Unit Cell Analysis Research Articles

Finite Element Analysis of Periodic Structures Without Constrained Meshes

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A finite element analysis is detailed of periodic structures without constrained meshes. The infinite periodic analysis domain is reduced to the unit cell analysis by means of the Floquet-Bloch decomposition, where an admittance-type matrix approach is carried out. Special emphasis is placed on the admittance-type matrix generation in such a way that the constrained meshing problem is no longer required. As a result, periodic ports are permitted in the unit cell, and the Floquet-Bloch periodic conditions are easily applied in the admittance-type matrix by means of a connection-like handling. Several infinite periodic antennas are shown to be analyzed appropriately. </para>

Long-term performance of a wide embankment on soft clay improved with prefabricated vertical drains

This paper presents the long-term performance of a wide geogrid-reinforced road embankment constructed on soft clay improved with prefabricated vertical drains (PVDs) at a freeway extension site 150 km north of Sydney in Australia. The foundation soil and the embankment were instrumented and monitored for about 400 days for excess pore-water pressure, earth pressure, and reinforcement tension, and for 9 years for displacement profiles. The embankment was constructed in stages and surcharged in an attempt to reduce post-construction settlement. As the embankment width was wide relative to the thickness of the soft clay, the settlement near the centre was modelled by a unit cell analysis. The equivalent horizontal permeability was determined by back analysis of the central zone using the first 12 months of settlement data. All other soil parameters were determined from the laboratory and field testing. The predicted pore-water pressure response over the first 400 days showed reasonable agreement with measured values. The same analysis was then continued to predict settlement over a period of 9 years. The predicted settlement was, however, smaller than the measured value at the centre region of the embankment.

Thermo-oxidative behavior of high-temperature PMR-15 resin and composites

The present study examines the thermo-oxidative behavior of high-temperature polymer matrix composite materials. Thermo-oxidative aging in neat resin is simulated with a diffusion-reaction model in which temperature, oxygen concentration and weight loss effects are considered. The thermo-oxidative behavior of the composite, on the other hand, is significantly different from that of the constituents as the composite microstructure, including the fiber/matrix interphase/interface, introduces anisotropy in the diffusion and oxidation behavior. Unit cell analyses are carried out using three-dimensional finite element analysis of repeated volume elements representing the fiber, matrix and interphase regions, and the resin oxidation model. Parametric studies illustrating the anisotropy in the oxidative region growth and the effect of fiber and interphase diffusivity on the oxidation layer growth are discussed. It is suggested that fiber–matrix debonding could provide additional diffusion paths to explain the extent of observed anisotropic oxidation growth.

Reduced-order simulation of large accelerator structures

Simulating electromagnetic waves inside finite periodic or almost periodic three-dimensional structures is important to research in linear particle acceleration, high power microwave generation, and photonic band gap structures. While eigenmodes of periodic structures can be determined from analysis of a single unit cell, based on Floquet theory, the general case of aperiodic structures, with defects or nonuniform properties, typically requires 3D electromagnetic simulation of the entire structure. When the structure is large and high accuracy is necessary this can require high-performance computing techniques to obtain even a few eigenmodes [Z. Li et al., Nucl. Instrum. Methods Phys. Res., Sect. A 558, 168 (2006)]. To confront this problem, we describe an efficient, field-based algorithm that can accurately determine the complete eigenmode spectrum for extended aperiodic structures, up to some chosen frequency limit. The new method combines domain decomposition with a nontraditional, dual eigenmode representation of the fields local to each cell of the structure. Two related boundary value eigenproblems are solved numerically in each cell, with (a) electrically shielded, and (b) magnetically shielded interfaces, to determine a combined set of basis fields. By using the dual solutions in our field representation we accurately represent both the electric and magnetic surface currents that mediate coupling at the interfaces between adjacent cells. The solution is uniformly convergent, so that typically only a few modes are used in each cell. We present results from 2D and 3D simulations that demonstrate the speed and low computational needs of the algorithm.

