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.

A Quantitative study of minimum sizes of representative volume elements of cubic polycrystals—numerical experiments

Abstract: The concept of representative volume element (RVE) plays a key role in correlating the properties of microscopically heterogeneous materials with those of their macroscopically homogenized ones. However, up to now little quantitative knowledge is available about RVE scales or sizes of various engineering materials, which have been becoming a necessity due to the rapid development of, for instance, microelectromechanical systems. A new and convenient definition of the minimum RVE size is introduced. Then more than 500 kinds of cubic polycrystalline material in the planar stress state are numerically tested. The major finding from these numerical experiments is that the RVE size for the effective shear modulus (as well as the Young's modulus) depends roughly linearly upon the anisotropy degree of the single crystal, while the effective area modulus does not. For the latter observation a theoretical proof is also given. With a maximum relative error 5%, all the materials tested (with one exception) have a minimal RVE size of 20 or less times as large as the grain size.

Micromechanical study of thermoelastic behavior of composites with periodic fiber waviness

Abstract: A finite element-based micromechanical modeling for fibrous materials is introduced for investigation of thermoelastic behavior of continuous fiber composites with fiber waviness. A periodic unit cell based on hexagonal fiber packing is assumed as a representative volume element. The orthotropic stiffness and thermal expansion parameters of the wavy fiber material are predicted by volume averaging stresses and strains. The thermal residual stresses generated per unit temperature change are studied in detail by volume averaging over slices (sub-volumes) of the representative volume element along the wavelength of the fiber, and also, within the fiber and the matrix individually. The sub-volume averaging scheme exposes the variation of the internal stresses and strains within the representative volume. It is shown that fiber waviness has a moderate impact on coefficients of thermal expansion, and the associated thermal (internal) stresses are generally little changed from those of a straight fiber material.

The Representative Volume Size in Static and Dynamic Micro-Macro Transitions

Abstract: Two homogenisation schemes (first-order or local, and second-order or non-local) are employed in this paper. In case second-order homogenisation is applied, it turns out that elastic behaviour at the micro-scale implies the appearance of second-order space and time derivatives of macroscopic strain in an otherwise elastic constitutive equation for the macroscopic stress. The coefficients of the second-order terms scale with the size of the Representative Volume Element (RVE) employed in the homogenisation scheme.