Showing papers on "Representative elementary volume published in 2004"

Lattice‐Boltzmann simulation of two‐phase flow in porous media

Abstract: [1] We simulate two-fluid-phase flow at the pore scale using a lattice Boltzmann (LB) approach. Using a parallel processing version of the Shan-Chen model that we developed, we simulate a set of ideal two-fluid systems and a model two-fluid-phase porous medium system comprised of a synthetic packing with a relatively uniform distribution of spheres. We use the set of ideal two-phase systems to validate the approach and provide parameter information, which we then use to simulate a sphere-pack system. The sphere-pack system is designed to mimic laboratory experiments conducted to evaluate the hysteretic capillary pressure saturation relation for a system consisting of water, tetrachloroethylene, and a glass bead porous medium. Good agreement is achieved between the measured hysteretic capillary pressure saturation relations and the LB simulations when comparing entry pressure, displacement slopes, irreducible saturation, and residual entrapment. Our results further show that while qualitatively similar results are obtained when comparing systems consisting of 1200 spheres and 150 spheres, there is a significant difference between these two levels, suggesting a lower bound on the size of a representative elementary volume.

Determining the equivalent permeability tensor for fractured rock masses using a stochastic REV approach: Method and application to the field data from Sellafield, UK

Abstract: A numerical procedure to determine the equivalent permeability tensor of a fractured rock is presented, using a stochastic REV (Representative Elementary Volume) concept that uses multiple realizat ...

Constitutive equations for ionic transport in porous shales

Abstract: [1] The constitutive coupled equations describing ionic transport in a porous shale are obtained at the scale of a representative elementary volume by volume averaging the local Nernst-Planck and Stokes equations. The final relationships check the Onsager reciprocity to the first order of perturbation of the state variables with respect to the thermostatic state. This state is characterized by a modified version of the Donnan equilibrium model, which accounts for the partition of the counterions between the Stern and diffuse Gouy-Chapman layers. After upscaling the local equations the material properties entering the macroscopic constitutive equations are explicitly related to the porosity of the shale, its cation exchange capacity, and some textural properties such as the electrical cementation exponent entering Archie's law. This new model is then applied to predict the salt filtering and electrodiffusion efficiencies of a shale layer.

Size of a representative volume element in a second-order computational homogenization framework

Abstract: In this paper the intrinsic role of the size of the microstructural representative volume element (RVE) in a second-order computational homogenization is investigated. The presented second-order computational homogenization is an extension of the classical first-order computational homogenization scheme and is based on a proper incorporation of the macroscopic gradient of the deformation tensor and the associated higher-order stress measure into the multiscale framework. The macroscopic homogenized continuum obtained through this scheme is the full second gradient continuum. It is demonstrated with several examples that the size of the microstructural RVE used in a second-order computational homogenization scheme may be related to the length scale of the associated macroscopic homogenized higher-order continuum. It is shown that the analytical second-order homogenization of a microstructurally homogeneous linearly elastic material leads to the second gradient elastic Mindlin’s continuum on the macroscale, where the resulting macroscopic length scale parameter is proportional to the RVE size. Several numerical microstructural and multiscale analyses reveal the significance of the contribution of the physical and geometrical nonlinearities in the relation between the RVE size and the calculated macroscopic response. Based on the obtained results, some conclusions are drawn with respect to the choice of the microstructural RVE in the second-order computational homogenization analysis.

Failure mechanisms in twill-weave laminates: FEM predictions vs. experiments

Abstract: The mechanics of woven fabric-based laminated composites is complex, but computational models can contribute to its enhanced understanding. In this work the architecture of a twill-weave graphite epoxy laminate was characterized experimentally by microscopy of polished sections. The mechanical response under tensile loading was then investigated and a microscopic assessement of the failure mechanisms was conducted. The finite element approach was used to predict stiffness and strength using a suitable representative volume element from the twill-weave laminate. The role of texture and crimp ratio on the macroscopic stiffness and strength was investigated. Progressive failure was simulated numerically and stress distributions in the model were correlated with observed damage mechanisms.

A micromechanical approach to the strength criterion of Drucker‐Prager materials reinforced by rigid inclusions

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

Finite element formulation for modelling large deformations in elasto-viscoplastic polycrystals

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 finiteelement 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.

