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.

Representative volumes and multi-scale modelling of quasi-brittle materials

Abstract: Several different approaches are available in order to describe material behaviour. Considering material on the higher (macro) level of observation constitutes the macroscopic approach. However, the key to understand a macro materials behaviour lies in its mesostructure. As such the mesoscopic approach can be used which is based on the detailed material description of the lower (meso) observational level. The main focus of this dissertation is the combination of the two above techniques -- the multi-scale approach. The idea is, by means of a hierarchical multi-scale procedure, to bring the homogenised information of the detailed mesostructural description to the macro-level in the form of effective properties. Thus, the homogeneous macrostructural behaviour is driven by the heterogeneous mesostructure. Traditionally, the size of a Representative Volume Element (RVE) of the material on the meso-level is chosen as a model parameter within the multi-scale framework. Two questions arise: what should this size be and how stable is this multi-scale model based on an RVE? As an answer to the first question, a unique procedure to determine the RVE size is proposed in the dissertation. An extensive study of this size sensitivity to different test and material parameters, both deterministic and stochastic, has been discussed. With knowledge of the RVE size, the multi-scale procedure can be introduced, in which the meso-level RVE plays the role of a macro-level length-scale parameter. However, the answer to the second question is not always positive. As an example the material behaviour due to mechanical loading can be considered. Although the results are stable and reliable in the linear-elastic and hardening regimes, the picture changes in softening. This is caused by the material developing strain localisation and as a consequence losing its statistical homogeneity. For such a material a Representative Volume cannot be found and as an inference cannot be used in the multi-scale framework. A conceptually new so-called coupled-volume multi-scale approach is introduced, based on abandoning the separation of scales principle. This approach does not require an RVE be a model parameter. The idea of the approach is to uniquely link the size of the mesostructural unit cell and element size of the discretised macrostructure. The results of this coupled-volume approach show stable and reliable behaviour in all mechanical regimes.

The Eshelby Tensors in a Finite Spherical Domain—Part II: Applications to Homogenization

Abstract: In this part of the work, the Eshelby tensors of a finite spherical domain are applied to various homogenization procedures estimating the effective material properties of multiphase composites. The Eshelby tensors of a finite domain can capture the boundary effect of a representative volume element as well as the size effect of the different phases. Therefore their application to homogenization does not only improve the accuracy of classical homogenization methods, but also leads to some novel homogenization theories. This paper highlights a few of them: a refined dilute suspension method and a modified Mori-Tanaka method, the exterior eigenstrain method, the dual-eigenstrain method, which is a generalized self-consistency method, a shell model, and new variational bounds depending on the different boundary conditions. To the best of the authors' knowledge, this is the first time that a multishell model is used to evaluate the Hashin-Shtrikman bounds for a multiple phase composite (n≥3), which can distinguish some of the subtleties of different microstructures.

XFEM modeling and homogenization of magnetoactive composites

Abstract: This paper addresses the application of the extended finite element method (XFEM) to the modeling of two-dimensional coupled magneto-mechanical field problems Continuum formulations of the stationary magnetic and the coupled magneto-mechanical boundary problem are outlined, and the corresponding weak forms are derived The XFEM is applied to generate numerical models of a representative volume element, characterizing a magnetoactive composite material Weak discontinuities occurring at material interfaces are modeled numerically by an enriched approximation of the primary field variables In order to reduce the complexity of the representation of curved interfaces, an element local approach is proposed which allows an automated computation of the level set values The composite’s effective behavior and its coupled magneto-mechanical response are computed numerically by a homogenization procedure The scale transition process is based on the energy equivalence condition, which is satisfied by using periodic boundary conditions

Multiscale modeling of the elastic moduli of CNT-reinforced polymers and fitting of efficiency parameters for the use of the extended rule-of-mixtures

Abstract: In this work, a bottom-up multiscale modeling approach is developed to estimate the effective elastic moduli of Carbon NanoTube (CNT)-reinforced polymer composites. The homogenization process comprises two successive steps, including an atomistic-based computational model and a micromechanics approach at the nano- and micro-scales, respectively. Firstly, the atomistic-based finite element model defines a cylindrical Representative Volume Element (RVE) that accounts for a carbon nanotube, the immediately surrounding matrix, and the CNT/polymer interface. The carbon-carbon bonds of the CNT are modeled using Timoshenko beams, whilst three-dimensional solid elements are used for the surrounding matrix. Through the application of four loading conditions, the RVEs are homogenized into transversely isotropic equivalent fibers by equating the associated strain energies. Secondly, the equivalent fibers are employed in a micromechanics approach to estimate the macroscopic response of non-dilute composites. This is performed using both the analytical Mori-Tanaka model and a computational RVE model with a hexagonal packing geometry. A wide spectrum of single- and multi-walled carbon nanotubes are studied, as well as two different polymeric matrices. Furthermore, the so-called efficiency parameters, imperative for the application of the simplified extended rule of mixtures, are characterized by polynomial expressions for practical filler contents. Finally, detailed parametric analyses are also provided to give insight into the sensitivity of the macroscopic response of CNT-reinforced polymer composites to microstructural features such as filler volume fraction, chirality or aspect ratio.