Unit Cell Analysis Research Articles

OBLIQUE INCIDENCE DESIGN OF MEANDER-LINE POLARIZERS FOR DIELECTRIC LENS ANTENNAS

A method to design planar multilayer meander-line polarizers is given. The proposed procedure is based on transmission line circuit theory and on full-wave unit cell analysis in frequency domain. The hybrid combination of those two techniques paves the way for the polarizer design process and avoids heavy full-wave optimizations. This procedure is originally aimed for polarizers acting on lens antennas and is suitable for plane waves impinging with arbitrary angles on the polarizer. To validate the proposed method, two polarizers have been manufactured in Ka-band, one for normal and one for oblique incidence. Designs, prototypes and measurements made on a complete Ka-band lens antenna subsystem are shown in this paper.

A homogenization theory for elastic–viscoplastic materials with misaligned internal structures

In this study, a homogenization theory for non-linear time-dependent materials is rebuilt for periodic elastic–viscoplastic materials with misaligned internal structures, by employing a unit cell defined for the aligned structure as an analysis domain. For this, it is shown that the perturbed velocity fields in such materials possess periodicity in the directions of misaligned unit cell arrangement. This periodicity is used as a novel boundary condition for unit cell analysis to rebuild the homogenization theory. The resulting theory is able to deal with arbitrary misalignment using the same unit cell, avoiding not only geometry and mesh generation of a unit cell for every misalignment, but also the influence of mesh dependence. To verify the theory, an elastic–viscoplastic analysis of plain-woven glass fiber/epoxy laminates with misaligned internal structures is performed. It is shown that the misalignment of internal structures affects viscoplastic properties of the plain-woven laminates both macroscopically and microscopically.

Quantum Coherence and Disorder-Specific Effects in Simulations of 2D Optical Spectra of One-Dimensional J-aggregates

Time-resolved two-dimensional photon-echo (2D PE) spectra of linear J-aggregates containing four molecules per unit cell--a model system for a concentrated water solution of the pseudo-isocyanine dye--is theoretically considered. Analysis of a single unit cell and the full-sized aggregate is consistently carried out. Spectral features of a single unit cell are sorted out by assigning them to specific double-sided Feynman diagrams. Two different approaches of disorder are employed, the resulting differences in the spectra are discussed, and the conditions for their utilization are described. Special attention is paid to quantum coherence dynamics of a single unit cell and the full-sized J-aggregate. Possibilities of probing quantum coherences, as well as performing quantum control via two-color 2D PE spectroscopy, are discussed.

Numerical modelling of failure of cement concrete using a unit cell approach

In this paper, a unit cell based approach is followed, where a unit cell consisting of one aggregate surrounded by mortar matrix is used for numerical simulation of mechanical response of cement concrete. Unit cell approach is a simple mathematical approximation that helps us to simplify the simulation of mechanical response of multi-phase composites. To model the failure of matrix, brittle cracking model is used, where the entire fracture zone is represented by a band of micro cracked material. Current study involves; (a) failure analysis of the concrete unit cell when it is subjected to tensile loads, and (b) parametric study of variation of peak strength with shape and volume fraction of aggregate. In this study, circular and square aggregates at various orientations are modelled. The simulation results predict that the peak tensile stresses are not very sensitive to the volume fraction of aggregates, when the unit cell is subjected to tensile loads. This paper effectively demonstrates the power of unit cell model in simulating the nonlinear mechanical response of cement concrete when it is subjected to tensile loading.

Effects of laminate misalignment on elastic–viscoplastic properties of ultrafine plate–fin structures: analysis using time dependent homogenisation theory

In this study, the elastic–viscoplastic properties of ultrafine plate–fin structures with laminate misalignment are investigated using the time dependent homogenisation theory. For this, it is first shown that, even though plate–fin structures have laminate misalignment, the distribution of perturbed velocity in the structures possesses periodicity. It is further shown that, by employing this periodicity as a boundary condition for unit cell analysis, a rectangular unit cell defined for a plate–fin structure without laminate misalignment can also be used as the analysis domain for plate–fin structures with laminate misalignment. The present method is then applied to the elastic–viscoplastic analysis of ultrafine plate–fin structures made of a Ni based alloy, subjected to uniaxial tension at high temperatures. Four cases of laminate misalignments are considered in the analysis. It is shown that the laminate misalignment can significantly affect the elastic–viscoplastic properties of the plate–fin structures.

