Role of exterior statistics-based boundary conditions for property-based statistically equivalent representative volume elements of polydispersed elastic composites

2018 ◽  
Vol 52 (21) ◽  
pp. 2919-2928 ◽  
Author(s):  
Dhirendra V Kubair ◽  
Maxwell Pinz ◽  
Kaitlin Kollins ◽  
Craig Przybyla ◽  
Somnath Ghosh
Keyword(s):  
Boundary Conditions ◽  
Matrix Composite ◽  
Representative Volume Element ◽  
Polymer Matrix ◽  
Microstructural Characterization ◽  
Experimental Tests ◽  
Volume Element ◽  
Polymer Matrix Composite ◽  
Representative Volume ◽  
Representative Volume Elements

The property-based statistically equivalent RVE or P-SERVE has been introduced in the literature as the smallest microstructural volume element in non-uniform microstructures that has effective material properties equivalent to those of the entire microstructure. An important consideration is the application of appropriate boundary conditions for optimal property-based statistically equivalent representative volume element domains. The exterior statistics-based boundary conditions have been developed, accounting for the statistics of fiber distributions and interactions in the domain exterior to the property-based statistically equivalent representative volume element. This paper is intended to validate the efficacy of the exterior statistics-based boundary condition-based property-based statistically equivalent representative volume elements for evaluating homogenized stiffnesses of a unidirectional polymer matrix composite with a polydispersed microstructure characterized by nonuniform dispersion of carbon fibers of varying sizes in an epoxy matrix. Experimental tests and microstructural characterization of the polymer matrix composite are conducted for calibration and validation of the model. Statistically equivalent microstructural volume elements are constructed from experimental micrographs for direct numerical simulations. The performance of the property-based statistically equivalent representative volume element with exterior statistics-based boundary conditions is compared with other boundary conditions, as well as with the statistical volume elements. The tests clearly show the significant advantages of the exterior statistics-based boundary conditions in terms of accuracy of the homogenized stiffness and efficiency.

Prediction of mechanical and thermal properties of polymer nanocomposites reinforced by coiled carbon nanotubes for possible application as impact absorbent

2019 ◽  
Vol 234 (4) ◽  
pp. 882-902
Author(s):  
Armin Kianfar ◽  
Mir Masoud Seyyed Fakhrabadi ◽  
Mahmoud Mosavi Mashhadi
Keyword(s):  
Thermal Conductivity ◽  
Carbon Nanotubes ◽  
Finite Element ◽  
Effective Thermal Conductivity ◽  
Representative Volume Element ◽  
Volume Element ◽  
Volume Fractions ◽  
Finite Element Software ◽  
Representative Volume ◽  
Representative Volume Elements

This paper presents three-dimensional finite element modeling of nanocomposite materials made from polyethylene polymer reinforced by coiled carbon nanotubes. A method of Python scripting was used to generate representative volume elements in order to determine the mechanical behavior in elastic and plastic zones as well as effective thermal conductivity using the finite element software. The properties of the nanocomposites are investigated by considering the interphase zone between carbon nanofillers and matrix. The effects of different volume fractions, geometrical parameters, and orientations of the nanofillers on the elastic and thermal characteristics of the nanocomposites are studied considering both cohesive interaction and perfect bonding between the fillers and matrix. Moreover, the effects of applying strain on the effective thermal conductivity of the representative volume elements are analyzed. The results reveal that both stress–strain curves and thermal conductivity coefficients of the nanocomposites are following similar trends vs. the changes of the volume fractions as well as the geometries and orientations of the coiled carbon nanotubes. Analysis of the tensile toughness of all samples reveals that it is affected by both stress and the number of fillers in the representative volume element. In addition, thermal-displacement analysis shows that thermal conductivity coefficient decreases by increasing the applied strain on the representative volume element, while the intensity of decrease of the nanocomposite thermal conductivity depends on the volume fraction and interaction of the nanofillers and interphase zone. Finally, crashworthiness analysis of the nanocomposite material proves that they are appropriate candidates for absorbing energy under impact loadings in comparison to metals.

scholarly journals Design of Reinforcement in Nano- and Microcomposites

Materials ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1474 ◽  
Author(s):  
Małgorzata Chwał ◽  
Aleksander Muc
Keyword(s):  
Boundary Conditions ◽  
Representative Volume Element ◽  
Optimization Problems ◽  
Volume Element ◽  
Numerical Homogenization ◽  
Representative Volume ◽  
Material Optimization ◽  
Design Variables ◽  
Element Shape ◽  
Dimensional Optimization

The application of numerical homogenization and optimization in the design of micro- and nanocomposite reinforcement is presented. The influence of boundary conditions, form of a representative volume element, shape and distribution of reinforcement are distinguished as having the crucial influence on a design of the reinforcement. The paper also shows that, in the optimization problems, the distributions of any design variables can be expressed by n-dimensional curves. It applies not only to the tasks of optimizing the shape of the edge of the structure or its mid-surface but also dimensional optimization or topology/material optimization. It is shown that the design of reinforcement may be conducted in different ways and 2D approaches may be expanding to 3D cases.