Reliability of Conventional Settlement Evaluation for Circular Foundations on Stone Columns

The unit cell idealization has been long adopted in the settlement prediction of stone column-reinforced soils. This paper tests the accuracy of this modeling concept against trusted settlement values of engineering foundations. It is believed that in order to bestow the outcome of this study adequate generality different soil properties and foundation geometries need to be considered. It was, nevertheless, found impracticable to collect field settlement records for all the analyzed cases. The authors, therefore, appealed to the back analysis concept to construct a reliable mathematical model, calibrated against settlement records of full-scale field load test. This model, which is capable of reproducing the real field settlements, is then employed as a generic tool to obtain trusted settlement values for a variety of cases with essential geometrical similarity. The investigation revealed that the unit cell analysis may, in some cases, lead to erroneous estimation for the settlements of foundations with limited extents. Correction factors, dependent on the treated soil properties as well as the foundation size, are introduced.

Prediction of the Elastic Modulus of Cement Paste as a Kinetic Hydration Model

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

Effect of architecture on mechanical properties of carbon/carbon composites

Three-directional orthogonal, 3-directional plain-woven and 4-directional in-plane composites are three architectures commonly used in components made of carbon/carbon composites. Homogenization and finite element analysis of a three-dimensional periodic unit cell characterizing the structure of the composite and periodic boundary conditions are used to compute the elastic moduli of carbon/carbon composites for different architectures. First, the mechanical properties of a fiber bundle are predicted assuming the fiber bundle to be a perfectly bonded uni-directional composite. Second, these properties are used to predict the mechanical properties of the multidirectional composite. Cohesive zone models are used to simulate the interfacial debonding at the fiber bundle/matrix interfaces. The application of cohesive zone model when there are debonds at the interface between the fiber bundle and the matrix results in a remarkable change in the values of shear modulus when compared to that obtained for perfectly bonded composites. The analysis predicts a significant effect of architecture on the properties of composite.

Macroscopic strength estimates for metal matrix composites embedding a ductile interphase

The influence of an interphase region on the macroscopic strength of unidirectional fiber-reinforced metal-matrix composites (MMCs) is investigated. The three phases of the composite are supposed to be elastic-perfectly plastic and to conform with J 2-plasticity. First, theoretical bounds to the macroscopic strength are derived, according to homogenization theory for heterogeneous periodic media: the gap between these bounds is quite narrow for certain stress conditions, volumetric proportions of the constituents, and ratios of the interphase-to-matrix strength. Then, a numerical model previously developed by Taliercio (2005) is employed to predict the macroscopic response of three-phase MMCs under any 3D stress through the analysis of a single representative unit cell. The model is applied to the numerical identification of the macroscopic strength properties of MMCs under uni-, bi- and triaxial stresses, in cases where the theoretical bounds are not sufficiently close to identify the actual macroscopic yield surface. The influence of the weakening interphase on the predicted macroscopic strength is critically discussed. A decrease in interphase strength is found to affect the transverse tensile and shear strength of the composite to a moderate extent, whereas the macroscopic longitudinal shear strength is extremely sensitive to the interphase strength.

A New Approach for the Analysis of Planar Distributed Two-Dimentional (2-D) Left-Haned (Lh) Structures

A new approach is proposed to analyze planar distributed 2-D LH structures. The 4-port S parameters of the unit cell combined with the Bloch-Floquet theory are used to determine the dispersion relations and Bloch impedance. The LH and RH frequency bands are identified by the signs of the real parts of the wave number and the Bloch impedance. Several advantages of the new approach over the previous unit cell analysis methods are presented. As an example, a capacitance-enhanced LH structure is designed and analyzed with the new approach. FDTD simulation is also performed to study the periodic LH structure with infinite arrays. The results of the simulation at the LH frequency band show the backward wave properties in consistent with those obtained by the proposed approach.

정자장 문제의 균질화 기법의 비교

Many engineering problems require the calculation of effective material properties of a structure which is composed of repeated micro-structures. The homogenization method has been used to calculate the effective (homogenized) properties of composites and several homogenization procedures for different physical fields have been introduced. This research describes the modified homogenization technique for magnetostatic problems. Assuming that the material is periodically repeated, its effective permeability can be prescribed by calculating the homogenized magnetic reluctivity using the finite element analysis of the micro unit cell. Validity of the suggested method is confirmed by comparing the results by the energy based method as well as the widely known homogenization method.

