Showing papers on "Representative elementary volume published in 2014"

A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media

Abstract: SUMMARY A hierarchical multiscale framework is proposed to model the mechanical behaviour of granular media. The framework employs a rigorous hierarchical coupling between the FEM and the discrete element method (DEM). To solve a BVP, the FEM is used to discretise the macroscopic geometric domain into an FEM mesh. A DEM assembly with memory of its loading history is embedded at each Gauss integration point of the mesh to serve as the representative volume element (RVE). The DEM assembly receives the global deformation at its Gauss point from the FEM as input boundary conditions and is solved to derive the required constitutive relation at the specific material point to advance the FEM computation. The DEM computation employs simple physically based contact laws in conjunction with Coulomb's friction for interparticle contacts to capture the loading-history dependence and highly nonlinear dissipative response of a granular material. The hierarchical scheme helps to avoid the phenomenological assumptions on constitutive relation in conventional continuum modelling and retains the computational efficiency of FEM in solving large-scale BVPs. The hierarchical structure also makes it ideal for distributed parallel computing to fully unleash its predictive power. Importantly, the framework offers rich information on the particle level with direct link to the macroscopic material response, which helps to shed lights on cross-scale understanding of granular media. The developed framework is first benchmarked by a simulation of single-element drained test and is then applied to the predictions of strain localisation for sand subject to monotonic biaxial compression, as well as the liquefaction and cyclic mobility of sand in cyclic simple shear tests. It is demonstrated that the proposed method may reproduce interesting experimental observations that are otherwise difficult to be captured by conventional FEM or pure DEM simulations, such as the inception of shear band under smooth symmetric boundary conditions, non-coaxial granular response, large dilation and rotation at the edges of shear band and critical state reached within the shear band. Copyright © 2014 John Wiley & Sons, Ltd.

A numerical two-scale homogenization scheme: the FE 2 -method

Abstract: A wide class of micro-heterogeneous materials is designed to satisfy the advanced challenges of modern materials occurring in a variety of technical applications The effective macroscopic properties of such materials are governed by the complex interaction of the individual constituents of the associated microstructure A sufficient macroscopic phenomenological description of these materials up to a certain order of accuracy can be very complicated or even impossible On the contrary, a whole resolution of the fine scale for the macroscopic boundary value problem by means of a classical discretization technique seems to be too elaborate

Mechanical properties of hybrid composites using finite element method based micromechanics

Abstract: A micromechanical analysis of the representative volume element of a unidirectional hybrid composite is performed using finite element method. The fibers are assumed to be circular and packed in a hexagonal array. The effects of volume fractions of the two different fibers used and also their relative locations within the unit cell are studied. Analytical results are obtained for all the elastic constants. Modified Halpin–Tsai equations are proposed for predicting the transverse and shear moduli of hybrid composites. Variability in mechanical properties due to different locations of the two fibers for the same volume fractions was studied. It is found that the variability in elastic constants and longitudinal strength properties was negligible. However, there was significant variability in the transverse strength properties. The results for hybrid composites are compared with single fiber composites.

Non linear constitutive models for lattice materials

Abstract: We use a computational homogenisation approach to derive a non linear constitutive model for lattice materials. A representative volume element (RVE) of the lattice is modelled by means of discrete structural elements, and macroscopic stress–strain relationships are numerically evaluated after applying appropriate periodic boundary conditions to the RVE. The influence of the choice of the RVE on the predictions of the model is discussed. The model has been used for the analysis of the hexagonal and the triangulated lattices subjected to large strains. The fidelity of the model has been demonstrated by analysing a plate with a central hole under prescribed in plane compressive and tensile loads, and then comparing the results from the discrete and the homogenised models.

