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Homogenization Method (homogenization + method)
Selected AbstractsModeling of Coating Process, Phase Changes, and Damage of Plasma Sprayed Thermal Barrier Coatings on Ni-Base Superalloys,ADVANCED ENGINEERING MATERIALS, Issue 3 2010Tilmann Beck The paper gives an overview on the modeling activities on plasma sprayed thermal barrier coating in the frame of TFB 63. In the first part, through-process modeling of the APS deposition of a ZrO2 based TBC is described. Starting from simulation of the plasma jet, heat transfer into the powder particles, particle melting, particle impact on the substrate surface, and solidification is simulated. A homogenization method is introduced to describe the mechanical properties of the resulting TBC. The second part shows simulation of interdiffusion and phase transformations of MCrAlY and intermetallic oxidation protection coatings on several cast Ni-base alloy substrates. Finally, FEM-based damage simulation of oxidation protection coatings by transversal fatigue cracks during thermomechanical fatigue loading as well as by delamination of the TBC during thermocyclic loading is discussed. [source] Elasto-plastic analysis of block structures through a homogenization methodINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2010G. de Felice Abstract The paper describes the development and numerical implementation of a constitutive relationship for modeling the elasto-plastic behavior of block structures with periodic texture, regarded at a macroscopic scale as homogenized anisotropic media. The macroscopic model is shown to retain memory of the mechanical characteristics of the joints and of the shape of the blocks. The overall mechanical properties display anisotropy and singularities in the yield surface, arising from the discrete nature of the block structure and the geometrical arrangement of the units. The model is formulated in the framework of multi-surface plasticity. It is implemented in an finite element (FE) code by means of two different algorithms: an implicit return mapping scheme and a minimization algorithm directly derived from the Haar,Karman principle. The model is validated against analytical and experimental results: the comparison between the homogenized continuum and the original block assembly shows a good agreement in terms of ultimate inelastic behavior, when the size of the block is small as compared with that of the whole assembly. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical simulation of bolt-supported tunnels by means of a multiphase model conceived as an improved homogenization procedureINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2008Patrick de Buhan Abstract This paper examines the possibility of applying a homogenization procedure to analyze the convergence of a tunnel reinforced by bolts, regarded as periodically distributed linear inclusions. Owing to the fact that a classical homogenization method fails to account for the interactions prevailing between the bolts and the surrounding ground and thus tends to significantly overestimate the reinforcement effect in terms of convergence reduction, a so-called multiphase model is presented and developed, aimed at improving the classical homogenization method. Indeed, according to this model, the bolt-reinforced ground is represented at the macroscopic scale as the superposition of two mutually interacting continuous phases, describing the ground and the reinforcement network, respectively. It is shown that such a multiphase approach can be interpreted as an extension of the homogenization procedure, thus making it possible to capture the ground,reinforcement interaction in a proper way, provided the constitutive parameters of the model and notably those relating to the interaction law can be identified from the reinforced ground characteristics. The numerical implementation of this model in a finite element method-based computer code is then carried out, and a first illustrative application is finally presented. Copyright © 2008 John Wiley & Sons, Ltd. [source] A homogenization method for estimating the bearing capacity of soils reinforced by columnsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2005B. Jellali Abstract The ultimate bearing capacity problem of a strip foundation resting on a soil reinforced by a group of regularly spaced columns is investigated in the situation when both the native soil and reinforcing material are purely cohesive. Making use of the yield design homogenization approach, it is shown that such a problem may be dealt with as a plane strain yield design problem, provided that the reinforced soil macroscopic strength condition has been previously determined. Lower and upper bound estimates for such a macroscopic criterion are obtained, thus giving evidence of the reinforced soil strong anisotropy. Performing the upper bound kinematic approach on the homogenized bearing capacity problem, by using the classical Prandtl's failure mechanism, makes it then possible to derive analytical upper bound estimates for the reinforced foundation bearing capacity, as a function of the reinforced soil parameters (volume fraction and cohesion ratio), as well as of the relative extension of the reinforced area. It is shown in particular that such an estimate is closer to the exact value of the ultimate bearing capacity, than that derived from a direct analysis which implicitly assumes that the reinforced soil is an isotropic material. Copyright © 2005 John Wiley & Sons, Ltd. [source] About Darcy's law in non-Galilean frameINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2004C. Geindreau Abstract This paper is aimed towards investigating the filtration law of an incompressible viscous Newtonian fluid through a rigid non-inertial porous medium (e.g. a porous medium placed in a centrifuge basket). The filtration law is obtained by upscaling the flow equations at the pore scale. The upscaling technique is the homogenization method of multiple scale expansions which rigorously gives the macroscopic behaviour and the effective properties without any prerequisite on the form of the macroscopic equations. The