A theory for plastic-bonded materials with a bimodal size distribution of filler particles

Abstract: Plastic-bonded materials are composites consisting of grains of filler material embedded in a polymeric matrix. A micromechanics model is proposed for investigating the mechanical behaviour of plastic-bonded materials having two disparate grain sizes. A hybrid theory is proposed to handle some aspects of the bimodal grain size distribution. Our model uses the first-order method of cells with an eight-cell representative volume element where one of the eight cells contains a large grain and the seven remaining cells contain a mixture of small grains embedded in the polymeric binder material. A Mori–Tanaka-based analysis is used to describe the small grain-binder mechanical response. The small grains in this analysis are assumed to be spherical and uniformly distributed in the binder. In this work, we use the explosive PBX 9501, in its unreacted state, as our test system. The explosive grain particle size distribution of PBX 9501 consists of two broad peaks centred at approximately 1 and 200 µm. The constitutive behaviour of the large explosive grains are assumed to be elastic-plastic and damage by way of micro-crack brittle fracture. Only linear elasticity of the small grains is considered. The rate and temperature dependence of the mechanical response of the polymer binder is accounted for by a generalized Maxwell viscoelasticity model. The theoretical uniaxial stress–strain response for PBX 9501 is reported for quasi-static and split Hopkinson pressure bar loading rates and compared to experimental measurements.

A micromechanics-based nonlocal constitutive equation for elastic composites containing randomly oriented spheroidal heterogeneities

Abstract: A micromechanics-based nonlocal constitutive equation relating the ensemble averages of stress and strain for a matrix containing a random distribution of randomly oriented spheroidal voids or inclusions is derived. The analysis employs J.R. Willis’ generalization of the Hashin–Shtrikman variational formulation to random linear elastic composite materials and builds on that of Drugan and Willis (J. Mech. Phys. Solids 44 (1996) 497) and Drugan (J. Mech. Phys. Solids 48 (2000) 1359), who derived completely explicit results for the case of isotropic, nonoverlapping identical spherical inclusions/voids. The model of impenetrable particles employed consists of identical particles with fixed spheroidal shape and random orientation. To facilitate a manageable statistical description, the spheroids are placed within concentric hard “security” spheres. The paper derives three main new results: (i) it is proved within the assumptions just outlined that the effects of inclusion shape and their spatial distribution are separable, for arbitrary inclusion shape (not just spheroids) and arbitrary spatial (statistical) distribution of their security spheres when employing up through two-point statistical information; (ii) closed-form analytical results are obtained from the Verlet–Weis improvement of the Percus–Yevick–Wertheim statistical model of a random distribution of nonoverlapping spherical particles/voids, leading to substantial improvements at higher inclusion/void volume fractions in the nonlocal constitutive equations of Drugan and Willis (1996) and Drugan (2000); (iii) approximate analytical nonlocal constitutive equations are derived for composites consisting of a matrix containing randomly oriented oblate or prolate spheroidal inclusions/voids, using the Verlet–Weis statistical model for the security sphere distribution. Among the specific implications of these new results, it is found that the minimum representative volume element (RVE) size estimate for composites containing spherical inclusions/voids using the Verlet–Weis improvement is significantly larger at higher inclusion/void volume fractions (≈0.3–0.64) than the estimates of Drugan and Willis (1996) and Drugan (2000), who used the Percus–Yevick–Wertheim model. Also, deviations in inclusion/void shape from spherical are shown to cause significant modifications to the nonlocal constitutive equations, as evidenced by nontrivial changes in predicted minimum RVE sizes.

Free flow at the interface of porous surfaces: A generalization of the taylor brush configuration

Abstract: A solution to the problem of shallow laminar water flow above a porous surface is essential when modeling phenomena such as erosion, resuspension, and mass transfer between the porous media and the flow above it. Previous studies proposed theoretical, experimental, and numerical insight with no single general solution to the problem. Many studies have used the Brinkman equation, while others showed that it does not represent the actual interface flow conditions. In this paper we show that the interface macroscopic velocity can be accurately modeled by introducing a modification to the Brinkman equation. A moving average approach was proved to be successful when choosing the correct representative elementary volume and comparing the macroscopic solution with the average microscopic flow. As the size of the representative elementary volume was found to be equal to the product of the square root of the permeability and an exponential function of the porosity, a general solution is now available for any brush configuration. Given the properties of the porous media (porosity and permeability), the flow height and its driving force, a complete macroscopic solution of the interface flow is obtained.