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Homogenization Procedure (homogenization + procedure)
Selected AbstractsHomogenization-based analysis of anisotropic damage in brittle materials with unilateral effect and interactions between microcracksINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2009Q. Z. Zhu Abstract This paper is devoted to micromechanical modeling of induced anisotropic damage in brittle geomaterials. The formulation of the model is based on a proper homogenization procedure by taking into account unilateral effects and interactions between microcracks. The homogenization procedure is developed in the framework of Eshelby's inclusion solution and Ponte-Castaneda and Willis (J. Mech. Phys. Solids 1995; 43:1919,1951) estimate. The homogenization technique is combined with the thermodynamics framework at microscopic level for the determination of damage evolution law. A rigorous crack opening,closure transition condition is established and an energy-release-rate-based damage criterion is proposed. Computational aspects on the implementation of micromechanical model are also discussed. The proposed model is evaluated by comparing numerical predictions with experimental data for various laboratory tests on concrete. Parametric studies on unilateral effects and influences of microcracks interactions are finally performed and analyzed. Copyright © 2008 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 second-order homogenization procedure for multi-scale analysis based on micropolar kinematicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2007Ragnar Larsson Abstract The paper presents a higher order homogenization scheme based on non-linear micropolar kinematics representing the macroscopic variation within a representative volume element (RVE) of the material. On the microstructural level the micro,macro kinematical coupling is introduced as a second-order Taylor series expansion of the macro displacement field, and the microstructural displacement variation is gathered in a fluctuation term. This approach relates strongly to second gradient continuum formulations, presented by, e.g. Kouznetsova et al. (Int. J. Numer. Meth. Engng 2002; 54:1235,1260), thus establishing a link between second gradient and micropolar theories. The major difference of the present approach as compared to second gradient formulations is that an additional constraint is placed on the higher order deformation gradient in terms of the micropolar stretch. The driving vehicle for the derivation of the homogenized macroscopic stress measures is the Hill,Mandel condition, postulating the equivalence of microscopic and macroscopic (homogenized) virtual work. Thereby, the resulting homogenization procedure yields not only a stress tensor, conjugated to the micropolar stretch tensor, but also the couple stress tensor, conjugated to the micropolar curvature tensor. The paper is concluded by a couple of numerical examples demonstrating the size effects imposed by the homogenization of stresses based on the micropolar kinematics. Copyright © 2006 John Wiley & Sons, Ltd. [source] Smart element method II.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2005An element based on the finite Eshelby tensor Abstract In this study, we apply the newly derived finite Eshelby tensor in a variational multiscale formulation to construct a smart element through a more accurate homogenization procedure. The so-called Neumann,Eshelby tensor for an inclusion in a finite domain is used in the fine scale feedback procedure to take into account the interactions among different scales and elements. Numerical experiments have been conducted to compare the performance and robustness of the new element to earlier formulations. The results showed that the smart element constructed via the Neumann,Eshelby tensor of a finite domain provides better numerical accuracy than that constructed via the Eshelby tensor of an infinite domain. Moreover, it can relieve volumetric locking. Copyright © 2005 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] A two-scale model for liquid-phase epitaxyMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2009Ch. Eck Abstract We study a model for liquid-phase epitaxy that is based on a continuum description of the transport processes in the liquid and a Burton,Cabrera,Frank (BCF) model for the growth of the solid by epitaxy. In order to develop a model that is capable to incorporate structures of a very small scale in the solid phase within a computation for a technically relevant macroscopic length scale, we apply homogenization methods. The result of the homogenization procedure is a two-scale model that consists of macroscopic equations for fluid flow and solute diffusion in the fluid volume, coupled to microscopic BCF models for the evolution of the microstructure in the solid phase. The obtained two-scale model is justified by an estimate for the model error that is valid under appropriate assumptions on the regularity of the solutions. This