural members fail. The experimental findings are applied to create and to optimize an engineering model for the fast and effective assessment of the structural response. The aim is the derivation of a validated model which is capable to predict the blast loading behavior of metal sheets including arbitrary dimensions, material properties, and screw connections. Results of this study can be integrated into a systematic risk and resilience management process to assess expected damage effects and the evaluation of robustness.

The Unified Theory of Tubesheet Design—Part I: Theoretical Foundation

Abstract The unified theory of tubesheet (TS) design for fixed TS heat exchangers (HEXs), floating head and U-tube HEXs is developed by removing the midplane symmetry (MPS) assumption, which assumes a geometric and loading plane of symmetry at the midway between the two TSs so that only half of the HEX or one TS need be considered. The unified theory can be successfully extended to all common types of HEXs, with arbitrary combinations of TS configurations for two TSs, and with arbitrary material properties and temperature for each component due to less assumptions. The effects of unperforated annual plate, TS flange, gravitational (e.g., dead-weight of tubes, catalyst inside tubes, shell side fluid and tube side fluid) and fluid flow pressure loss, bending stiffness of the tubes, TS in-plane stretch, pressure in TS perforations as well as temperature gradient across TS are also evaluated by the unified theory. Theoretical analysis shows that the existing theories of TS design can be derived from the unified theory as special deductions. The limitations and problems faced in the existing theories and codes are systematically reviewed and solutions to these limitations and problems are also provided by the unified theory. Numerical comparisons indicate that predictions given by the unified theory agree well with finite element analysis (FEA), while ASME results are not accurate or not correct and may lead to unsafety design.

Fabrication of Non‐Uniform Nanolattices with Spatially Varying Geometry and Material Composition

AbstractThe fabrication of periodic 3D nanostructures with uniform material properties has been widely investigated and is important for applications in photonics, mechanics, and energy storage. However, creating nanostructures with spatially varying lattice geometry and material composition is still largely an unexplored challenge in nanofabrication. This work presents the fabrication of non‐uniform nanolattices by patterning multiple layers of 3D nanostructures using phase shift lithography and atomic layer deposition. By controlling the processing parameters, the lattice geometry and material composition of each individual nanolattice layer can be tailored to create arbitrary material property profiles. Using the proposed method, a five‐layer nanolattice with spatially varying porosity and oxide materials has been demonstrated. This process can be used to create gradient‐index antireflection nanostructures, and a fabricated four‐layer nanolattice structure consisting of TiO2 and Al2O3 with gradually varying porosity reduces more than 90% of the specular reflectance from a silicon substrate. By enabling nanolattices with arbitrary profiles in physical properties, the demonstrated technique can find broad applications in nanophotonics, graded filters, energy storage systems, and nanoarchitected films.

Numerical simulation of noise in pulsed Brillouin scattering

We present a numerical method for modeling noise in stimulated Brillouin scattering (SBS). The model applies to dynamic cases such as optical pulses and accounts for both thermal noise and phase noise from the input lasers. Using this model, we compute the statistical properties of the optical and acoustic power in the pulsed spontaneous and stimulated Brillouin cases, and investigate the effects of gain and pulse width on noise levels. We find that thermal noise plays an important role in the statistical properties of the fields and that laser phase noise impacts the SBS interaction when the laser coherence time is close to the time scale of the optical pulses. This algorithm is applicable to arbitrary waveguide geometries and material properties and, thus, presents a versatile way of performing noise-based SBS numerical simulations, which are important in signal processing, sensing, microwave photonics, and opto-acoustic memory storage.

An innovative method for surmounting the constrained torsional problems of stocky beams with arbitrary noncircular cross-sectional shapes and with arbitrary elastic material properties

The constrained torsion problems of stocky beams, being still an unsurmountable challenge in solid mechanics, will be solved by the innovative method proposed, and the computational results of numerical examples signifying that the beam model proposed is reasonable and the numerical analysis methodology of nodal line method is effective. The creative cruxes are as followings:•a type of innovative beam model—stocky beam in solid mechanics analysis is defined, which uses the stress state of the beam to distinguish whether a structural member is a beam or not, and the axis of the stocky beam is the locus of the minimum torsional stiffness centre of all its cross sections;•the warpages of all cross sections of a stocky beam are depicted as a mathematical expression that signifies a family of curved surfaces evolved from Prandtl's membrane shapes;•the constrained torsion problem of a stocky beam can be transformed into the boundary value problem of a set of ordinary differential equations by using the nodal line method developed.