1121 積層ずれを有する平織積層板の均質化弾-粘塑性解析手法の開発(OS11.機能性材料の応力解析と機能発現に関する数値シミュレーション(5),OS・一般セッション講演)

In this study, the elastic-viscoplastic behavior of plain-woven GFRP laminates in which plain fabrics are stacked with misalignment is analyzed using a homogenization theory. For this, a novel boundary condition for unit cell analysis is proposed based on the periodicity and point-symmetry of internal structures in plain-woven laminates. Using the boundary condition, the homogenization theory for non-linear time-dependent composites developed by the authors is rebuilt for plain-woven laminates with misaligned plain fabrics. As an application of the present theory, the elastic-viscoplastic analysis of plain-woven glass fiber/epoxy laminates with misaligned plain fabrics is performed.

Numerical Simulation of the Elastic Moduli of Cement Paste As a Three Dimensional Unit Cell

This paper describes a numerical method for estimating the elastic moduli of cement paste. The cement paste is modeled as a unit cell which consists of three components: the unhydrated cement grain, the gel, and the capillary pore. In the unit cell, the volume fractions of the constituents are quantified using a single kinetic function calculating the degree of hydration. The elastic moduli of cement paste are calculated from the total displacements of constituents when a uniform pressure is applied to the gel contact area. The cement paste is assumed to be a homogenous isotropic matrix. Numerical simulations were conducted through the finite element analysis of the three-dimensional periodic unit cell. The model predictions are compared with experimental results. The predicted trends are in good agreement with experimental observations. This approach and some of the results might also be relevant for other technical applications.

Competition between structural and electronic factors in (Al/In) doped lanthanum manganites

X-ray structure parameters of La 0.7Ca 0.3Mn 0.96(In x Al (1 −x) ) 0.04O 3 perovskite manganites determined from the Rietveld analysis of the orthorhombic unit cell, space group Pbnm, showed strong dependence on x. Resistivity ( ρ) and ac magnetic susceptibility ( χ) measurements showed decrease in the metallic-to-semiconductor transition temperature T ρ and the ferromagnetic-to-paramagnetic Curie temperature T C as x increases. The large drop in T ρ and T C for x=0.0 and 1.0 is ascribed to the difference between the electronic configuration (E-factor) and ionic radius (structure factor) of the dopants and the Mn 3+ ions. Decrease in T ρ and T C for samples (0.2< x<0.8) is mainly due to the size mismatch between the A and B sites (structure factor).

Equilibrium Core Composition Search Methodologies for Pebble Bed Reactors

The capability to perform depletion analysis of pebble bed reactors has been traditionally limited to a few dedicated codes that are designed for helium-cooled reactors, rely on pregenerated problem-dependent group cross sections, and have limited flexibility in the materials and in the geometries they can model. This paper presents a newly developed tool to search for pebble bed reactor core equilibrium composition and calculate its neutronic characteristics. It uses MCNP for transport calculations and ORIGEN2 for depletion calculations and can generate effective one-group cross sections “on-the-fly” as pebbles move through the core using point-energy cross sections. This tool can be used for any coolant type including liquid salt, can model complex geometries, and can account for any level of heterogeneity. Also developed are two simplified methodologies that are based on unit-cell analysis and can considerably reduce the required computational time; they are useful for parametric studies.

Numerical estimation of effective elastic moduli of syntactic foams

The macroscopic elastic behavior of hollow microsphere filled composites, collectively known as syntactic foams, is studied using analytical and numerical methods. In the analytical model, the effective bulk modulus is first estimated, and then using solid harmonics appropriate for a uniaxial tensile field, the effective Poisson's ratio of the composite is determined. The macroscale material properties are also estimated using finite element (FE) analysis of representative unit cells. Using the analytical model, the applicability of unit cell FE methods in the estimation of effective elastic properties of the syntactic foam is assessed. The influence of particle distribution on the elastic moduli is studied using a full three-dimensional (3D) FE method. The moduli obtained for different distributions showed little scatter, and the average values of bulk modulus match closely with the analytical results.

A hybrid modeling concept for ultra low cycle fatigue of metallic structures based on micropore damage and unit cell models

The paper presents a concept for life-time predictions of metallic structures subjected to ultra low cycle fatigue. The proposed hybrid strategy is characterized by a combination of unit cell analyses on a microstructural level and a micropore damage model used for structural analyses on the macroscopic level. To account for the large plastic deformations evolving during cyclic loading, an advanced elasto-plastic model using a B ari–H assan-type kinematic hardening rule based on a superposition of several kinematic hardening laws according to A rmstrong-F rederick is employed. Micromechanically oriented unit cell analyses are used for a calibration of the model parameters of a macroscopic G urson-type model. Numerical results include the validation of the macroscopic G urson model based on laboratory test results on steel specimens as well as a prototype application to a life-time prediction of a metallic spherical pressure vessel subjected to earthquake loading.