estimate is proved for a phase field approximation of the BCF model. Copyright © 2008 John Wiley & Sons, Ltd. [source] On diffusion of a single-phase, slightly compressible fluid through a randomly fissured mediumMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2001Steve Wright In this paper, the Douglas,Peszy,ska,Showalter model of diffusion through a partially fissured medium is given a stochastic formulation using the framework for problems in random media as set forth by Jikov, Kozlov and Oleinik. The concept of stochastic two-scale convergence in the mean is then used to homogenize the randomized micromodels which result. As a consequence of this homogenization procedure, exact stochastic generalizations of results obtained by Clark and Showalter on diffusion through periodically fissured media are derived. Copyright © 2001 John Wiley & Sons, Ltd. [source] Evaluation of different RNA extraction methods for small quantities of plant tissue: Combined effects of reagent type and homogenization procedure on RNA quality-integrity and yieldPHYSIOLOGIA PLANTARUM, Issue 1 2006Mary Portillo Highly sensitive techniques for transcriptome analysis, such as microarrays, complementary DNA-amplified fragment length polymorphisms (cDNA-AFLPs), and others currently used in functional genomics require a high RNA quality and integrity, as well as reproducibility among extractions of replicates from the same tissue. There are, however, few technical papers comparing different homogenization techniques and reagents to extract RNA from small quantities of plant tissue. We extracted RNA from tomato seedlings with the three different commercial reagents TRIZOL LS®, TRIZOL®, and TRI Reagent® in combination with pulverization, homogenization-maceration in a mortar, and homogenization with mild vibration plus glass beads, and evaluated total RNA integrity-quality and yield. Pulverization under liquid nitrogen combined with TRIZOL LS® as extraction reagent and homogenization-maceration in mortar with TRI Reagent®, are the procedures that rendered higher RNA yield, integrity and quality, as well as reproducibility among independent RNA extractions. In contrast, short mild vibration pulses (4500 r.p.m. for 5 s) mixed with glass beads, rendered low extraction efficiency and caused, in most cases, partial RNA degradation. [source] Aspects of a direct homogenization procedure for electro-mechanically coupled problemsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Marc-André Keip The aim of this work is to discuss a micro,macro homogenization procedure for electro,mechanically coupled problems. In this context a two,scale homogenization ansatz for ferroelectric ceramics based on an FE2 -approach is presented. The microscopic discretization of the heterogeneous structure of the polycrystalline material allows for the incorporation of microscopic effects, which are necessary to determine the corresponding overall macroscopic material response. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Simulation of polycrystalline ferroelectrics based on discrete orientation distribution functionsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Ingo Kurzhöfer Ferroelectric materials exhibit a spontaneous polarization, which can be reversed by an applied electric field of sufficient magnitude. The resulting nonlinearities are expressed by characteristic dielectric and butterfly hysteresis loops. These effects are correlated to the structure of the crystal and especially to the axis of spontaneous polarization in case of single crystals. We start with a representative meso scale, where the domains consist of unit cells with equal spontaneous polarization. Each domain is modeled within a coordinate invariant formulation for an assumed transversely isotropic material as presented in [10], in this context see also [8]. In this investigation we obtain the macroscopic polycrystalline quantities via a simple homogenization procedure, where discrete orientation distribution functions are used to approximate the different domains. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Effective Dynamic Material Properties of Foam-like MicrostructuresPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005S. Alvermann The effective material parameters of a microstructured material can be found using homogenization procedures based on calculations of a Representative Volume Element (RVE) of the material. In our approach the RVE is calculated in frequency domain and inertia is taken into account, leading to a frequency dependent behavior of the RVE. With the frequency response of the RVE, effective dynamic properties of the material are calculated using an optimization procedure. Due to the frequency dependent material behavior on the microscale a viscoelastic constitutive equation is applied on the macroscale. An example calculation is presented for an auxetic 2-D foam-like microstructure which is modelled as a plane frame structure. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||