Showing papers on "Representative elementary volume published in 1997"

Representative volume element size for elastic composites: A numerical study

Abstract: Monte Carlo (MC) runs are employed to generate statistically independent realizations of a periodic elastic composite with a disordered unit cell made up of 8, 27, and 64 nonoverlapping identical spheres. In the limit of an infinite number of spheres in the disordered unit cell, this periodic composite obeys the Percus-Yevick hard-sphere statistics. By construction, the MC realizations studied have the same inclusion fraction. A constant-strain-tetrahedra displacement-based finite element code with an iterative solver is used to calculate the overall elastic constants of these periodic MC realizations. It appears that the scatter in the individual elastic constants already obtained with a few dozen spheres in the disordered unit cell is remarkably small and the averages obtained with varying numbers of spheres are practically stationary.

Evaluation of the higher-order theory for functionally graded materials via the finite-element method

Abstract: A comparison is presented between the predictions of the finite-element analysis and a recently developed higher-order theory for functionally graded materials subjected to a through-thickness temperature gradient. In contrast to existing micromechanical theories that utilize classical (i.e. uncoupled) homogenization schemes to calculate micro-level and macro-level stress and displacement fields in materials with uniform or nonuniform fibre spacing (i.e. functionally graded materials), the new theory explicitly couples the microstructural details with the macrostructure of the composite. Previous thermo-elastic analysis has demonstrated that such coupling is necessary when: the temperature gradient is large with respect to the dimension of the reinforcement; the characteristic dimension of the reinforcement is large relative to the global dimensions of the composite and the number of reinforcing fibers or inclusions is small. In these circumstances, the standard micromechanical analyses based on the concept of the representative volume element used to determine average or effective properties of macroscopically homogeneous composites produce questionable results. The comparison between the results of the finite-element method and the higher-order theory presented herein establishes the theory's accuracy in predicting thermal and stress fields within composites with a finite number of fibers in the thickness direction subjected to a through-thickness thermal gradient.

Effects of Damage Distribution on Evolution

Abstract: Recent micromechanically inspired phenomenological theories using internal state variable (ISV) representations of damage have been used to predict the thermomechanical behavior of microcracked solids. These models do not, in an explicit manner, account for distributions of microcracks in a representative volume element (RVE) and have been used successfully only to determine the effective moduli of damaged solids. It has been demonstrated that while the distribution and interaction of damage entities within an RVE generally have a minor effect on the effective moduli, it has a significant effect on the evolution of damage and failure at the macroscale. Damage evolution rates, in general, cannot be described adequately by such theories because of their inability to account for interactions between damage entities in an arbitrary distribution. Key issues pertaining to the development of viable damage evolution equations using a continuum damage mechanics approach are addressed. In particular, limitations associated with the use of ISVs that can be expressed either in terms of macroscopically measurable quantities or through a spatial average of the geometric features of individual damage entities are discussed. Numerical simulations of evolving crack systems in two-dimensional perfectly brittle solids indicate that "effective stress" models may have difficulty in characterizing damage evolution in brittle microcracked solids when the damage consists of cracks of variable size or spatial distributions. An argument for implementing ISVs based on higher-order moments of the damage distribution within an RVE is presented.

Macroscopic measure of the rate of deformation produced by micro-shear banding

Abstract: PHYSICAL MODEL of shear strain rate produced by active micro-shear bands in metals is formulated and mathematical idealization of micro-shear bands system by means of the theory of singular surface of order one is proposed. Extension of the known averaging procedure over the representative volume element traversed by a strong discontinuity surface is presented. As a result, the macroscopic measure of velocity gradient produced in the course of elastic-plastic deformation with micro-shear banding is derived. The corresponding macroscopic measures of the rate of deformation and material spin, necessary to formulate constitutive description, are also determined.

Numerical Simulations by Homogenization of Two-Phase Flow Through Randomly Heterogeneous Porous Media

Abstract: We consider the behavior of incompressible two-phase flow in heterogeneous reservoirs with randomly placed heterogeneities; that is, a porous medium with permeability A and porosity Ф which are statistically homogeneous random fields oscillating at the dimensionless scale e. Using the tools of stochastic homogenization we get the nonlinear effective equations which govern the flow behavior in a homogeneous medium being equivalent, in the sense of homogenization theory, to the original one. The computation of the effective permeability tensor A hom is done by solving auxiliary stochastic problems, similar to the ones for the linear one-phase flow case. Under ergodicity assumption, and using the primal and dual formulation of these auxiliary problems, we design a numerical algorithm computing both the effective parameters and the minimal volume on which these effective properties are valid. The validity of our algorithm is tested on a two-phase groundwater flow with injection of one-phase from a well.

