Home About us Contact
|
Home About us Contact | ||
|
|
||
Representative Volume Element (representative + volume_element)
Selected AbstractsMicrostructure and Transport Properties of Cellular Materials: Representative Volume ElementADVANCED ENGINEERING MATERIALS, Issue 10 2009Emmanuel Brun The representative volume element (RVE) plays a central role in efforts to predict the effective thermo-physical and transport properties of heterogeneous materials. A quantitative definition of its size is proposed in this work. It is shown that RVE depends on the morphological or physical property being investigated. The methodology is applied to real samples of open-celled materials (such as metallic foam) whose structure is obtained from X-Ray microtomography. [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] A new Cosserat-like constitutive model for bedded salt rocksINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2009Yin-Ping Li Abstract Salt rocks are commonly used as geologic host rocks for storage of gas and crude oil, and are being considered for the disposal of radioactive waste. Different from the salt rock domes in many countries, the salt rock formations in China are usually laminar with many alternating layers, i.e. rock salt, anhydrite, and/or mudstone. Considering the unique stratigraphic characteristics of these salt rocks, a new Cosserat-like medium constitutive model is proposed in order to facilitate efficient modeling of the mechanical behavior of these formations. In this model, a new representative volume element, containing two different layers, is employed to simulate the compatibility of the meso-displacement between two different layers and also the bending effect. A new method for the deformation and failure analysis of bedded salt rocks is derived therefrom. Having the macro-average stresses, the conventional stresses in the different layers can be obtained in sequence. The conventional stresses can then be utilized in a routine way for the strength and failure analysis. For the initial numerical modeling, the new Cosserat-like medium is reduced to a transversely isotropic one. The simplified constitutive model for layered media is then implemented into FLAC3D codes. A test sample validates that the results by using the numerical model are in good agreement with that by using the built-in model, and the mesh size for the new model is reduced greatly. Finally, an application for the stability of oil storage caverns in deep thinly bedded salt rocks is carried out. The effects on convergence of storage caverns and on the failure of surrounding rock due to the presence of the mudstone interlayers (hard phase) are discussed in detail. Copyright © 2009 John Wiley & Sons, Ltd. [source] Does a representative volume element exist for fatigue life prediction?INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2008The case of aggregate composites Abstract In a previous work, discrete modeling and a statistical approach were used to quantify the minimal representative volume element (RVE) size for aggregate composites, such as bituminous materials in the linear elastic regime (Comput. Mater. Sci. 2005; 33:467,490). In this paper, the discrete model is extended to strain-softening behavior under cyclic loading. The existence of a RVE for fatigue life prediction is numerically proved and its minimal size is determined. It is found that it is much larger than the minimal RVE size in the elastic regime. Copyright © 2007 John Wiley & Sons, Ltd. [source] Localized failure of fibre-reinforced elastic,plastic materials subjected to plane strain loadingINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2007Dunja Peri Abstract We consider discontinuous bifurcations as the indicator of a localized failure for a class of composites that are characterized by elastic fibres reinforcing an elastic,plastic matrix. A macroscopic tangent stiffness tensor for the fibre-reinforced composite is developed by consistently homogenizing the contribution of fibres in a spherical representative volume element. Analytical solutions are derived for the critical hardening modulus and corresponding bifurcation directions for the case of plane strain loading. Properties of the solutions are further illustrated on the example of the non-associated Drucker,Prager model at onset of yielding. Results show that presence of fibres decreases the critical hardening modulus, thus inhibiting the onset of strain localization. The rate of decrease in the critical hardening modulus is the highest for pure shear, followed by uniaxial tension, uniaxial compression, biaxial tension and biaxial compression. The main fibre parameters that control the onset of strain localization are their volumetric content and their stiffness modulus whereby very stiff fibres can produce the most significant decrease in the critical hardening modulus, especially for the state of biaxial tension. The critical hardening modulus for the non-associated Drucker,Prager model exhibits a full range of localization modes including compaction bands, dilation bands, and transition in the form of shear bands regardless of the presence of fibres. Presence of fibres affects bifurcation directions, except in the case when Poisson's ratio of the matrix is equal to 0.25. The results demonstrate stabilizing effects of fibres by which they provide the control against the onset of strain localization. Copyright © 2006 John Wiley & Sons, Ltd. [source] A micromechanical approach to the strength criterion of Drucker-Prager materials reinforced by rigid inclusionsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7-8 2004Jean-François Barthélémy Abstract At the microscopic scale, concrete can be considered as a frictional matrix (cement paste) surrounding rigid inclusions (aggregate or sand inclusions). The present paper proposes a theoretical approach to the strength criterion of such a composite material. It is shown that the macroscopic stress states on the yield surface can be obtained from the solution to non-linear viscous problems defined on a representative volume element. The practical determination of the yield surface implements a non-linear homogenization scheme based on the modified secant method. The role of the interface between the matrix and the inclusions is also investigated. Two extreme