A strain-rate dependent 3-D micromechanical model for finite element simulations of plain weave composite structures

Abstract A new 3-D constitutive model is developed for finite element simulations of plain weave composites (PWC) structures and implemented in the explicit finite element software DYNA3D. The aim of this work is to develop a material model for PWC which incorporates their significant deformation characteristics like strain rate sensitivity, progressive failure phenomena, and nonlinearity in shear and yet is computationally efficient. The constitutive relations are obtained using micromechanical analysis of a simple representative unit cell developed earlier in [1] to predict the mechanical properties of PWC. The matrix is modeled as a viscoplastic strain-rate dependent material, thereby incorporating strain-rate sensitivity in the composite model. Nonlinearity in shear is modeled using an explicit strain dependent relation for shear moduli of the constituents. A set of strain based failure criteria and corresponding stiffness degradations is used to model the progressive failure behavior. The constituents are checked for various modes of failure at each time step and if found to have failed, their moduli are reduced based on the mode. Only fiber breakage is assumed as ultimate failure of the composite. Initially, the yarns and the matrix are assumed to be transversely isotropic and isotropic materials respectively. They become orthotropic with the advent of initial failure. Experimental results available in the literature are used to verify the model’s predictions.

Variational asymptotic method for unit cell homogenization of periodically heterogeneous materials

A new micromechanics model, namely, the variational asymptotic method for unit cell homogenization (VAMUCH), is developed to predict the effective properties of periodically heterogeneous materials and recover the local fields. Considering the periodicity as a small parameter, we can formulate a variational statement of the unit cell through an asymptotic expansion of the energy functional. It is shown that the governing differential equations and periodic boundary conditions of mathematical homogenization theories (MHT) can be reproduced from this variational statement. In comparison to other approaches, VAMUCH does not rely on ad hoc assumptions, has the same rigor as MHT, has a straightforward numerical implementation, and can calculate the complete set of properties simultaneously without using multiple loadings. This theory is implemented using the finite element method and an engineering program, VAMUCH, is developed for micromechanical analysis of unit cells. Many examples of binary composites, fiber reinforced composites, and particle reinforced composites are used to demonstrate the application, power, and accuracy of the theory and the code of VAMUCH.

Electromagnetic Modelling of Fine Features in Photonic Applications

Straightforward application of numerical modelling approaches to Photonic Band-Gap structures demands the use of fine meshes, notably finer that the size of a single scattering element, in order that high accuracy is achieved. However simulations employing sufficiently fine meshing to correctly represent the geometry of the scatterers lead to very long computational run-times and huge memory consumption. Such direct numerical approaches to PBG characterisation are only suited to the analysis of single unit cells or for benchmarking. In practice, the computational overheads significantly increase when one deals with an array of cells or when modelling the global behaviour of a large number of devices integrated on a single substrate. Therefore in order to model the macroscopic response of PBG structures the possibility of employing meshes of much larger size than the individual scattering elements has been explored. A suitable approach, initially developed for Electromagnetic Compatibility predictions, has been modified to permit modelling of Photonic Crystal Waveguides. The method provides second order accuracy and leaves a designer with the flexibility to discretise the entire problem space with an arbitrary number of scatterers per mesh cell. Results are first presented for small clusters of scatterers and subsequently for complete photonic structures.

Evaluation of Elastic and Creep Properties of Perforated Materials by Finite Element Analysis Imposing Periodic Boundary Conditions

In the analysis of materials containing regularly placed in-homogeneities, the evaluation of homogenized properties is an important issue. Common procedure for the homogenization is to define a unit cell, load it somehow, and investigate its structural response. A periodic variation of strain appears when the periodically heterogeneous material is under uniform macro-stress, and therefore, the implementation of this characteristic behavior would be essential to the material characterization based on a unit cell analysis. With the method proposed here, conventional finite element analysis tools can be used with no modification, and it is applicable to the skew-arrayed in-homogeneity problems. The orthotropic elastic and creep properties of materials with voids are examined, and the accuracy and effectiveness are demonstrated.