Multiple NDE Techniques for the Measurement of Constituent Volume Fractions in Metal Matrix Composites

Abstract: Multiple nondestructive evaluation (NDE) techniques are developed for determining the constituent volume fractions of silicon carbide particulate (SiCp) reinforced aluminum (Al) matrix composites. The composite constituents studied include SiCp reinforcement and intermetallic compounds formed during the processing stage. The proposed techniques employ measurements of ultrasonic velocity and eddy current conductivity, together with theoretical models that relate the effective anisotropic properties of the composites to their microstructures. The SiCp volume fraction is calculated first by coupling the measured velocity with the two-phase (SiCp and Al matrix) model prediction. The intermetallics concentration then is calculated using the three-phase (SiCp, intermetallics and Al matrix) model with the measured conductivity. The methods are shown to be reliable in determining the volume fractions of the reinforcement and the intermetallic phase. The techniques may be adopted in a production unit for the quality assessment of the metal matrix particulate composite extrusions.

Fluorescence imaging techniques: Application to measuring flow and transport in refractive index-matched porous media

Abstract: Publisher Summary This chapter is part of an extensive research in laboratories to understand the nature of the microscopic flow and transport processes within porous media. A novel non-intrusive imaging approach has been used to observe the pore-scale flow and transport behavior at high resolution and high accuracy. This chapter reports on: fluorescent particle tracking velocimetry and concentration imaging techniques, direct experimental evaluation of dispersive fluxes and dispersion coefficients, estimates of representative elementary volume (REV), correlations of velocity and concentration results within the porous medium, and 3-D plots of results to gain insights to the pore-scale flow and transport processes. The overall objective is to use these findings toward gaining an understanding of chemical flow and transport in a porous medium and, as a result, provide the basis for improved modeling of these processes. Traditionally, there have been three different approaches to the modelling of flow and transport in porous media. The first approach is a statistical method treating the porous media as a random structure. The second is a geometrical approach assuming a similar geometry to the porous media under study to solve the conservation equations. The third approach (continuum) is a volume averaging procedure that helps to describe porous medium transport in terms of macroscopic rather than microscopic scale variables. All three approaches result in undetermined parameters that must be evaluated from experiments.

Effective elastic properties of particulate-reinforced compossite materials

Abstract: A numerical approach for determination of the effective properties of particulate composite materials has been developed. A representative volume element (RVE) of the composite material is analyzed with help of the finite-element method. Uniform boundary displacements or tractions are applied on the boundaries of the RVE for introducing the known average strain in the RVE. Local stress and strain distributions in the RVE are calculated using the finite-element method. Different effective elastic constants can be calculated by averaging the local fields corresponding to different sets of boundary conditions. The present approach allows us to determine the effective properties of particle-reinforced composites with acceptable accuracy. The calculated effective properties of the composite are between the upper and lower Hashin—Shtrikman bounds. The results based on the present approach lead to higher stiffness of composites in comparison with analytical approaches.

Microscopic and mesoscopic damage localization

Abstract: Initial defects are the main cause of the failure of structures made of brittle or quasi-brittle materials. The aim of this paper is to model within the framework of continuum damage mechanics these defects and their influence on the mechanical behavior of the structure they lie in by using a strain localization criterion. The microscopic and mesoscopic conditions for localization are studied by utilizing isotropic or anisotropic damage variables. A representative volume element (RVE) containing one defect is defined and the failure criterion of such an RVE is derived. The initial defect is modeled by an initial damage parameter. The evolution law of this damage value depends upon the nature of induced damage. Finally, an extension of this study to the case of high-cycle fatigue is proposed.

A formulation of continuum mechanics as a dimensional reduction of a finite-dimensional dynamical system

Abstract: IN THE PAPER a generalized formulation of the continuum mechanics is suggested. The generalization consists in the assumption that the energy balance equation is not satisfied for all subbodies of a body but only for their chosen family. This formulation leads to fields in the continuum which create a finite-dimensional space. With the help of the chosen family of subbodies, a volume of averaging related to the continuum model is defined. This volume is connected with a more elementary dynamical system which takes part in determination of the form of constitutive equations. In general, the mechanical model of the continuum is seen as a dimensional reduction of the more elementary dynamical system related to another continuum or to a discrete set of material points.