modellings are considered: perfect bonding and non-frictional interfaces. In both cases, the method yields a macroscopic strength criterion of the Drucker,Prager type. The macroscopic friction angle is a function of that of the matrix and of the volume fraction of the inclusions. In the case of perfect bonding, the inclusions have a reinforcing effect. In contrast, this may not be true for a non-frictional interface. Copyright © 2004 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] Finite element formulation for modelling large deformations in elasto-viscoplastic polycrystalsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004Karel Matou Abstract Anisotropic, elasto-viscoplastic behaviour in polycrystalline materials is modelled using a new, updated Lagrangian formulation based on a three-field form of the Hu-Washizu variational principle to create a stable finite element method in the context of nearly incompressible behaviour. The meso-scale is characterized by a representative volume element, which contains grains governed by single crystal behaviour. A new, fully implicit, two-level, backward Euler integration scheme together with an efficient finite element formulation, including consistent linearization, is presented. The proposed finite element model is capable of predicting non-homogeneous meso-fields, which, for example, may impact subsequent recrystallization. Finally, simple deformations involving an aluminium alloy are considered in order to demonstrate the algorithm. Copyright © 2004 John Wiley & Sons, Ltd. [source] A numerical method for computing the response of composites with periodic microstructurePROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Sven Kassbohm Dipl.-Ing. The stress-strain response of a periodic structure due to an applied eigenstrain field is investigated. The periodic structure allows reduction of the problem to a representative volume element (RVE) problem. A review of Fourier series as a particular method of solving the set of differential equations is given, and an example problem is studied. Results of the latter method are compared to results obtained using discrete Fourier transforms in a different way. [source] Computational homogenization of uncoupled consolidation in micro-heterogeneous porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2010Fredrik Larsson Abstract Variationally consistent homogenization is exploited for the analysis of transient uncoupled consolidation in micro-heterogeneous porous solids, whereby the classical approach of first-order homogenization for stationary problems is extended to transient problems. Homogenization is then carried out in the spatial domain on representative volume elements (RVE), which are introduced in quadrature points in standard fashion. Along with the classical averages, a higher-order conservation quantity is obtained. An iterative FE2 -algorithm is devised for the case of nonlinear permeability and storage coefficients, and it is applied to pore pressure changes in asphalt-concrete (particle composite). Various parametric studies are carried out, in particular, with respect to the influence of the ,substructure length scale' that is represented by the size of the RVE's. Copyright © 2009 John Wiley & Sons, Ltd. [source] Cracking risk of partially saturated porous media,Part I: Microporoelasticity modelINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2010Bernhard Pichler Abstract Drying of deformable porous media results in their shrinkage, and it may cause cracking provided that shrinkage deformations are hindered by kinematic constraints. This is the motivation to develop a thermodynamics-based microporoelasticity model for the assessment of cracking risk in partially saturated porous geomaterials. The study refers to 3D representative volume elements of porous media, including a two-scale double-porosity material with a pore network comprising (at the mesoscale) 3D mesocracks in the form of oblate spheroids, and (at the microscale) spherical micropores of different sizes. Surface tensions prevailing in all interfaces between solid, liquid, and gaseous matters are taken into account. To establish a thermodynamics-based crack propagation criterion for a two-scale double-porosity material, the potential energy of the solid is derived, accounting,in particular,for mesocrack geometry changes (main original contribution) and for effective micropore pressures, which depend (due to surface tensions) on the pore radius. Differentiating the potential energy with respect to crack density parameter yields the thermodynamical driving force for crack propagation, which is shown to be governed by an effective macrostrain. It is found that drying-related stresses in partially saturated mesocracks reduce the cracking risk. The drying-related effective underpressures in spherical micropores, in turn, result in a tensile eigenstress of the matrix in which the mesocracks are embedded. This way, micropores increase the mesocracking risk. Model application to the assessment of cracking risk during drying of argillite is the topic of the companion paper (Part II). Copyright © 2009 John Wiley & Sons, Ltd. [source] Variationally consistent computational homogenization of transient heat flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Fredrik Larsson Abstract A framework for variationally consistent homogenization, combined with a generalized macro-homogeneity condition, is exploited for the analysis of non-linear transient heat conduction. Within this framework the classical approach of (model-based) first-order homogenization for stationary problems is extended to transient problems. Homogenization is then carried out in the spatial domain on representative volume elements (RVE), which are (in practice) introduced in quadrature points in standard fashion. Along with the classical averages, a higher order conservation quantity is obtained. An iterative FE2 -algorithm is devised for the case of non-linear diffusion and storage coefficients, and it is applied to transient heat conduction in a strongly heterogeneous particle composite. Parametric studies are carried out, in particular with respect to the influence of the ,internal length' associated with the second-order conservation quantity. Copyright © 2009 John Wiley & Sons, Ltd. [source] | ||||||||||