The torsional centre position of stocky beams with arbitrary noncircular cross-sectional shapes and with arbitrary elastic material properties

The aim of this study focuses on torsional centre position of the cross section of a complex section stocky beam (CSSB), a new type of model for structural members with arbitrary noncircular cross-sectional shapes and with arbitrary elastic material properties and with length-to-height or length-to-width ratio no more than 3 encountered in modern civil engineering structures. The nodal-line method is utilized to describe the shapes of the out-of-plane warpages of all cross sections of a CSSB under restrained torsional conditions by employing n unknown displacement functions of nodal lines, together with n quadratic interpolation functions inspired and evolved by the shape of Prandtl’ membrane. The governing ordinary differential equations are established by employing the principle of energy in elasticity. Based on the fact that the torsional stiffness of cross section of the same CSSB stays unchangeable with the change of the torque modes exerted to it, and on the computational results of the change rate of torsional angle due to the individual action of each torque corresponding to three torque modes, a formula for calculating two coordinates of the torsional centre position of the cross section is formulated. The computational results of numerical examples are demonstrated to verify the rationality and correctness of the formula.

Modeling method for periodic cracks in functionally graded strips with arbitrary properties

A piecewise exponential model is developed to investigate the problems of periodic cracks in functionally graded strips with arbitrary material properties. The problem of a row of embedded cracks vertical to strip surfaces under a mode I load in a functionally graded strip with arbitrary nonhomogeneous properties is considered in a plane elasticity state. The true properties of functionally graded materials (FGMs) are approached by a series of sub-layers with material properties varying exponentially and without losing continuity. The thicknesses of different sub-layers can be set to improve calculation accuracy and efficiency. The formulation for doing so is derived using Fourier integral transformation and Fourier series, and the problem is finally reduced to an integral equation with Cauchy-type singularity. Crack-surface displacement derivative is selected as an auxiliary function and is numerically solved to calculate the stress intensity factors (SIFs) at crack tips. The results of previous research are compared with those of the current study to verify the present model. Four representative functions of material properties are considered and the SIFs are presented. The effects of crack spacing, nonhomogeneous properties and crack length on SIFs are discussed. The conclusions are beneficial to the knowledge of fracture behaviors of FGMs.

A Physics-Based TCAD Simulator for Superconducting Electronics Based on Josephson Junctions

Superconducting electronics are promising candidates for complementing semiconductor electronics. However, a comprehensive suite of superconducting design and simulation tools that is necessary to streamline and automate the design process is either nonexistent or very limited. Here, we describe Synopsys' advances in the technology computer-aided design (TCAD) front for physics-based simulation of superconducting electronics based on Josephson junctions (JJs). We employ Keldysh-Gor'kov-Nambu Green's function formalism within the context of the self-consistent mean-field theory of Bogoliubov and de-Gennes to simulate the equilibrium and transport properties of JJ-based devices in one dimension. Using these Green's functions, we calculate various electrical properties and effects, including order parameter and proximity effect, current-phase characteristics and current-density distribution for arbitrary temperatures, material properties and composition, and device dimensions. We further expand the TCAD simulator using the Floquet-Keldysh-Gor'kov-Nambu Green's function for calculating current-voltage characteristics of JJs in nonequilibrium and capture various quantum mechanical effects including multiple Andreev reflections (MAR) for constant applied voltage.

Symmetries of the [formula omitted] approximation to the Boltzmann neutron transport equation

This work explores conditional translation and scaling symmetries of a P3 approximation to the one-dimensional (1D) Boltzmann neutron transport equation with arbitrary material properties. The principal outcomes of this analysis are twofold: 1) the identification of symmetries using Lie group theory is exhaustive, and thus provides definitive insight into scenarios where the differential equation(s) under consideration are expected to hold across phase space position or dimensional scale; and 2) invariance under transformations may be leveraged to construct changes of variables under which reduced-order structures or exact solutions with special properties may be derived. In support of these goals, this work includes the application of Lie group theory to the aforementioned neutron transport model. A variety of conditional translation and scaling symmetries are obtained (e.g., depending on the functional form of various macroscopic cross section functions), and an example scaleinvariant numerical solution of the 1D spherical P3 equations is provided.

Optical theorems and physical bounds on absorption in lossy media.

Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary optimization techniques. The first version is formulated in terms of polarization currents (or equivalent currents) inside the scatterer and generalizes previous results given for a lossless medium. The corresponding bound is referred to here as a variational bound and is valid for an arbitrary geometry with a given material property. The second version is formulated in terms of the T-matrix parameters of an arbitrary linear scatterer circumscribed by a spherical volume and gives a new fundamental upper bound on the total absorption of an inclusion with an arbitrary material property (including general bianisotropic materials). The two bounds are fundamentally different as they are based on different assumptions regarding the structure and the material property. Numerical examples including homogeneous and layered (core-shell) spheres are given to demonstrate that the two bounds provide complimentary information in a given scattering problem.