FEM × DEM modelling of cohesive granular materials: Numerical homogenisation and multi-scale simulations

Abstract: The article presents a multi-scale modelling approach of cohesive granular materials, its numerical implementation and its results. At microscopic level, Discrete Element Method (DEM) is used to model dense grains packing. At the macroscopic level, the numerical solution is obtained by a Finite Element Method (FEM). In order to bridge the micro- and macro-scales, the concept of Representative Elementary Volume (REV) is applied, in which the average REV stress and the consistent tangent operators are obtained in each macroscopic integration point as the results of DEM’s simulation. In this way, the numerical constitutive law is determined through the detailed modelling of the microstructure, taking into account the nature of granular materials. We first elaborate the principle of the computation homogenisation (FEM × DEM), then demonstrate the features of our multiscale computation in terms of a biaxial compression test. Macroscopic strain location is observed and discussed.

Representative elementary volume assessment of three-dimensional x-ray microtomography images of heterogeneous materials: application to limestones.

Abstract: Over the last 15 years, x-ray microtomography has become a useful technique to obtain morphological, structural, and topological information on materials. Moreover, these three-dimensional (3D) images can be used as input data to assess certain properties (e.g., permeability) or to simulate phenomena (e.g., transfer properties). In order to capture all the features of interest, high spatial resolution is required. This involves imaging small samples, raising the question of the representativity of the data sets. In this article, we (i) present a methodology to analyze the microstructural properties of complex porous media from 3D images, (ii) assess statistical representative elementary volumes (REVs) for such materials; and (iii) establish criteria to delimit these REVs. In the context of cultural heritage conservation, a statistical study was done on 30 quarry samples for three sorts of stones. We first present the principles of x-ray microtomography experiments and emphasize the care that must be taken in the 3D image segmentation steps. Results show that statistical REVs exist for these media and are reached for the image sizes studied (1300×1300×1000 voxels) for two characteristics: porosity and chord length distributions. Furthermore, the estimators used (porosity, autocorrelation function, and chord length distributions) are sufficiently sensitive to quantitatively distinguish these three porous media from each other. Lastly, this study puts forward criteria based on the above-mentioned estimators to evaluate the REVs. These criteria avoid having to repeat the statistical study for each new material studied. This is particularly relevant to quantitatively monitor the modifications in materials (weathering, deformation . . . ) or to determine the smallest 3D volume for simulation in order to reduce computing time.

Representative elementary volumes for 3D modeling of mass transport in cementitious materials

Abstract: Representative elementary volumes (REV) are of major importance for modeling the transport properties of multi-scale porous materials. REVs can be used to schematize heterogeneous microstructures and form the basis of a numerical analysis. In this paper, the most appropriate REV size for numerical modeling for mass transport in hydrating cement paste is investigated. Numerous series (264) of virtual three-dimensional (3D) microstructures with different porosities and pore morphologies were generated using Hymostruc, a numerical simulation model for cement hydration and microstructure development. The influence of the initial particle size distribution, hydration evolution, numerical resolution and type of transport boundary conditions (periodic versus non-periodic) was investigated. The effective diffusivity was obtained by using a 3D finite difference scheme. The connectivity, dead-end porosity, tortuosity and constrictivity of the capillary pore network was evaluated. Based on a statistical chi-square analysis, it was concluded that the REV size largely depends on the complexity of the pore morphology, which in its turn, primarily depends on the degree of cement hydration, i.e. the porosity of the simulated microstructure, the employed numerical resolution as well as on the initial particle size distribution of the unhydrated cement grains. Furthermore, the results proved that employing periodic boundary conditions can effectively decrease the variability of the calculated effective properties and, thus, lower the size of an REV.

Investigation of stress transfer in carbon nanotube reinforced composites using a multi-scale finite element approach

Abstract: This paper describes a micromechanical hybrid finite element approach to study the stress transfer in single-walled carbon nanotube reinforced composites A three-dimensional representative volume element of composite has been considered in this analysis The nanotube is modeled taking into account its atomistic microstructure The matrix material is modeled as continuum utilizing appropriate solid finite elements Spring-based elements are used to describe the behavior of the single-walled carbon nanotubes The interfacial effects between the two materials are simulated by appropriate stiffness variations defining a heterogeneous region The model presents a reasonable behavior, with respect to composite effective mechanical properties, comparing with results available in the literature The effects of carbon nanotube volume fraction, interfacial stiffness and elastic modulus of matrix on stresses are analyzed in details