derived filtration law is similar to Darcy's law, but the tensor of permeability presents the following remarkable properties: it depends upon the angular velocity of the porous matrix, it verifies Hall,Onsager's relationship and it is a non-symmetric tensor. We thus deduce that, under rotation, an isotropic porous medium leads to a non-isotropic effective permeability. In this paper, we present the results of numerical simulations of the flow through rotating porous media. This allows us to highlight the deviations of the flow due to Coriolis effects at both the microscopic scale (i.e. the pore scale), and the macroscopic scale (i.e. the sample scale). The above results confirm that for an isotropic medium, phenomenological laws already proposed in the literature fails at reproducing three-dimensional Coriolis effects in all types of pores geometry. We show that Coriolis effects may lead to significant variations of the permeability measured during centrifuge tests when the inverse Ekman number Ek,1 is ,,(1). These variations are estimated to be less than 5% if Ek,1<0.2, which is the case of classical geotechnical centrifuge tests. We finally conclude by showing that available experimental data from tests carried out in centrifuges are not sufficient to determining the effective tensor of permeability of rotating porous media. Copyright © 2004 John Wiley & Sons, Ltd. [source] Numerical solutions for flow in porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2003J.G. Wang Abstract A numerical approach is proposed to model the flow in porous media using homogenization theory. The proposed concept involves the analyses of micro-true flow at pore-level and macro-seepage flow at macro-level. Macro-seepage and microscopic characteristic flow equations are first derived from the Navier,Stokes equation at low Reynolds number through a two-scale homogenization method. This homogenization method adopts an asymptotic expansion of velocity and pressure through the micro-structures of porous media. A slightly compressible condition is introduced to express the characteristic flow through only characteristic velocity. This characteristic flow is then numerically solved using a penalty FEM scheme. Reduced integration technique is introduced for the volumetric term to avoid mesh locking. Finally, the numerical model is examined using two sets of permeability test data on clay and one set of permeability test data on sand. The numerical predictions agree well with the experimental data if constraint water film is considered for clay and two-dimensional cross-connection effect is included for sand. Copyright © 2003 John Wiley & Sons, Ltd. [source] Coupled damage and plasticity modelling in transient dynamic analysis of concreteINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2002Fabrice Gatuingt Abstract In a concrete structure subjected to an explosion, for example a concrete slab, the material is subjected to various states of stress which lead to many modes of rupture. Closer to the explosive, a state of strong hydrostatic compression is observed. This state of stress produces an irreversible compaction of the material. Away from the zone of explosion, confinement decreases and the material undergoes compression with a state of stress, which is slightly triaxial. Finally, the compression wave can be reflected on a free surface and becomes a tensile wave, which by interaction with the compression wave, produces scabbing. We present, in this paper, a model aimed at describing these three failure modes. It is based on visco-plasticity and rate dependent damage in which a homogenization method is used in order to include the variation of the material porosity due to compaction. The model predictions are compared with several experiments performed on the same concrete. Computations of split Hopkinson tests on confined concrete, a tensile test with scabbing, and an explosion on a concrete slab are presented. Copyright © 2001 John Wiley & Sons, Ltd. [source] Design and application of layered composites with the prescribed magnetic permeabilityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2010Jae Seok Choi Abstract This research aims to design the microstructure with the prescribed magnetic permeability and proposes a design method to control the magnetic flux flow using layered microstructures. In the optimization problem for the microstructure design, the objective function is set up to minimize the difference between the homogenized magnetic permeability during the design process and the prescribed permeability based on the so-called inverse homogenization method. Based on the microstructure design result, a microstructure composed of layered materials is proposed for the purpose of the efficient magnetic flux control. In addition, its analytical calculation is added to confirm the feasibility of the optimized results. The layered composite of a very thin ferromagnetic material is expected to guide the magnetic flux and the performance of the magnetic system can be improved by turning the microstructures appropriately. Optimal rotation angles of microstructures are determined using the homogenization design method. The proposed design method is applied to an example to confirm its feasibility. Copyright © 2009 John Wiley & Sons, Ltd. [source] Smart element method I. The Zienkiewicz,Zhu feedbackINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2005Shaofan Li Abstract A new error control finite element formulation is developed and implemented based on the variational multiscale method, the inclusion theory in homogenization, and the Zienkiewicz,Zhu error estimator. By synthesizing variational multiscale method in computational mechanics, the equivalent eigenstrain principle in micromechanics, and the Zienkiewicz,Zhu error estimator in the finite element method (FEM), the new finite element formulation can automatically detect and subsequently homogenize its own discretization errors in a self-adaptive and a self-adjusting manner. It is the first finite element formulation that combines an optimal feedback mechanism and a precisely defined homogenization procedure to reduce its own discretization errors and hence