Characterization of a Highly Purified, Fully Active, Crystallizable RC–LH1–PufX Core Complex from Rhodobacter sphaeroides

Photosynthetic complexes in bacteria absorb light and undergo photochemistry with high quantum efficiency. We describe the isolation of a highly purified, active, reaction center-light-harvesting 1-PufX complex (RC-LH1-PufX core complex) from a strain of the photosynthetic bacterium, Rhodobacter sphaeroides, which lacks the light-harvesting 2 (LH2) and contains a 6 histidine tag on the H subunit of the RC. The complex was solubilized with diheptanoyl-sn-glycero-3-phosphocholine (DHPC), and purified by Ni-affinity, size-exclusion and ion-exchange chromatography in dodecyl maltoside. SDS-PAGE analysis shows the complex to be highly purified. The quantum efficiency was determined by measuring the charge separation (DQA --> D+QA -) in the RC as a function of light intensity. The RC-LH1-PufX complex had a quantum efficiency of 0.95 +/- 0.05, indicating full activity. The stoichiometry of LH1 subunits per RC was determined by two independent methods: (i) solvent extraction and absorbance spectroscopy of bacteriochlorophyll, and (ii) density scanning of the SDS-PAGE bands. The average stoichiometry from the two measurements was 13.3 +/- 0.9 LH1/RC. The presence of PufX was observed in SDS-PAGE gels at a stoichiometry of 1.1 +/- 0.1/RC. Crystals of the core complex have been obtained which diffract X-rays to 12 A. A preliminary analysis of the space group and unit cell analysis indicated a P1 space group with unit cell dimensions of a = 76.3 A, b = 137.2 A, c = 137.5 A; alpha = 60.0 degrees , beta = 89.95 degrees , gamma =90.02 degrees .

Ductility of bulk metallic glasses and their composites with ductile reinforcements: A numerical study

Yield behavior of bulk metallic glasses containing voids is elucidated by using unit-cell analyses and the relevant material parameters; and the results are compared with the available constitutive models. These analyses clearly show that caution is needed when transferring the constitutive models associated with void growth and ductile damage in usual metallic materials to bulk metallic glasses, largely because of the different deformation modes in bulk metallic glasses resulting from the pressure dependency of the yield surface and intrinsic softening behavior. With the constitutive model calibrated from the unit-cell analysis, the influences of a wide range of parameters (mechanical properties, volume fraction and morphology of ductile reinforcements) on the ductility of metallic glass composites are explored. The results indicate that, even though the ductile reinforcements may alter the evolution and morphology of the shear bands, the overall failure behavior is still controlled by the metallic glass matrix, leading to very little or no improvement in the composite ductility in comparison to the ductility of metallic glass matrix. The results are compared with experimental studies available in the literature.

Mechanics of Sintering Materials with Bimodal Pore Distribution. I. Effective Characteristics of Biporous Materials and Equations for the Evolution of Pores of Different Radii

A model of sintering for materials with bimodal pore distribution is formulated as a generalization of the continuum isotropic theory of sintering. In contrast to known models that only contain one behavioral parameter, i.e. porosity, the model suggested is described by two parameters for each type of pore. The evolution equations for each type of pore as well as the effective viscosity coefficients and Laplace pressure (sintering potential) are determined by unit cell analysis.

Finite-volume direct averaging micromechanics of heterogeneous materials with elastic–plastic phases

In this communication, we extend the recently re-constructed micromechanics model called high-fidelity generalized method of cells (Bansal, Y., Pindera, M.-J., 2005. A second look at the higher-order theory for periodic multiphase materials. J. Appl. Mech. 72 (2), 177–195.) by incorporating inelastic response capability for the individual phases. The re-construction, based on the local/global stiffness matrix approach, has simplified the model’s theoretical framework and substantially increased its computational efficiency as well as implementability, enabling analysis of unit cells with realistic multiphase microstructures previously unattainable in the original formulation developed by Aboudi et al. (Aboudi, J., Pindera, M-J., Arnold, S.M., 2001. Linear thermoelastic higher-order theory for periodic multiphase materials. J. Appl. Mech. 68 (5), 697–707; Aboudi, J., Pindera, M-J, Arnold, S.M., 2003. Higher-order theory for periodic multiphase materials with inelastic phases. Int. J. Plasticity 19 (6), 805–847.) with an accuracy approaching finite-element solutions. Just as importantly, the re-construction has revealed the model to be based on a finite-volume, direct averaging approach with clearly discernible similarities to, and differences with, the finite-element method and the finite-volume technique used in computational fluid mechanics. Herein, easily programmable closed-form expressions have been derived for the thermo-inelastic contributions to the local stiffness matrix equations that facilitate incorporation of different inelastic constitutive theories for the phase response. The re-constructed model is then employed to investigate orientational and architectural effects in unidirectional metal matrix composites characterized by multi-inclusion unit cells. Classical incremental plasticity theory with isotropic hardening is employed for the matrix response for consistency and comparison with previously reported results by Aboudi et al. (2003). Unit cells representative of a square array of fibers rotated by an angle about the fiber axis, which lack planes of material symmetry in the rotated coordinate system in which the micromechanical analysis is performed, belong in the first category. New results are presented for such rotated unidirectional porous composites which suggest guidelines for optimizing stiffness and ductility of this class of light-weight materials relative to dominant loading directions. Strengthening effects due to fiber clustering, which require highly discretized multi-inclusion unit cells, fall in the second category. It is demonstrated that the previously documented results for particulate composites, explained by the clustering-induced alteration of stress invariants which govern plastic strain evolution, are recovered for unidirectional composites as well.