scholarly journals Influence of Boundary Conditions on Numerical Homogenization of High Performance Concrete

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1009
Author(s):  
Arkadiusz Denisiewicz ◽  
Mieczysław Kuczma ◽  
Krzysztof Kula ◽  
Tomasz Socha
Keyword(s):  
Experimental Data ◽  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Representative Volume Element ◽  
High Performance ◽  
High Performance Concrete ◽  
Volume Element ◽  
Numerical Homogenization ◽  
Representative Volume

Concrete is the most widely used construction material nowadays. We are concerned with the computational modelling and laboratory testing of high-performance concrete (HPC). The idea of HPC is to enhance the functionality and sustainability of normal concrete, especially by its greater ductility as well as higher compressive, tensile, and flexural strengths. In this paper, the influence of three types (linear displacement, uniform traction, and periodic) of boundary conditions used in numerical homogenization on the calculated values of HPC properties is determined and compared with experimental data. We take into account the softening behavior of HPC due to the development of damage (micro-cracks), which finally leads to failure. The results of numerical simulations of the HPC samples were obtained by using the Abaqus package that we supplemented with our in-house finite element method (FEM) computer programs written in Python and the homogenization toolbox Homtools. This has allowed us to better account for the nonlinear response of concrete. In studying the microstructure of HPC, we considered a two-dimensional representative volume element using the finite element method. Because of the random character of the arrangement of concrete’s components, we utilized a stochastic method to generate the representative volume element (RVE) structure. Different constitutive models were used for the components of HPC: quartz sand—linear elastic, steel fibers—ideal elastic-plastic, and cement matrix—concrete damage plasticity. The numerical results obtained are compared with our own experimental data and those from the literature, and a good agreement can be observed.

Modeling of Cementitious Representative Volume Element with Additives

2017 ◽  
Vol 08 (02) ◽  
pp. 1750003 ◽  
Author(s):  
M. M. Shahzamanian ◽  
W. J. Basirun
Keyword(s):  
Finite Element ◽  
Fly Ash ◽  
Boundary Conditions ◽  
Elastic Properties ◽  
Representative Volume Element ◽  
Volume Element ◽  
Type I ◽  
Element Analysis ◽  
Representative Volume ◽  
Mesh Density

CEMHYD3D has been employed to simulate the representative volume element (RVE) of cementitious systems (Type I cement) containing fly ash (Class F) through a voxel-based finite element analysis (FEA) approach. Three-dimensional microstructures composed of voxels are generated for a heterogeneous cementitious material consisting of various constituent phases. The primary focus is to simulate a cementitious RVE containing fly ash and to present the homogenized macromechanical properties obtained from its analysis. Simple kinematic uniform boundary conditions as well as periodic boundary conditions were imposed on the RVE to obtain the principal and shear moduli. Our current work considers the effect of fly ash percentage on the elastic properties based on the mass and volume replacements. RVEs with lengths of 50, 100 and 200[Formula: see text][Formula: see text] at different degrees of hydration are generated, and the elastic properties are modeled and simulated. In general, the elastic properties of a cementitious RVE with fly ash replacement for cement based on mass and volume differ from each other. Moreover, the finite element (FE) mesh density effect is studied. Results indicate that mechanical properties decrease with increasing mesh density.

scholarly journals Systematic study of homogenization and the utility of circular simplified representative volume element

2019 ◽  
Vol 24 (9) ◽  
pp. 2961-2985 ◽  
Author(s):  
Soheil Firooz ◽  
Saba Saeb ◽  
George Chatzigeorgiou ◽  
Fodil Meraghni ◽  
Paul Steinmann ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Representative Volume Element ◽  
Systematic Study ◽  
Linear Displacement ◽  
Volume Element ◽  
Composite Cylinder ◽  
The Finite Element Method ◽  
Numerical Computations ◽  
Various Boundary Conditions ◽  
Representative Volume

Although both computational and analytical homogenization are well-established today, a thorough and systematic study to compare them is missing in the literature. This manuscript aims to provide an exhaustive comparison of numerical computations and analytical estimates, such as Voigt, Reuss, Hashin–Shtrikman, and composite cylinder assemblage. The numerical computations are associated with canonical boundary conditions imposed on either tetragonal, hexagonal, or circular representative volume elements using the finite-element method. The circular representative volume element is employed to capture an effective isotropic material response suitable for comparison with associated analytical estimates. The analytical results from composite cylinder assemblage are in excellent agreement with the numerical results obtained from a circular representative volume element. We observe that the circular representative volume element renders identical responses for both linear displacement and periodic boundary conditions. In addition, the behaviors of periodic and random microstructures with different inclusion distributions are examined under various boundary conditions. Strikingly, for some specific microstructures, the effective shear modulus does not lie within the Hashin–Shtrikman bounds. Finally, numerical simulations are carried out at finite deformations to compare different representative volume element types in the nonlinear regime. Unlike other canonical boundary conditions, the uniform traction boundary conditions result in nearly identical effective responses for all types of representative volume element, indicating that they are less sensitive with respect to the underlying microstructure. The numerical examples furnish adequate information to serve as benchmarks.

Sign in / Sign up

Export Citation Format

Share Document