to control numerical pollutions. The paper focuses on the following two issues: (1) how to combine a multiscale method with the existing finite element error estimate criterion through a feedback mechanism, and (2) convergence study. It has been shown that by combining the proposed variational multiscale homogenization method with the Zienkiewicz,Zhu error estimator a clear improvement can be made on the coarse scale computation. It is also shown that when the finite element mesh is refined, the solution obtained by the variational eigenstrain multiscale method will converge to the exact solution. Copyright © 2004 John Wiley & Sons, Ltd. [source] Numerical derivation of contact mechanics interface laws using a finite element approach for large 3D deformationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004Alex Alves Bandeira Abstract In this work a homogenization method is presented to obtain by numerical simulation interface laws for normal contact pressure based on statistical surface models. For this purpose and assuming elastic behaviour of the asperities, the interface law of Kragelsky et al. (Friction and Wear,Calculation Methods, Pergamon, 1982) is chosen for comparison. The non-penetration condition and interface models for contact that take into account the surface micro-structure are investigated in detail. A theoretical basis for the three-dimensional contact problem with finite deformations is shortly presented. The augmented Lagrangian method is then used to solve the contact problem with friction. The algorithms for frictional contact are derived based on a slip rule using backward Euler integration like in plasticity. Special attention was dedicated to the consistent derivation of the contact equations between finite element surfaces. A matrix formulation for a node-to-surface contact element is derived consisting of a master surface segment with four nodes and a contacting slave node. It was also necessary to consider the special cases of node-to-edge contact and node-to-node contact in order to achieve the desired asymptotic quadratic convergence in the Newton method. A numerical example is selected to show the ability of the contact formulation and the algorithm to represent interface law for rough surfaces. Copyright © 2003 John Wiley & Sons, Ltd. [source] Solid lipid nanoparticles (SLN) as carriers for the topical delivery of econazole nitrate: in-vitro characterization, ex-vivo and in-vivo studiesJOURNAL OF PHARMACY AND PHARMACOLOGY: AN INTERNATI ONAL JOURNAL OF PHARMACEUTICAL SCIENCE, Issue 8 2007Vanna Sanna Solid lipid nanoparticles (SLN) designed for topical administration of econazole nitrate (ECN), were prepared by o/w high-shear homogenization method using different ratios of lipid and drug (5:1 and 10:1). SLN were characterized in terms of particle size, morphology, encapsulation efficiency and crystalline structure. After incorporation of SLN into hydrogels, rheological measurements were performed, and ex-vivo drug permeation tests were carried out using porcine stratum corneum (SC). In-vivo study of percutaneous absorption of ECN as a function of application time and composition of gels was carried out by tape-stripping technique. Penetration tests of the drug from a conventional gel were performed as comparison. High-shear homogenization method resulted in a good technique for preparation of ECN-loaded SLN. Particles had a mean diameter of about 150 nm and a regular shape and smooth surface. The encapsulation efficiency values were about 100%. Ex-vivo tests showed that SLN were able to control the drug release through the SC; the release rate depended upon the lipid content on the nanoparticles. In-vivo studies demonstrated that SLN promoted a rapid penetration of ECN through the SC after 1 h and improved the diffusion of the drug in the deeper skin layers after 3 h of application compared with the reference gel. [source] Second order homogenization method based on higher order finite elementsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005A. D?ster Modeling materials with lattice-like microstructures like open-cell foams requires an extended continuum mechanical setting on the macroscopic scale, e. g. a micropolar or micromorphic theory. In order to avoid the formulation of constitutive equations a higher order numerical homogenization scheme (FE2) is proposed. Therefore, each integration point possesses its own microstructure which, in the present case, consists of beam-like elements representing the cell walls. In this paper, the microstructures are discretized by continuum-based higher order locking free finite elements with high aspect ratios, leading to a numerically efficient treatment of a local displacement-driven boundary value problem according to the macroscopic strain and curvature. The resulting stress distributions in the microstructures are homogenized to macroscopic stresses and couple stresses. The approach is demonstrated by a numerical example. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Asymptotic evaluation of effective complex moduli of fibre-reinforced viscoelastic composite materialsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003I. Andrianov Prof. Dr. Sc. We propose an asymptotic approach for the evaluation of effective complex moduli of viscoelastic fibre-reinforced composite materials. Our method is based on the homogenization technique. We start with a non-trivial expansion of the input plane-strain boundary value problem by ratios of visco-elastic constants. This allows to simplify the governing equations to forms analogous to the complex transport problem. Then we apply the asymptotic homogenization method, coming from the original problem on multi-connected domain to the cell problem, defined on a unit cell of the periodic structure. For the analytical solution of the cell problem we apply the boundary perturbation technique, the asymptotic expansion by a distance between two neighbouring fibres and the method of two-point Padé approximants. As results we derive uniform analytical representations for effective complex moduli, valid for all values of the components volume fractions and properties. [source] | ||||||||||