Finite element modeling of soft soil treated with prefabricated vertical drains

The Changi East Reclamation Project in Singapore consists of land reclamation and ground improvement works of the foreshore for the future expansion of the Changi International airport. Modeling of the deformation behavior of marine clay under reclamation fills and surcharge was carried out by the finite element method with the Plaxis 2 dimensional numerical modeling software. The analyses included the modeling of the consolidation behavior of marine clay under reclamation fills with and without prefabricated vertical drains. Modeling of the marine clay with vertical drains was carried out by both the axi-symmetric unit cell and full-scale analysis methods. Modeling of marine clay which was not treated with prefabricated vertical drains was carried out by means of full-scale analysis. The numerical analysis of marine clay deformation with and without vertical drain was carried out at two case study locations namely the Pilot Test Site and <i>In situ</i> Test Site. The test sites comprise of vertical drain treated sub-areas and untreated sub-areas which were reclaimed and preloaded under the same conditions. The results of the finite element modeling analysis was compared with that obtained by means of observational methods. Reasonable agreements were obtained from the finite element modeling analysis as compared to the actual field settlements for both the vertical drain treated embankments as well as the untreated control embankments at both the <i>In situ</i> Test Site and Pilot Test Site. The axi-symmetric unit cell and the full scale analysis of vertical drains were found to be in excellent agreement with each other and with the actual field settlement results. Ultimate settlement and degree of consolidation assessed by using Asaoka, Hyperbolic, piezometer and finite element modeling methods have also been compared for each of the sites and are also found to be in good agreement.

Homogenization-based multi-scale damage theory

The research of modern mechanics reveals that the damage and failure of structures should be considered on different scales. The present paper is dedicated to establishing the multi-scale damage theory for the nonlinear structural analysis. Starting from the asymptotic expansion based homogenization theory, the multi-scale energy integration is proposed to bridge the gap between the micro and macro scales. By recalling the Helmholtz free energy based damage definition, the damage variable is represented by the multi-scale energy integration. Hence the damage evolution could be numerically simulated on the basis of the unit cell analysis rather than the experimental data identification. Finally the framework of the multi-scale damage theory is established by transforming the multi-scale damage evolution into the conventional continuum damage mechanics. The agreement between the simulated results and the benchmark results indicates the validity and effectiveness of the proposed theory.

Void growth and coalescence in f.c.c. single crystals

In this study, we investigate deformation behavior of f.c.c. single crystals containing microvoids by using three-dimensional finite element methods. The unit cell analysis has been conducted to study the effect of stress triaxialities, crystallographic orientations and initial void volume fractions on the growth and coalescence of voids in f.c.c. single crystals. The locally homogeneous constitutive model for the rate-dependent single crystal plasticity is implemented into a finite element program (ABAQUS) by means of the user-defined subroutine (UMAT). To identify the effect of stress triaxiality and the crystallographic orientation on the void evolution, the stress triaxiality was kept constant during deformation. The numerical results showed that the stress triaxiality and the deformation mode specified by the crystallographic orientation have a competitive effect on the evolution of voids. For the low level of stress triaxiality, the deformation mode is mainly determined by the crystallographic orientation. For high stress triaxiality, however, the deviation from the specific deformation mode is large even for incipient void growth and the void growth rate is mainly determined by stress triaxiality and the initial void volume fraction. For the small initial void volume fraction, the growth rate of a void is rapid compared with the large one and the effect of the initial crystallographic orientation is significant.

Predicting the long-term performance of a wide embankment on soft soil using an elastic–viscoplastic model

This paper presents modelling of the consolidation of foundation soil under a wide embankment constructed over soft soil. An elastic–viscoplastic (EVP) constitutive model is used to represent the foundation soil for the coupled finite element analysis (FEA). A unit-cell analysis is carried out to capture the maximum settlement and the development of excess pore-water pressure with time below the centreline of the embankment for a long period (9 years). A new function for capturing the varying nature of the creep or secondary compression coefficient is proposed and used in association with the EVP model. The input material parameters for this study were determined from extensive laboratory experiments except for the equivalent horizontal permeability, which was systematically estimated by using vertical permeability data obtained from one-dimensional consolidation tests and by back-analysing the first 12 months of field settlement data. Comparisons are made among the predictions obtained adopting an elastoplastic modified Cam clay model and the EVP model with constant and varying creep coefficients for the foundation soil and the corresponding field data. The predictions with the EVP model are found to be better than those with the elastoplastic model and the use of a varying creep coefficient for the EVP model seems to further improve its predicting ability.