On the role of material properties in ascending thoracic aortic aneurysms

One of the obstacles standing before the biomechanical analysis of an ascending thoracic aortic aneurysm (ATAA) is the difficulty in obtaining patient-specific material properties. This study aimed to evaluate differences on ATAA-related stress predictions resulting from the elastostatic analysis based on the optimization of arbitrary material properties versus the application of patient-specific material properties determined from ex-vivo biaxial testing. Specifically, the elastostatic analysis relies the on the fact that, if the aortic wall stress does not depend on material properties, the aorta has to be statistically determinate. Finite element analysis (FEA) was applied to a group of nine patients who underwent both angio-CT imaging to reconstruct ATAA anatomies and surgical repair of diseased aorta to collect tissue samples for experimental material testing. Tissue samples cut from excised ATAA rings were tested under equibiaxial loading conditions to obtain experimentally-derived material parameters by fitting stress-strain profiles. FEAs were carried out using both optimized and experimentally-derived material parameters to predict and compare the stress distribution using the mean absolute percentage error (MAPE). Although physiological strains were below yield point (range of 0.08–0.25), elastostatic analysis led to errors on the stress predictions that depended on the type of constitutive model (highest MAPE of 0.7545 for Yeoh model and 0.7683 for Fung model) and ATAA geometry (lowest MAPE of 0.0349 for patient P.7). Elastostatic analysis needs better understanding of its application for determining aneurysm mechanics, and patient-specific material parameters are essential for reliable accurate stress predictions in ATAAs.

Born approximation of acoustic radiation force and torque on soft objects of arbitrary shape

When the density and compressibility of an object are similar to the corresponding properties of the surrounding fluid, and the dominant contribution to the acoustic radiation force depends on gradients of the energy densities as occurs in plane standing waves, the Born approximation may be used to calculate both the radiation force and torque. The approximation consists of integrating the monopole and dipole contributions to the force throughout the volume of the object, and thus it is applicable to objects with arbitrary shapes and material property distributions. Here, an axisymmetric object in a plane standing wave is considered, resulting in one-dimensional integral expressions for the radiation force and torque. The integrals are evaluated analytically for homogeneous spheres and cylinders. The accuracy of the approximation is assessed via comparison with full solutions for spheres and prolate spheroids based on eigenfunction expansions for the corresponding scattering problem. Different densities and compressibilities of the object and the surrounding medium, as well as different sizes, shapes, and orientations of the object relative to the standing wave field, are considered. Limitations of the approximation and potential extensions to more complex wave fields are discussed. [T.S.J. supported by the ARL:UT McKinney Fellowship in Acoustics.]

Analysis of Thermoelectric Generators with General Material Property Variations

A theoretical analysis is performed on thermoelectric generators of functionally graded materials with arbitrary material property variations described by power series. The temperature field is obtained by the power series method of ordinary differential equations. The thermoelectric energy conversion efficiency is calculated and maximized as a function of the current density. Systematic numerical studies are performed for exponential, linear, and trigonometric material property variations. Our theoretical model with general material property variation allows us to explore for higher efficiency more flexibly. The maximum efficiency found is about 25% which is substantially higher than what is in the literature on the same topic.

Cross-Sectional Design and Analysis of Multiscale Carbon Nanotubes-Reinforced Composite Beams and Blades

The present work addresses with the cross-sectional design and analysis of fiber-reinforced multiscale composite beams of general cross-sectional shape and arbitrary anisotropic material properties and investigates the effect of carbon nanotubes (CNTs) on their stiffness properties. The three-dimensional strain field was formulated in terms of one-dimensional strains and a three-dimensional warping displacement. The bulk material properties of the multiscale composite were predicted using Halpin–Tsai equations and fiber micromechanics. The carbon nanotubes were assumed to be uniformly distributed and randomly oriented throughout the polymer matrix. The variational asymptotic beam section (VABS) was used to numerically evaluate the stiffness and mass matrices of four test cases: strip, circular pipe, box beam and airfoil. The influence of CNTs weight percentage and volume fraction of fibers was investigated through a detailed parametric study. The numerical results indicate that the inclusion of a small weight percentage of carbon nanotubes in the polymer matrix is sufficient to induce a significant improvement in stiffness properties.

SOLUTION OF ADHESIVE CONTACT PROBLEM ON THE BASIS OF THE KNOWN SOLUTION FOR NON-ADHESIVE ONE

The well-known procedure of reducing an adhesive contact problem to the corresponding non-adhesive one is generalized in this short communication to contacts with an arbitrary contact shape and arbitrary material properties (e.g. non homogeneous or gradient media). The only additional assumption is that the sequence of contact configurations in an adhesive contact should be exactly the same as that of contact configurations in a non-adhesive one. This assumption restricts the applicability of the present method. Nonetheless, the method can be applied to many classes of contact problems exactly and also be used for approximate analyses.

Illusion optics by single and twin cylindrical cavity cloaks

Creating optical illusion by using interior cavity cloak in 2D is discussed in this paper. An antiobject is embedded in the cloak shell and the corresponding imaginary object (under transformation optics) is observed in virtual space instead of any other object which was really exist inside the cavity cloak in physical space. Cylindrical single (twin) cavity cloak is used in this paper, that making one (two) object with arbitrary shape and material properties appears exactly like another object(s) with different shape and material make up for an observer who lies outside the cloaking shell. The simulation results prove that this illusion device with the proposed parameters is operationally possible. The advantage of using internal cloak instead of folded geometry which is usually used is that there is no negative refraction in the structure of the device.