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.

Prediction of elastic properties of carbon nanotube reinforced composites

Abstract: In this paper, the macroscopic elastic properties of carbon nanotube reinforced composites are evaluated through analysing the elastic deformation of a representative volume element (RVE) under various loading conditions. This RVE contains three components, i.e. a carbon nanotube, a transition layer between the nanotube and polymer matrix and an outer polymer matrix body. First, based on the force field theory of molecular mechanics and computational structural mechanics, an equivalent beam model is constructed to model the carbon nanotube effectively. The explicit relationships between the material properties of the equivalent beam element and the force constants have been set-up. Second, to describe the interaction between the nanotube and the outer polymer matrix at the level of atoms, the molecular mechanics and molecular dynamics computations have been performed to obtain the thickness and material properties of the transition layer. Moreover, an efficient three-dimensional eight-noded brick finite element is employed to model the transition layer and the outer polymer matrix. The macroscopic behaviours of the RVE can then be evaluated through the traditional finite element method. In the numerical simulations, the influences of various important factors, such as the stiffness of transition layer and geometry of RVE, on the final macroscopic material properties of composites have been investigated in detail.

Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization

Abstract: Formulation of the scale transition equations coupling the microscopic and macroscopic variables in the second-order computational homogenization of heterogeneous materials and the enforcement of generalized boundary conditions for the representative volume element (RVE) are considered. The proposed formulation builds on current approaches by allowing any type of RVE boundary conditions (e.g. displacement, traction, periodic) and arbitrary shapes of RVE to be applied in a unified manner. The formulation offers a useful geometric interpretation for the assumptions associated with the microstructural displacement fluctuation field within the RVE, which is here extended to second-order computational homogenization. A unified approach to the enforcement of the boundary conditions has been undertaken using multiple constraint projection matrices. The results of an illustrative shear layer model problem indicate that the displacement and traction RVE boundary conditions provide the upper and lower bounds of the response determined via second-order computational homogenization, and the solution associated with the periodic RVE boundary conditions lies between them.