scholarly journals From representative volume element of interacting particles to the extraction of their effective properties

2021 ◽  
Author(s):  
Timothée Guerra ◽  
Domingos De Sousa Meneses ◽  
Olivier Rozenbaum ◽  
Cédric Blanchard
Keyword(s):  
Representative Volume Element ◽  
Effective Properties ◽  
Volume Element ◽  
Interacting Particles ◽  
Representative Volume

On the size of representative volume element for Darcy law in random media

2006 ◽  
Vol 462 (2074) ◽  
pp. 2949-2963 ◽  
Author(s):  
X Du ◽  
M Ostoja-Starzewski
Keyword(s):  
Representative Volume Element ◽  
Random Media ◽  
Effective Properties ◽  
Finite Size ◽  
Hard Core ◽  
Volume Element ◽  
Dirichlet Boundary Conditions ◽  
Darcy Law ◽  
Representative Volume ◽  
Micro Channels

Most studies of effective properties of random heterogeneous materials are based on the assumption of the existence of a representative volume element (RVE), without quantitatively specifying its size L relative to that of the micro-heterogeneity d . In this paper, we study the finite-size scaling trend to RVE of the Darcy law for Stokesian flow in random porous media, without invoking any periodic structure assumptions, but only assuming the microstructure's statistics to be spatially homogeneous and ergodic. By analogy to the existing methodology in thermomechanics of random materials, we first formulate a Hill–Mandel condition for the Darcy flow velocity and pressure gradient fields. This dictates uniform Neumann and Dirichlet boundary conditions, which, with the help of two variational principles, lead to scale-dependent hierarchies on effective (RVE level) permeability. To quantitatively assess the scaling trend towards the RVE, these hierarchies are computed for various porosities of random disc systems, where the disc centres are generated by a planar hard-core Poisson point field. Overall, it turns out that the higher is the density of random discs—or, equivalently, the narrower are the micro-channels in the system—the smaller is the size of RVE pertaining to the Darcy law.

scholarly journals Representative volume element based micromechanical modelling of rod shaped glass filled epoxy composites

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Aanchna Sharma ◽  
Yashwant Munde ◽  
Vinod Kushvaha
Keyword(s):  
Representative Volume Element ◽  
Poisson’S Ratio ◽  
Volume Fraction ◽  
Tensile Modulus ◽  
Volume Element ◽  
Poisson's Ratio ◽  
Epoxy Composites ◽  
Micromechanical Modeling ◽  
Representative Volume ◽  
Shaped Glass

AbstractIn this study, Representative Volume Element based micromechanical modeling technique has been implemented to assess the mechanical properties of glass filled epoxy composites. Rod shaped glass fillers having an aspect ratio of 80 were used for preparing the epoxy composite. The three-dimensional unit cell model of representative volume element was prepared with finite element analysis tool ANSYS 19 using the periodic square and hexagonal array with an assumption that there is a perfect bonding between the filler and the epoxy matrix. Results revealed that the tensile modulus increases and Poisson’s ratio decreases with increase in the volume fraction of the filler. To study the effect of filler volume fraction, the pulse echo techniques were used to experimentally measure the tensile modulus and Poisson’s ratio for 5% to 15% volume fraction of the filler. A good agreement was found between the RVE based predicted values and the experimental results.

Localization simulation of forming-induced residual stresses of composite using prescribed boundary

2021 ◽  
pp. 073168442094118
Author(s):  
Qi Wu ◽  
Hongzhou Zhai ◽  
Nobuhiro Yoshikawa ◽  
Tomotaka Ogasawara ◽  
Naoki Morita
Keyword(s):  
Residual Stresses ◽  
Representative Volume Element ◽  
Computational Cost ◽  
Volume Element ◽  
Thermoplastic Composite ◽  
Structural Deformation ◽  
Element Analysis ◽  
Micro Scale ◽  
Representative Volume ◽  
Localization Approach

A novel localization approach that seamlessly bridges the macro- and micro-scale models is proposed and used to model the forming-induced residual stresses within a representative volume element of a fiber reinforced composite. The approach uses a prescribed boundary that is theoretically deduced by integrating the asymptotic expansion of a composite and the equal strain transfer, thus rendering the simulation setting to be easier than conventional approaches. When the localization approach is used for the finite element analysis, the temperature and residual stresses within an ideal cubic representative volume element are precisely simulated, given a sandwiched thermoplastic composite is formed under one-side cooling condition. The simulation results, after being validated, show that the temperature gradient has an impact on the local residual stresses, especially on the in-plane normal stress transverse to the fiber, and consequently, influences the structural deformation. This newly designed localization approach demonstrates the advantages of enhanced precision and reduced computational cost owing to the fast modeling of the finely meshed representative volume element. This is beneficial for a detailed understanding of the actual residual stresses at the micro-scale.

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