Casting microporosity growth in single-crystal superalloys by a three-dimensional unit cell analysis

Finite element (FE) analysis is employed to investigate casting microporosity growth in nickel-base single-crystal superalloys DD3. Based on a finite deformation rate-dependent crystallographic constitutive equation, the simulation of casting microporosity in a three-dimensional unit cell model was carried out under variation in a range of parameters including triaxiality, Lode parameter and a type of different slip systems activated and loading orientation. The FE results show that the stress triaxiality has profound effects on growth behaviour, volume fraction of casting microporosity and shape transition; the Lode parameter is an important parameter for casting microporosity growth and shape transition as well as triaxiality. Large local cumulative shear strain around casting microporosity plays an important role in driving casting microporosity growth; the high casting microporosity volume fraction corresponds to big cumulative shear strain. The operative slip systems type and loading orientation has a remarkable effect on casting microporosity growth, which is associated with the Schmid Factor and the Young's modulus of orientation.

Finite element modelling of marine clay deformation under reclamation fills

The ongoing Changi East Reclamation Project in Singapore consists of land reclamation and ground improvement of the foreshore for the future expansion of Changi International Airport. The deformation behaviour of marine clay under reclamation fills and surcharge was modelled by the finite element method (FEM) with Plaxis numerical modelling software. The analyses included modelling the consolidation behaviour of marine clay under reclamation fills with and without prefabricated vertical drains. Marine clay with vertical drains was modelled by both the axisymmetric unit cell and full-scale analysis methods. Marine clay that was not treated with prefabricated vertical drains was modelled by means of full-scale analysis. The numerical analysis was carried out at two case study locations: the pilot test site and the in situ test site. The test sites comprise vertical drain treated and untreated sub-areas that were reclaimed and preloaded under the same conditions. The result of the FEM analysis was compared with that obtained by means of observational methods. The vertical drain performance was verified for the in situ test site by using the value of Ch obtained from back-analysis by the Asaoka method and by FEM with Plaxis. Le Projet de Changi East qui se poursuit actuellement à Singapour consiste à récupérer des terres sur la mer et à améliorer le sol du littoral en vue de l'agrandissement futur de l'aéroport international de Changi. Le comportement de déformation de l'argile marine sous les remblais de récupération a été modélisé par la méthode d'éléments finis (FEM) avec le logiciel de modélisation numérique Plaxis. Les analyses comprenaient la modélisation du comportement de consolidation de l'argile marine sous les remblais de récupération avec et sans drains verticaux préfabriqués. L'argile marine avec drains verticaux a été modélisée à la fois par cellule unitaire axisymétrique et par des méthodes d'analyse grandeur nature. L'argile marine qui n'a pas été traitée avec des drains verticaux préfabriqués a été modélisée au moyen d'analyses de grandeur nature. Des analyses numériques ont été effectuées dans deux endroits d'étude: les sites d'essai pilote et les sites d'essai in situ. Les sites d'essai sont composés de sous-zones traitées et non traitées par des drains verticaux, zones qui ont été récupérées et préchargées dans les mêmes conditions. Nous avons comparé les résultats des analyses FEM avec celles obtenues au moyen de méthodes observationnelles. La performance du drain vertical a été vérifiée pour le site d'essai in situ en utilisant la valeur de Ch venant d'une rétro-analyse par la méthode Asaoka et par FEM avec Plaxis.