Stress distribution in outer and inner plies of textile laminates and novel boundary conditions for unit cell analysis

The local stress–strain distribution in a unit cell of a textile laminate depends on the distance of the ply to the surface, the number of plies in the laminate, and the stacking sequence. A conventional meso FE analysis employs boundary conditions for a unit cell of the textile composite based on the assumption of periodicity in the thickness direction. In that case, the stress concentration can be drastically underestimated, especially in outer plies. This paper describes the interaction of plies, local stresses and displacements. To avoid the analysis of the whole laminate and to reduce it to the boundary value problem on one unit cell only, novel boundary conditions are introduced. These conditions are based on the analysis of a single unit cell: they account for the number of the plies in the laminate, distinguish between the outer and inner plies, and reproduce the meso stress–strain state with good precision.

Effect of Finite Thickness and Free Edges on Stresses in Plain Weave Composites

Many years ago, free edge effects were studied extensively, perhaps excessively, for ordinary tape laminate composites. Various techniques were used to show that the free edge effects extended only a short distance from the free edge and that stacking sequence had a significant impact on interlaminar stresses, which could cause premature failure. In contrast, the analytical study of woven composites has focused on periodic analysis of unit cells. Since such analyses assume an infinite array of unit cells, free edge effects were not considered. This article investigates the significance of traction free surfaces on stresses in woven composites. Effects due to both free edge and free lateral surfaces (due to finite thickness) were investigated. The significance of the free edge effect was found to be sensitive to the waviness of the plain weave mat. Also, the stress distribution is quite different for finite and infinitely thick stacks of woven mats.

Single fibre and multifibre unit cell analysis of strength and cracking of unidirectional composites

Numerical simulations of damage evolution in composites reinforced with single and multifibre are presented. Several types of unit cell models are considered: single fibre unit cell, multiple fibre unit cell with one and several damageable sections per fibres, unit cells with homogeneous and inhomogeneous interfaces, etc. Two numerical damage models, cohesive elements, and damageable layers are employed for the simulation of the damage evolution in single fibre and multifibre unit cells. The two modelling approaches were compared and lead to the very close results. Competition among the different damageable parts in composites (matrix cracks, fibre/matrix interface damage and fibre fracture) was observed in the simulations. The strength of interface begins to influence the deformation behaviour of the cell only after the fibre is broken. In this case, the higher interface layer strength leads to the higher stiffness of the damaged material. The damage in the composites begins by fibre breakage, which causes the interface damage, followed by matrix cracking.

Design and Analysis of Three-Dimensionalized ELC Metamaterial Unit Cell

The use of a three-dimensional electric-LC (3D-ELC) resonator to obtain a minimally refractive and strongly transmissive composite metamaterial is explored. The 3D-ELC repeated unit cell consists of two ELC elements that, when put together, may be used to generate responding electric dipole moments in the x¿, y¿, and z¿ directions. When embedded inside a host material whose permittivity is significantly greater than unity, the repeated 3D-ELC metamaterial can be used to depress the effective dielectric constant of the resulting composite material to a near-unity value in all Cartesian directions. The concept of designing a unity-index metamaterial-with the properties of free space-may prove useful in creating mechanically durable materials for use as radomes or other enclosures for radiating structures.

Structure and Thermal Behavior of a Cellulose I−Ethylenediamine Complex

We prepared highly crystalline samples of a cellulose I-ethylenediamine (EDA) complex by immersing oriented films of algal (Cladophora) cellulose microcrystals in EDA at room temperature for a few days. The unit-cell parameters were determined to be a = 0.455, b = 1.133, and c = 1.037 nm (fiber repeat) and gamma = 94.02 degrees. The space group was P2(1). On the basis of unit cell, density, and thermogravimetry analyses, the asymmetric unit is composed of one anhydrous glucose residue and one EDA molecule. The chemical and thermal stabilities of the cellulose I-EDA complex were also investigated by the use of X-ray diffraction. When the cellulose I-EDA complex was immersed in methanol or water at room temperature, cellulose III I or I beta was obtained, respectively. However, immersion in a nonpolar solvent such as toluene did not affect the crystal structure of the complex. The cellulose I-EDA complex was stable up to a temperature of approximately 130 degrees C, whereas the boiling point of EDA is 117 degrees C. This thermal stability of the complex is probably caused by intermolecular hydrogen bonds between EDA molecules and cellulose. When heated above 150 degrees C, the cellulose I-EDA complex decomposed into cellulose I beta.