Representative elementary volume

About: Representative elementary volume is a research topic. Over the lifetime, 4105 publications have been published within this topic receiving 86863 citations.

Visco-Elastic Waves in Rock-Like Composites

Abstract: The subject of this paper is the treatment of rocks - and, especially, fluid-saturated and partially saturated reservoir rocks, as composite visco-elastic media. By this we mean to study and partially answer the question of how the effective material (frequency-dependent and complex-valued stiffness/density) parameters can be estimated from a knowledge of the constituents of the rocks, their volume fractions, the statistical distribution of sizes, shapes, orientations and positions of the individual particles (minerals of quartz, clay, etc.) and cavities (pores, cracks, etc.); in addition to parameters related to the fluid and its ability to flow, at the scale of the microstructure as well as that of the wavelength (assumed to be long compared to the scale-size of the microstructure). Our approach is to develop and combine a theory of stochastic waves with established results for the micromechanics of defects in solids, as well as state-of-the-art models of wave-induced fluid flow. Specifically, we first derive an exact formal expression for the effective material parameters in terms of a dynamic T-matrix for the material, which satisfies a single integral equation of the Lippmann-Schwinger type (known from quantum scattering theory), but formulated in an abstract vector space, associated with the combination of the strain and velocity fields into a more general state vector Ψ. Inclusions-based models are developed on the basis of standard many-body techniques, known from the static T-matrix approach as well as nuclear collision theory. The t-matrix of a low-aspect-ratio spheroidal crack is expressed in terms of the familiar displacement discontinuity parameters of Hudson, via the so-called K-tensor, which is of interest in itself, for example, when connecting cracks to pores (in the presence of multiple solid constituents) on the basis of an expression for the t-matrix of a communicating cavity. The present theory can in principle be used beyond the Rayleigh limit, but explicit estimates of the effective material parameters have so far been derived only under the assumption that (scattering attenuation can be ignored) the wavelength is large compared to the scale-size of a representative volume element. Starting with the dynamic equations of motion, we show that the behaviour of the mean wave in the Rayleigh limit is indeed determined by the effective stiffness tensor associated with a static theory of composites, in conjunction with the spatially averaged density for the heterogeneous material as a whole. Thus, we have provided justification to the procedure we used in a series of related papers, where we started out with the static equilibrium condition and employed the elastic/visco-elastic correspondence principle. Numerical examples (dealing with the effects of randomly oriented cracks on the isotropic velocity and attenuation spectra of a dual porosity model of clay-sand mixtures, and the effects of spatial distribution on the anisotropic attenuation spectra of fully aligned cracks that are partially saturated with two different fluids) will be provided in order to complement those in our earlier papers.

Fast statistical homogenization procedure (FSHP) for particle random composites using virtual element method

Abstract: Mechanical behaviour of particle composite materials is growing of interest to engineering applications. A computational homogenization procedure in conjunction with a statistical approach have been successfully adopted for the definition of the representative volume element (RVE) size, that in random media is an unknown of the problem, and of the related equivalent elastic moduli. Drawback of such a statistical approach to homogenization is the high computational cost, which prevents the possibility to perform series of parametric analyses. In this work, we propose a so-called fast statistical homogenization procedure (FSHP) developed within an integrated framework that automates all the steps to perform. Furthermore within the FSHP, we adopt the numerical framework of the virtual element method for numerical simulations to reduce the computational burden. The computational strategies and the discretization adopted allow us to efficiently solve the series (hundreds) of simulations and to rapidly converge to the RVE size detection.

Size-dependent optimal microstructure design based on couple-stress theory

Abstract: The purpose of this paper is to propose a size-dependent topology optimization formulation of periodic cellular material microstructures, based on the effective couple-stress continuum model. The present formulation consists of finding the optimal layout of material that minimizes the mean compliance of the macrostructure subject to the constraint of permitted material volume fraction. We determine the effective macroscopic couple-stress constitutive constants by analyzing a unit cell with specified boundary conditions with the representative volume element (RVE) method, based on equivalence of strain energy. The computational model is established by the finite element (FE) method, and the design density and FE stiffness of the RVE are related by the solid isotropic material with penalization power (SIMP) law. The required sensitivity formulation for gradient-based optimization algorithm is also derived. Numerical examples demonstrate that this present formulation can express the size effect during the optimization procedure and provide precise topologies without increase in computational cost.